<?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>raa2a.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 1040149 was started by veroff on b146-09,
Wed Apr 29 18:50:46 2026
The command was "prover9 -f raa2a.in".
]]></heading>

<proof number="1" length="4375" max_count="54">

<comments><![CDATA[
% Proof 1 at 263.58 (+ 0.03) seconds: "aK1".
% Length of proof: 4375 (0 new hints)
% Level of proof: 283
% Maximum clause weight: 54.000
% Given clauses in run: 5032
% Given clauses in proof: 4358 (0 new hints)
]]></comments>

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

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

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

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

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

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

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

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

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

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

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

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

  <clause id="13" type="assumption">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,y,z)
    ]]></literal>
    <attribute><![CDATA[
      label("associator")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="15" type="assumption">
    <literal><![CDATA[
      (x * y) \ (y * x) = K(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label("commutator")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

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

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

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

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

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

  <clause id="24" type="assumption">
    <literal><![CDATA[
      T(L(x,y,z),u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

  <clause id="28" type="assumption">
    <literal><![CDATA[
      L(R(x,y,z),u,w) = R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="30" type="assumption">
    <literal><![CDATA[
      L(L(x,y,z),u,w) = L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      R(R(x,y,z),u,w) = R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      (x * y) * (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(a(x,y,z),u,w) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aa1")
    ]]></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="62" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = z \ y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 6")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="63" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("Transitivity =")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

  <clause id="68">
    <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="69">
    <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="70">
    <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="71">
    <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="72">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(10(a,2),10(a,1,2))].">
      <j1 rule="para" parents="10 10"/>
    </justification>
  </clause>

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

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

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

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

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

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

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

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

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

  <clause id="82">
    <literal><![CDATA[
      (x * (y * z)) * 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="84">
    <literal><![CDATA[
      x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="85">
    <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="86">
    <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="88">
    <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="89">
    <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="90">
    <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="91">
    <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="92">
    <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="93">
    <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="94">
    <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="96">
    <literal><![CDATA[
      ((x * 1) * y) / y = R(x,1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="97">
    <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="98">
    <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="99">
    <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="100">
    <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="101">
    <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="102">
    <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="103">
    <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="104">
    <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="105">
    <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="106">
    <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="109">
    <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="110">
    <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="111">
    <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="112">
    <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="113">
    <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="114">
    <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="115">
    <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="116">
    <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="117">
    <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="118">
    <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="119">
    <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="120">
    <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="123">
    <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="124">
    <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="125">
    <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="126">
    <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="127">
    <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="128">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,33,a)].">
      <j1 rule="hyper" parents="52 33"/>
    </justification>
  </clause>

  <clause id="129">
    <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="130">
    <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="131">
    <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="132">
    <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="133">
    <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="134">
    <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="136">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 12 10"/>
    </justification>
  </clause>

  <clause id="138">
    <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="139">
    <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="140">
    <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="141">
    <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="142">
    <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="143">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,65,a,b,8,a)].">
      <j1 rule="hyper" parents="63 65 8"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),65(a,1,1))].">
      <j1 rule="para" parents="10 65"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(65(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="65 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(66(a,2),7(a,1,1))].">
      <j1 rule="para" parents="66 7"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(66(a,2),8(a,1,2))].">
      <j1 rule="para" parents="66 8"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),74(a,1,2))].">
      <j1 rule="para" parents="10 74"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),74(a,1,2))].">
      <j1 rule="para" parents="12 74"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(74(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="74 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,27,a,b,101,a(flip))].">
      <j1 rule="hyper" parents="42 27 101"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,101,a(flip))].">
      <j1 rule="hyper" parents="41 25 101"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,101,a(flip))].">
      <j1 rule="hyper" parents="40 23 101"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(101(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="101 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,76,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 76 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,76,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 76 10"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,76,a)].">
      <j1 rule="hyper" parents="57 76"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="36 20 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),76(a,1,2))].">
      <j1 rule="para" parents="14 76"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),76(a,1,2))].">
      <j1 rule="para" parents="18 76"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),76(a,1,2))].">
      <j1 rule="para" parents="22 76"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(76(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="76 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(76(a,2),76(a,1,2))].">
      <j1 rule="para" parents="76 76"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      (x / y) \ x = y / 1
    ]]></literal>
    <justification jstring="[hyper(63,a,79,a,b,74,a(flip))].">
      <j1 rule="hyper" parents="63 79 74"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,79,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 79 10"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,79,a)].">
      <j1 rule="hyper" parents="57 79"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      ((x / (y / z)) \ x) * z = y
    ]]></literal>
    <justification jstring="[hyper(37,a,11,a,b,79,a(flip))].">
      <j1 rule="hyper" parents="37 11 79"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(36,a,76,a,b,79,a(flip))].">
      <j1 rule="hyper" parents="36 76 79"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(79(a,1),39(a,1))].">
      <j1 rule="para" parents="79 39"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(79(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="79 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,22,a,b,143,a)].">
      <j1 rule="hyper" parents="63 22 143"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,174,a)].">
      <j1 rule="hyper" parents="54 174"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      T(x,y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),174(a,1,2))].">
      <j1 rule="para" parents="10 174"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(148(a,1),44(a,2))].">
      <j1 rule="para" parents="148 44"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(12(a,2),145(a,1,1))].">
      <j1 rule="para" parents="12 145"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,2),151(a,1,2))].">
      <j1 rule="para" parents="10 151"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,152,a(flip))].">
      <j1 rule="hyper" parents="40 23 152"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      (x \ 1) * (x * x) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a(flip),b,69,a(flip))].">
      <j1 rule="hyper" parents="34 32 69"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      (x * ((x \ 1) * y)) \ y = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(69(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="69 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(69(a,1),20(a,2,1))].">
      <j1 rule="para" parents="69 20"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(70(a,1),18(a,2,2))].">
      <j1 rule="para" parents="70 18"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ y = a(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="77 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),20(a,2,1))].">
      <j1 rule="para" parents="77 20"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),18(a,2,2))].">
      <j1 rule="para" parents="78 18"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,102,a,b,10,a)].">
      <j1 rule="hyper" parents="63 102 10"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,102,a)].">
      <j1 rule="hyper" parents="58 102"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,102,a)].">
      <j1 rule="hyper" parents="57 102"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,12,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="34 12 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="35 12 102"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(10(a,2),102(a,1,2))].">
      <j1 rule="para" parents="10 102"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="102 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(102(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="102 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(102(a,1),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="102 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),102(a,1,2))].">
      <j1 rule="para" parents="23 102"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),102(a,1,2))].">
      <j1 rule="para" parents="25 102"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),102(a,1,2))].">
      <j1 rule="para" parents="27 102"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(102(a,1),34(a,1))].">
      <j1 rule="para" parents="102 34"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(102(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="102 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(102(a,2),44(a,1))].">
      <j1 rule="para" parents="102 44"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(154(a,1),102(a,1,2))].">
      <j1 rule="para" parents="154 102"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(104(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(104(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(104(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="104 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(128(a,1),50(a,2))].">
      <j1 rule="para" parents="128 50"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(138(a,2),119(a,1))].">
      <j1 rule="para" parents="138 119"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(140(a,2),116(a,1))].">
      <j1 rule="para" parents="140 116"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(140(a,2),117(a,1))].">
      <j1 rule="para" parents="140 117"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,142,a(flip))].">
      <j1 rule="hyper" parents="34 10 142"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(142(a,2),119(a,1))].">
      <j1 rule="para" parents="142 119"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(142(a,2),120(a,1))].">
      <j1 rule="para" parents="142 120"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,144,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,144,a)].">
      <j1 rule="hyper" parents="63 16 144"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,149,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,150,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),164(a,1,1))].">
      <j1 rule="para" parents="10 164"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(167(a,2),151(a,1))].">
      <j1 rule="para" parents="167 151"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,184,a)].">
      <j1 rule="hyper" parents="35 12 184"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="194 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(194(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="194 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(194(a,1),154(a,1,2))].">
      <j1 rule="para" parents="194 154"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(102(a,1),118(a,1)),flip(b)].">
      <j1 rule="para" parents="102 118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(164(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="164 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),214(a,1,1))].">
      <j1 rule="para" parents="10 214"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(102(a,2),214(a,1,1))].">
      <j1 rule="para" parents="102 214"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(139(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="139 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(11(a,1),224(a,1,1))].">
      <j1 rule="para" parents="11 224"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(164(a,1),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="164 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(104(a,2),237(a,1))].">
      <j1 rule="para" parents="104 237"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(142(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="142 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(72(a,1),18(a,2,2))].">
      <j1 rule="para" parents="72 18"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      x * (x \ (y * z)) = y * (u * (u \ z))
    ]]></literal>
    <justification jstring="[para(71(a,1),72(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="71 72"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(118,a,81,a)].">
      <j1 rule="hyper" parents="118 81"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,77,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="63 77 85"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,85,a,b,10,a)].">
      <j1 rule="hyper" parents="63 85 10"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),85(a,1,1))].">
      <j1 rule="para" parents="10 85"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),85(a,1,1))].">
      <j1 rule="para" parents="12 85"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(85(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="85 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(85(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="85 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      T(x * y,K(y,x)) = K(y,x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(85(a,1),22(a,2,2))].">
      <j1 rule="para" parents="85 22"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(85(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="85 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(85(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="85 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(62,a,103,a)].">
      <j1 rule="hyper" parents="62 103"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,103,a)].">
      <j1 rule="hyper" parents="58 103"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,103,a)].">
      <j1 rule="hyper" parents="57 103"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(103(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="103 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),109(a,1))].">
      <j1 rule="para" parents="7 109"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[hyper(257,a,10,a(flip),b,129,a),flip(a)].">
      <j1 rule="hyper" parents="257 10 129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(136(a,2),44(a,1))].">
      <j1 rule="para" parents="136 44"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(136(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="136 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(137(a,1),44(a,1))].">
      <j1 rule="para" parents="137 44"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(141(a,2),43(a,1))].">
      <j1 rule="para" parents="141 43"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(141(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="141 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(141(a,1),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="141 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(156(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="156 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(168(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="168 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(257,a,10,a(flip),b,169,a),flip(a)].">
      <j1 rule="hyper" parents="257 10 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(191(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="191 18"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="191 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,102,a,b,220,a)].">
      <j1 rule="hyper" parents="257 102 220"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,220,a(flip))].">
      <j1 rule="hyper" parents="123 220"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(118,a,220,a(flip))].">
      <j1 rule="hyper" parents="118 220"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(220(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="220 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(258(a,1),20(a,2,1))].">
      <j1 rule="para" parents="258 20"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(276(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="276 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      x \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),89(a,1,1))].">
      <j1 rule="para" parents="8 89"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(281(a,1),237(a,1))].">
      <j1 rule="para" parents="281 237"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      (x * y) / y = R(x,1,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),96(a,1,1,1))].">
      <j1 rule="para" parents="8 96"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(215,a,285,a),flip(a)].">
      <j1 rule="hyper" parents="215 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(181,a,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="181 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,187,a)].">
      <j1 rule="hyper" parents="57 187"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(181,a,187,a(flip))].">
      <j1 rule="hyper" parents="181 187"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(173,a,187,a(flip))].">
      <j1 rule="hyper" parents="173 187"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,187,a(flip))].">
      <j1 rule="hyper" parents="125 187"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),187(a,2,1))].">
      <j1 rule="para" parents="10 187"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),187(a,2,1))].">
      <j1 rule="para" parents="12 187"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(187(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="187 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(187(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="187 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(165,a,189,a(flip))].">
      <j1 rule="hyper" parents="165 189"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),189(a,2,2))].">
      <j1 rule="para" parents="10 189"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),189(a,2,2))].">
      <j1 rule="para" parents="12 189"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(189(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="189 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),205(a,1,2))].">
      <j1 rule="para" parents="23 205"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),232(a,1,2))].">
      <j1 rule="para" parents="23 232"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      x * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(25(a,2),232(a,1,2))].">
      <j1 rule="para" parents="25 232"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      x * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(27(a,2),232(a,1,2))].">
      <j1 rule="para" parents="27 232"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(139(a,2),235(a,1,1))].">
      <j1 rule="para" parents="139 235"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),239(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="10 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(290(a,1),25(a,2,1))].">
      <j1 rule="para" parents="290 25"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      x \ (x / L(y \ 1,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(118,a,291,a(flip))].">
      <j1 rule="hyper" parents="118 291"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(291(a,1),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="291 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(76(a,1),297(a,1,1,1))].">
      <j1 rule="para" parents="76 297"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(297(a,1),233(a,1,2)),flip(b)].">
      <j1 rule="para" parents="297 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),306(a,1,1))].">
      <j1 rule="para" parents="11 306"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(76(a,1),306(a,1,1))].">
      <j1 rule="para" parents="76 306"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),238(a,1))].">
      <j1 rule="para" parents="105 238"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,20,a,b,149,a(flip))].">
      <j1 rule="hyper" parents="111 20 149"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(111,a,18,a,b,144,a(flip))].">
      <j1 rule="hyper" parents="111 18 144"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(102(a,1),111(b,1)),flip(c)].">
      <j1 rule="para" parents="102 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(112,a,20,a,b,149,a(flip))].">
      <j1 rule="hyper" parents="112 20 149"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (((y * x) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(113,a,187,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="113 187 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      T(x,x \ y) \ (((x \ y) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(113,a,103,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="113 103 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(114,a,103,a,b,76,a)].">
      <j1 rule="hyper" parents="114 103 76"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="114 31 20"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="114 29 20"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="114 27 20"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,168,a,b,168,a)].">
      <j1 rule="hyper" parents="115 168 168"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,103,a,b,79,a)].">
      <j1 rule="hyper" parents="115 103 79"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(115,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="115 30 18"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(115,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="115 29 18"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = a(x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(115,a,128,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 128 18"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,103,a(flip),b,79,a)].">
      <j1 rule="hyper" parents="115 103 79"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 25 18"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(196(a,1),18(a,2,2))].">
      <j1 rule="para" parents="196 18"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),200(a,1,2,1))].">
      <j1 rule="para" parents="22 200"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),200(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="104 200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),200(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="194 200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(103(a,1),200(a,1,2,1))].">
      <j1 rule="para" parents="103 200"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(227,a,208,a)].">
      <j1 rule="hyper" parents="227 208"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(227,a,226,a)].">
      <j1 rule="hyper" parents="227 226"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(226(a,1),49(a,2)),flip(b)].">
      <j1 rule="para" parents="226 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(226(a,1),234(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="226 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,228,a)].">
      <j1 rule="hyper" parents="54 228"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      K(x \ 1,x) * K(x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[para(220(a,2),245(a,1,1))].">
      <j1 rule="para" parents="220 245"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(246(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="246 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(246(a,1),43(a,1))].">
      <j1 rule="para" parents="246 43"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(246(a,1),204(a,2))].">
      <j1 rule="para" parents="246 204"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(247(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="247 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(112,a,192,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="112 192 90"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(112,a,131,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="112 131 90"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,193,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="63 193 90"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,130,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="63 130 90"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,129,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="63 129 90"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      L(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a,b,90,a),flip(a)].">
      <j1 rule="hyper" parents="34 32 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,196,a(flip),b,90,a),flip(a)].">
      <j1 rule="hyper" parents="34 196 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(111,a,77,a(flip),b,90,a(flip))].">
      <j1 rule="hyper" parents="111 77 90"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(90(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="90 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="90 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="90 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="90 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="90 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      a(x,y,z * z) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,355,a)].">
      <j1 rule="hyper" parents="53 355"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[para(7(a,1),363(a,1,3))].">
      <j1 rule="para" parents="7 363"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,364,a)].">
      <j1 rule="hyper" parents="52 364"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      T(a(x,y,z) * u,a(x,y,z)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,356,a(flip),b,128,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 356 128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(356(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="356 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(257,a,144,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="257 144 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(257,a,88,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="257 88 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(181,a,92,a(flip))].">
      <j1 rule="hyper" parents="181 92"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),92(a,2,1))].">
      <j1 rule="para" parents="10 92"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(102(a,1),92(a,2,1))].">
      <j1 rule="para" parents="102 92"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(90(a,1),92(a,2,2))].">
      <j1 rule="para" parents="90 92"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[hyper(112,a,98,a,b,xx)].">
      <j1 rule="hyper" parents="112 98"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(111,a,258,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="111 258 98"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(111,a,130,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="111 130 98"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(111,a,129,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="111 129 98"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(111,a,102,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="111 102 98"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,131,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="63 131 98"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,32,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="35 32 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(111,a,98,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="111 98 90"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      (R(x,y,z) * ((y * z) * u)) \ (((x * y) * z) * u) = a(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(98(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="98 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(98(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="98 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(98(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="98 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(98(a,1),44(a,1))].">
      <j1 rule="para" parents="98 44"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * z
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(98(a,2),44(a,1))].">
      <j1 rule="para" parents="98 44"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(98(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="98 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(220(a,2),98(a,1,2))].">
      <j1 rule="para" parents="220 98"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),383(a,1,3))].">
      <j1 rule="para" parents="7 383"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(394(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="394 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(257,a,150,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="257 150 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,149,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="257 149 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(257,a,133,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="257 133 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),99(a,2,2))].">
      <j1 rule="para" parents="10 99"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),99(a,2,2))].">
      <j1 rule="para" parents="12 99"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[para(102(a,1),99(a,2,2))].">
      <j1 rule="para" parents="102 99"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(99(a,2),104(a,1,1))].">
      <j1 rule="para" parents="99 104"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(206(a,1),99(a,2,2))].">
      <j1 rule="para" parents="206 99"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(98(a,1),99(a,2,1))].">
      <j1 rule="para" parents="98 99"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(98(a,1),99(a,2,2))].">
      <j1 rule="para" parents="98 99"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(99(a,2),99(a,1,1))].">
      <j1 rule="para" parents="99 99"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(85(a,1),160(a,1,2,1))].">
      <j1 rule="para" parents="85 160"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(111,a,30,a,b,219,a)].">
      <j1 rule="hyper" parents="111 30 219"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      x \ R(L(y,x \ 1,x),z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(111,a,29,a,b,219,a)].">
      <j1 rule="hyper" parents="111 29 219"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,25,a(flip),b,219,a)].">
      <j1 rule="hyper" parents="111 25 219"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(229,a,221,a),flip(a)].">
      <j1 rule="hyper" parents="229 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(112,a,29,a(flip),b,221,a)].">
      <j1 rule="hyper" parents="112 29 221"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      R(x,y,y \ 1) * L(z,y \ 1,x * y) = (x * y) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(114,a,221,a(flip),b,163,a)].">
      <j1 rule="hyper" parents="114 221 163"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      L((x \ 1) \ 1,x \ 1,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(221(a,1),187(a,2,1))].">
      <j1 rule="para" parents="221 187"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,31,a,b,222,a)].">
      <j1 rule="hyper" parents="112 31 222"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,29,a(flip),b,222,a)].">
      <j1 rule="hyper" parents="112 29 222"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,27,a(flip),b,222,a)].">
      <j1 rule="hyper" parents="112 27 222"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      K(x,1 / x) * x = R(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(244(a,2),222(a,1,1))].">
      <j1 rule="para" parents="244 222"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(212,a,241,a),flip(a)].">
      <j1 rule="hyper" parents="212 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(79(a,1),241(a,1,1))].">
      <j1 rule="para" parents="79 241"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      u \ (a(x,y,z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(241(a,1),212(a,1))].">
      <j1 rule="para" parents="241 212"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(136(a,1),260(a,1))].">
      <j1 rule="para" parents="136 260"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(76(a,1),261(a,1,1,1))].">
      <j1 rule="para" parents="76 261"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      ((x \ 1) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(276(a,1),261(a,1,1,1))].">
      <j1 rule="para" parents="276 261"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(9(a,1),263(a,1,2))].">
      <j1 rule="para" parents="9 263"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      x * T(y,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      (y * x) / u = z
    ]]></literal>
    <justification jstring="[para(22(a,2),263(a,1,2))].">
      <j1 rule="para" parents="22 263"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(141(a,2),263(a,1))].">
      <j1 rule="para" parents="141 263"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(102(a,1),265(a,1,2))].">
      <j1 rule="para" parents="102 265"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),266(a,2,2))].">
      <j1 rule="para" parents="22 266"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(66(a,1),268(a,1,2,2))].">
      <j1 rule="para" parents="66 268"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(141(a,2),268(a,1,2))].">
      <j1 rule="para" parents="141 268"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(219(a,1),268(a,1))].">
      <j1 rule="para" parents="219 268"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      x \ y != z / (u \ z)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(157(a,2),271(a,2))].">
      <j1 rule="para" parents="157 271"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(111,a,30,a,b,288,a)].">
      <j1 rule="hyper" parents="111 30 288"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(294(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="294 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      (x / y) \ (L(y \ 1,y,x / y) * x) = K(x \ (x / y),x)
    ]]></literal>
    <justification jstring="[para(294(a,2),86(a,1,2,1))].">
      <j1 rule="para" parents="294 86"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(114,a,298,a(flip),b,76,a)].">
      <j1 rule="hyper" parents="114 298 76"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(298(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="298 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      R(R(1 / x,x,x \ y),y,z) = ((x \ y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(298(a,2),99(a,1,1))].">
      <j1 rule="para" parents="298 99"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(99(a,2),305(a,1))].">
      <j1 rule="para" parents="99 305"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      x / ((y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(310(a,1),233(a,1,2)),flip(b)].">
      <j1 rule="para" parents="310 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ u) \ u = w
    ]]></literal>
    <justification jstring="[para(27(a,2),313(a,1))].">
      <j1 rule="para" parents="27 313"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(351(a,1),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="351 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(370(a,1),25(a,2,1))].">
      <j1 rule="para" parents="370 25"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(370(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="370 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(397(a,1),27(a,2,1))].">
      <j1 rule="para" parents="397 27"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      R(((x * (y * z)) / z) / y,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,11,a(flip),b,398,a),flip(a)].">
      <j1 rule="hyper" parents="257 11 398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      (x / (y * y)) / z = x / (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,383,a(flip),b,398,a)].">
      <j1 rule="hyper" parents="63 383 398"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(12(a,2),423(a,1,1))].">
      <j1 rule="para" parents="12 423"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(136(a,1),423(a,1,1))].">
      <j1 rule="para" parents="136 423"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(160(a,2),428(a,1))].">
      <j1 rule="para" parents="160 428"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(292(a,1),430(a,1,2))].">
      <j1 rule="para" parents="292 430"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,90,a(flip),b,201,a)].">
      <j1 rule="hyper" parents="63 90 201"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(104(a,1),201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="104 201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(103(a,1),201(a,1,2,1))].">
      <j1 rule="para" parents="103 201"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(257,a,98,a(flip),b,202,a),flip(a)].">
      <j1 rule="hyper" parents="257 98 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(111,a,98,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="111 98 202"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(104(a,1),202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="104 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(194(a,1),202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="194 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(103(a,1),202(a,1,2,1))].">
      <j1 rule="para" parents="103 202"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(203,a,327,a,b,272,a)].">
      <j1 rule="hyper" parents="203 327 272"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(203,a,192,a(flip),b,90,a),flip(a)].">
      <j1 rule="hyper" parents="203 192 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,468,a)].">
      <j1 rule="hyper" parents="63 25 468"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(468(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="468 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      T(L(x,x \ 1,x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,177,a(flip),b,469,a),flip(a)].">
      <j1 rule="hyper" parents="257 177 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(227,a,469,a)].">
      <j1 rule="hyper" parents="227 469"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,226,a,b,469,a)].">
      <j1 rule="hyper" parents="40 226 469"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),473(a,1,2))].">
      <j1 rule="para" parents="10 473"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(227,a,209,a)].">
      <j1 rule="hyper" parents="227 209"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(227,a,210,a)].">
      <j1 rule="hyper" parents="227 210"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(189(a,1),210(a,1,1))].">
      <j1 rule="para" parents="189 210"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(99(a,1),210(a,1,1))].">
      <j1 rule="para" parents="99 210"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(299(a,1),210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="299 210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(397(a,1),210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="397 210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,477,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 477 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(477(a,1),232(a,1,2))].">
      <j1 rule="para" parents="477 232"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(242(a,1),43(a,1))].">
      <j1 rule="para" parents="242 43"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(u,w) = w \ (x * z)
    ]]></literal>
    <justification jstring="[para(242(a,1),204(a,1))].">
      <j1 rule="para" parents="242 204"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(111,a,254,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="111 254 85"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,(x \ y) \ y) = u
    ]]></literal>
    <justification jstring="[para(255(a,2),252(a,1,1))].">
      <j1 rule="para" parents="255 252"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(102(a,1),311(a,1,2))].">
      <j1 rule="para" parents="102 311"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x = x * T(y,((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,255,a(flip),b,337,a)].">
      <j1 rule="hyper" parents="63 255 337"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      ((x / y) * T(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),339(a,1,1,2,1))].">
      <j1 rule="para" parents="79 339"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(339(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="339 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(104(a,1),340(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="104 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(340(a,1),239(a,1,1)),flip(b)].">
      <j1 rule="para" parents="340 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      ((x * y) * z) / ((y * z) * a(x,y,z)) = R(x,y * z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(112,a,82,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="112 82 98"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = (x * y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(70(a,1),82(a,1,1))].">
      <j1 rule="para" parents="70 82"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(82(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="82 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(115,a,30,a,b,91,a)].">
      <j1 rule="hyper" parents="115 30 91"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ u) * w) = u * w
    ]]></literal>
    <justification jstring="[hyper(115,a,128,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="115 128 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      x * T(L(y,z \ x,z),u) = z * ((z \ x) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,25,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="115 25 91"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      x * R(L(y,z,x / z),u,w) = (x / z) * (z * R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(115,a,29,a,b,93,a)].">
      <j1 rule="hyper" parents="115 29 93"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(172,a,355,a(flip),b,94,a(flip))].">
      <j1 rule="hyper" parents="172 355 94"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      (a(x,y,z) * u) / w = a(x,y,z) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(172,a,128,a(flip),b,94,a(flip))].">
      <j1 rule="hyper" parents="172 128 94"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      R((x * (y / z)) \ (x * y),u,w) = L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),29(a,1,1))].">
      <j1 rule="para" parents="94 29"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      (x * (y / (z * z))) / u = (x * y) / (u * (z * z))
    ]]></literal>
    <justification jstring="[para(503(a,1),453(a,1,1))].">
      <j1 rule="para" parents="503 453"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      L(x,y \ 1,y) \ x = a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(219(a,1),185(a,1,1))].">
      <j1 rule="para" parents="219 185"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      a(1 / x,x,x \ 1) = (1 / x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(70(a,1),188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = T(R(y,x,K(x,y)),z) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(249(a,1),336(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="249 336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(111,a,102,a(flip),b,289,a)].">
      <j1 rule="hyper" parents="111 102 289"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(115,a,295,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="115 295 18"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(306,a,300,a),flip(a)].">
      <j1 rule="hyper" parents="306 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(103(a,1),301(a,1,2))].">
      <j1 rule="para" parents="103 301"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),302(a,1,2,1))].">
      <j1 rule="para" parents="22 302"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,104,a(flip),b,307,a),flip(a)].">
      <j1 rule="hyper" parents="257 104 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(111,a,307,a(flip),b,288,a)].">
      <j1 rule="hyper" parents="111 307 288"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,16,a,b,334,a)].">
      <j1 rule="hyper" parents="257 16 334"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(334(a,1),25(a,2,1))].">
      <j1 rule="para" parents="334 25"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      L(x \ T(x,y),x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(334(a,2),252(a,1))].">
      <j1 rule="para" parents="334 252"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(350(a,1),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="350 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,201,a(flip),b,353,a(flip))].">
      <j1 rule="hyper" parents="111 201 353"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(353(a,1),43(a,1))].">
      <j1 rule="para" parents="353 43"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(203,a,131,a(flip),b,354,a),flip(a)].">
      <j1 rule="hyper" parents="203 131 354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,201,a(flip),b,354,a),flip(a)].">
      <j1 rule="hyper" parents="63 201 354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(371(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="371 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(318,a,129,a(flip),b,382,a)].">
      <j1 rule="hyper" parents="318 129 382"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(29(a,1),382(a,1,1))].">
      <j1 rule="para" parents="29 382"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(31(a,1),382(a,1,1))].">
      <j1 rule="para" parents="31 382"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,383,a(flip),b,400,a),flip(a)].">
      <j1 rule="hyper" parents="63 383 400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(400(a,1),27(a,2,1))].">
      <j1 rule="para" parents="400 27"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      (x * (y * y)) / y = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),532(a,2,2))].">
      <j1 rule="para" parents="225 532"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      R(x,y,y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,377,a(flip),b,535,a),flip(a)].">
      <j1 rule="hyper" parents="63 377 535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      R(x,y,y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,320,a,b,536,a)].">
      <j1 rule="hyper" parents="37 320 536"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),431(a,1))].">
      <j1 rule="para" parents="22 431"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      ((x * y) / (z * y)) * z = z * R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,478,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 478 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),478(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      T(x * (y \ 1),y) = R(y \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,537,a(flip),b,480,a),flip(a)].">
      <j1 rule="hyper" parents="63 537 480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      (1 / x) * R(x,1 / x,y) = (y / ((1 / x) * y)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),481(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(111,a,221,a(flip),b,497,a)].">
      <j1 rule="hyper" parents="111 221 497"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      a(x / y,y,y \ 1) = (x / y) \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(111,a,129,a(flip),b,497,a),flip(a)].">
      <j1 rule="hyper" parents="111 129 497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      L(x,y,(1 / z) \ (z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(509(a,1),128(a,1,3))].">
      <j1 rule="para" parents="509 128"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(150(a,1),540(a,2,1)),flip(a)].">
      <j1 rule="para" parents="150 540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(540(a,2),226(a,1,1))].">
      <j1 rule="para" parents="540 226"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,548,a)].">
      <j1 rule="hyper" parents="63 27 548"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),549(a,1,1,2))].">
      <j1 rule="para" parents="12 549"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(549(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="549 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(550(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="550 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(174(a,1),550(a,1,1))].">
      <j1 rule="para" parents="174 550"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,27,a,b,106,a)].">
      <j1 rule="hyper" parents="257 27 106"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),236(a,1,2))].">
      <j1 rule="para" parents="25 236"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29(a,2),236(a,1,2))].">
      <j1 rule="para" parents="29 236"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      (a(x,y,z) * u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * (u * w) = v5
    ]]></literal>
    <justification jstring="[para(128(a,1),236(a,1,2))].">
      <j1 rule="para" parents="128 236"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,98,a,b,331,a(flip))].">
      <j1 rule="hyper" parents="35 98 331"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      (a(x,y,z) * (u * (w * v5))) \ (((a(x,y,z) * u) * w) * v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(331(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="331 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ ((a(x,y,z) * u) * (w * v5)) = L(v5,w,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(331(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="331 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = R(a(x,y,z),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(257,a,560,a,b,560,a)].">
      <j1 rule="hyper" parents="257 560 560"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      R(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(563(a,1),395(a,1)),flip(b)].">
      <j1 rule="para" parents="563 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * (x * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(220(a,2),361(a,1,1))].">
      <j1 rule="para" parents="220 361"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      (x * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ (x \ z),y,x) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),362(a,1,2))].">
      <j1 rule="para" parents="72 362"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(u,z,y),y * z,x) = w
    ]]></literal>
    <justification jstring="[para(90(a,1),362(a,1,2,2))].">
      <j1 rule="para" parents="90 362"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),y * (z * u),x) = w
    ]]></literal>
    <justification jstring="[para(82(a,1),362(a,1,2,2))].">
      <j1 rule="para" parents="82 362"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (x * (a(y,z,u) * (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(v5,a(y,z,u) * w,x) = v6
    ]]></literal>
    <justification jstring="[para(331(a,1),362(a,1,2,2))].">
      <j1 rule="para" parents="331 362"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      L(x,x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(277(a,1),435(a,1,1))].">
      <j1 rule="para" parents="277 435"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      x / K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      R(x,x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(220(a,2),445(a,1,2))].">
      <j1 rule="para" parents="220 445"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) \ (x * R(y / x,z,u)) = K(x,R(y / x,z,u))
    ]]></literal>
    <justification jstring="[para(464(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="464 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <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(249(a,1),464(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="249 464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(231,a,465,a)].">
      <j1 rule="hyper" parents="231 465"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,465,a),flip(a)].">
      <j1 rule="hyper" parents="123 465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      (x * R(y,z,z \ x)) / (z \ x) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(112,a,465,a(flip),b,382,a(flip))].">
      <j1 rule="hyper" parents="112 465 382"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),475(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(475(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="475 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(475(a,1),239(a,1,1)),flip(b)].">
      <j1 rule="para" parents="475 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(241(a,1),475(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="241 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(293(a,1),475(a,1,1,2))].">
      <j1 rule="para" parents="293 475"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(520(a,2),475(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="520 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(476(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="476 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(227,a,493,a)].">
      <j1 rule="hyper" parents="227 493"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(115,a,493,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 493 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(203,a,131,a(flip),b,500,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 131 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(104(a,1),554(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[para(189(a,1),576(a,2,1,2))].">
      <j1 rule="para" parents="189 576"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(396(a,1),576(a,2,1,2))].">
      <j1 rule="para" parents="396 576"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(398(a,1),576(a,2,1,2))].">
      <j1 rule="para" parents="398 576"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(576(a,1),231(a,1,1))].">
      <j1 rule="para" parents="576 231"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(578(a,2),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="578 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[para(187(a,1),578(a,2,1,2))].">
      <j1 rule="para" parents="187 578"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[para(90(a,1),578(a,2,1))].">
      <j1 rule="para" parents="90 578"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(92(a,1),578(a,2,1,2))].">
      <j1 rule="para" parents="92 578"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(294(a,1),578(a,2,1,2))].">
      <j1 rule="para" parents="294 578"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(371(a,1),578(a,2,1,2))].">
      <j1 rule="para" parents="371 578"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      ((x * y) * R(T(z,y),u,w)) / (R(z,u,w) * y) = R(x,y,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(27(a,2),198(a,1,1,2))].">
      <j1 rule="para" parents="27 198"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,296,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 296 18"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      L((x * y) \ x,y,1 / y) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(290(a,1),296(a,1,1)),flip(a)].">
      <j1 rule="para" parents="290 296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),602(a,1,1,1))].">
      <j1 rule="para" parents="10 602"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(398(a,1),326(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="398 326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(92(a,1),333(a,1,2,1))].">
      <j1 rule="para" parents="92 333"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(241(a,1),333(a,1,2,1))].">
      <j1 rule="para" parents="241 333"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[para(468(a,1),333(a,1,2,1))].">
      <j1 rule="para" parents="468 333"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(374(a,1),25(a,2,1))].">
      <j1 rule="para" parents="374 25"/>
    </justification>
  </clause>

  <clause id="612">
    <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(374(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="374 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w),T(x,y),y) = L((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(374(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="374 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(368(a,1),411(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="368 411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(396(a,1),418(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="396 418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(115,a,439,a,b,93,a),flip(a)].">
      <j1 rule="hyper" parents="115 439 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(442(a,2),382(a,1,1))].">
      <j1 rule="para" parents="442 382"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,449,a(flip),b,288,a)].">
      <j1 rule="hyper" parents="111 449 288"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[hyper(112,a,451,a(flip),b,221,a)].">
      <j1 rule="hyper" parents="112 451 221"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[hyper(257,a,289,a(flip),b,459,a)].">
      <j1 rule="hyper" parents="257 289 459"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[para(549(a,1),462(a,1,2))].">
      <j1 rule="para" parents="549 462"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(111,a,69,a(flip),b,621,a)].">
      <j1 rule="hyper" parents="111 69 621"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(621(a,1),402(a,2,1))].">
      <j1 rule="para" parents="621 402"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(220(a,2),623(a,1,1))].">
      <j1 rule="para" parents="220 623"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      K(x \ 1,x) \ x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a(flip),b,625,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,103,a(flip),b,625,a)].">
      <j1 rule="hyper" parents="115 103 625"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      L(T(R(x,y,z),u),u,x) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[para(27(a,1),470(a,1,1))].">
      <j1 rule="para" parents="27 470"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T((y * x) / x,x / (y * x))
    ]]></literal>
    <justification jstring="[para(189(a,2),479(a,1,2))].">
      <j1 rule="para" parents="189 479"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x / y) = z
    ]]></literal>
    <justification jstring="[para(479(a,2),232(a,1,2))].">
      <j1 rule="para" parents="479 232"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(293(a,1),524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="293 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(371(a,1),524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="371 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(z,x) = u
    ]]></literal>
    <justification jstring="[para(527(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="527 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,529,a)].">
      <j1 rule="hyper" parents="63 27 529"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      L(((x / y) \ (x * (y \ 1))) \ z,a(x / y,y,y \ 1),x / y) = (x * (y \ 1)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(545(a,2),371(a,1,2))].">
      <j1 rule="para" parents="545 371"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(22(a,2),581(a,2,1,2))].">
      <j1 rule="para" parents="22 581"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(628(a,1),201(a,1,2))].">
      <j1 rule="para" parents="628 201"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      R(T(x / y,x),y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,9,a(flip),b,634,a),flip(a)].">
      <j1 rule="hyper" parents="257 9 634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(634(a,1),382(a,1,1))].">
      <j1 rule="para" parents="634 382"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(491(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="491 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),586(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 586"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(586(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="586 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),587(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(99(a,2),587(a,1,1,1,2))].">
      <j1 rule="para" parents="99 587"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(403(a,1),589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="403 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(517,a,614,a),flip(a)].">
      <j1 rule="hyper" parents="517 614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,614,a)].">
      <j1 rule="hyper" parents="118 614"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(432,a,614,a(flip))].">
      <j1 rule="hyper" parents="432 614"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),614(a,2,2,1))].">
      <j1 rule="para" parents="8 614"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),614(a,2,2,1))].">
      <j1 rule="para" parents="10 614"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,338,a(flip),b,649,a)].">
      <j1 rule="hyper" parents="63 338 649"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(492,a,615,a)].">
      <j1 rule="hyper" parents="492 615"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),615(a,2,1,1))].">
      <j1 rule="para" parents="7 615"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(104(a,1),615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(492,a,654,a)].">
      <j1 rule="hyper" parents="492 654"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(654(a,1),492(a,1))].">
      <j1 rule="para" parents="654 492"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),656(a,1,2,1))].">
      <j1 rule="para" parents="79 656"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(318,a,xx,b,658,a),flip(a)].">
      <j1 rule="hyper" parents="318 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(270,a,658,a),flip(a)].">
      <j1 rule="hyper" parents="270 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(123,a,658,a)].">
      <j1 rule="hyper" parents="123 658"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(658(a,1),270(a,1))].">
      <j1 rule="para" parents="658 270"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      T((T(x,y) * (1 / x)) / T(x,y),T(x,y) / x) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(658(a,1),473(a,1,2))].">
      <j1 rule="para" parents="658 473"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,294,a,b,659,a)].">
      <j1 rule="hyper" parents="63 294 659"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(432,a,618,a)].">
      <j1 rule="hyper" parents="432 618"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,336,a(flip),b,619,a),flip(a)].">
      <j1 rule="hyper" parents="257 336 619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,86,a(flip),b,631,a),flip(a)].">
      <j1 rule="hyper" parents="257 86 631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),667(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(647(a,1),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="647 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(112,a,650,a(flip),b,336,a)].">
      <j1 rule="hyper" parents="112 650 336"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),652(a,2,1,1))].">
      <j1 rule="para" parents="12 652"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),655(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,667,a(flip),b,668,a)].">
      <j1 rule="hyper" parents="257 667 668"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,668,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="111 668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(68(a,1),673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="68 673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),675(a,1,1,2))].">
      <j1 rule="para" parents="12 675"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(118,a,671,a),flip(a)].">
      <j1 rule="hyper" parents="118 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = ((x * y) \ x) * T(((x * y) \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(674(a,1),660(a,1,1))].">
      <j1 rule="para" parents="674 660"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      R(R(x,y \ 1,y),z,u) * K(y \ 1,y) = (R(x,z,u) * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(220(a,2),324(a,1,2))].">
      <j1 rule="para" parents="220 324"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(99(a,1),324(a,1,1,1))].">
      <j1 rule="para" parents="99 324"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(398(a,1),325(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="398 325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * ((y / z) * z)
    ]]></literal>
    <justification jstring="[para(400(a,1),325(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="400 325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (x * z),u,w) = x * (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(92(a,1),329(a,1,2,1))].">
      <j1 rule="para" parents="92 329"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(241(a,1),329(a,1,2,1))].">
      <j1 rule="para" parents="241 329"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(468(a,1),329(a,1,2,1))].">
      <j1 rule="para" parents="468 329"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(187(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="187 330"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(92(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="92 330"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(241(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="241 330"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      (R(x / y,y,z) * y) \ (x * z) = L(z,y,R(x / y,y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),384(a,1,2,1))].">
      <j1 rule="para" parents="12 384"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(368(a,1),409(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="368 409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(368(a,1),410(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="368 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(397(a,1),413(a,1,1,1))].">
      <j1 rule="para" parents="397 413"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y
    ]]></literal>
    <justification jstring="[para(396(a,1),416(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="396 416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      L(T(x / ((1 / x) * x),y),z,u) / x = L(T(1 / (1 / x),y),z,u) * (1 / x)
    ]]></literal>
    <justification jstring="[para(300(a,2),417(a,1,1,1))].">
      <j1 rule="para" parents="300 417"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(290(a,1),437(a,1,2,1))].">
      <j1 rule="para" parents="290 437"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(518(a,1),437(a,1,2,1))].">
      <j1 rule="para" parents="518 437"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,288,a,b,450,a)].">
      <j1 rule="hyper" parents="63 288 450"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(293(a,1),501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="293 501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(371(a,1),501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="371 501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(114,a,533,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="114 533 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[para(298(a,1),577(a,1,1,2))].">
      <j1 rule="para" parents="298 577"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      ((x / y) * (y / ((x / y) * y))) / (x / y) = (((x / y) * (1 / (x / y))) * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,400,a(flip),b,590,a),flip(a)].">
      <j1 rule="hyper" parents="63 400 590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      L(T(x / y,z),u,w) * y != v5
    ]]></literal>
    <literal><![CDATA[
      y * L(T(y \ x,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(339(a,1),594(a,1,1,1))].">
      <j1 rule="para" parents="339 594"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(115,a,595,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 595 18"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ 1)) / z)) = u
    ]]></literal>
    <justification jstring="[para(595(a,1),236(a,1,2))].">
      <j1 rule="para" parents="595 236"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),645(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),556(a,1,2,1))].">
      <j1 rule="para" parents="92 556"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(241(a,1),556(a,1,2,1))].">
      <j1 rule="para" parents="241 556"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(302,a,610,a),flip(a)].">
      <j1 rule="hyper" parents="302 610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(200(a,1),711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="200 711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(318,a,131,a(flip),b,712,a)].">
      <j1 rule="hyper" parents="318 131 712"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(268,a,712,a),flip(a)].">
      <j1 rule="hyper" parents="268 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(257,a,131,a(flip),b,712,a),flip(a)].">
      <j1 rule="hyper" parents="257 131 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(111,a,131,a(flip),b,712,a)].">
      <j1 rule="hyper" parents="111 131 712"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(111,a,72,a(flip),b,712,a),flip(a)].">
      <j1 rule="hyper" parents="111 72 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(111,a,70,a(flip),b,712,a),flip(a)].">
      <j1 rule="hyper" parents="111 70 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,712,a),flip(a)].">
      <j1 rule="hyper" parents="63 192 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(104(a,1),712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(203,a,12,a,b,719,a)].">
      <j1 rule="hyper" parents="203 12 719"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,719,a)].">
      <j1 rule="hyper" parents="123 719"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(118,a,719,a)].">
      <j1 rule="hyper" parents="118 719"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(115,a,719,a(flip),b,357,a),flip(a)].">
      <j1 rule="hyper" parents="115 719 357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(719(a,1),239(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="719 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(725(a,1),670(a,2,1))].">
      <j1 rule="para" parents="725 670"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(726(a,1),665(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="726 665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(715(a,1),43(a,1))].">
      <j1 rule="para" parents="715 43"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(203,a,102,a,b,716,a),flip(a)].">
      <j1 rule="hyper" parents="203 102 716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,353,a,b,716,a),flip(a)].">
      <j1 rule="hyper" parents="34 353 716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      x * (T(x,y) \ (T(x,y) / x)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(34,a,247,a,b,716,a),flip(a)].">
      <j1 rule="hyper" parents="34 247 716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,718,a),flip(a)].">
      <j1 rule="hyper" parents="118 718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(737(a,2),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="737 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,353,a,b,720,a),flip(a)].">
      <j1 rule="hyper" parents="34 353 720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(124,a,730,a)].">
      <j1 rule="hyper" parents="124 730"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(336(a,1),722(a,1,2))].">
      <j1 rule="para" parents="336 722"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      x * T(1 / x,T(x,y)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(659(a,1),735(a,1,2))].">
      <j1 rule="para" parents="659 735"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(275(a,1),616(a,1,2))].">
      <j1 rule="para" parents="275 616"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(492,a,617,a),flip(a)].">
      <j1 rule="hyper" parents="492 617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(346,a,620,a)].">
      <j1 rule="hyper" parents="346 620"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[hyper(112,a,746,a,b,336,a)].">
      <j1 rule="hyper" parents="112 746 336"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(336(a,1),639(a,2,1))].">
      <j1 rule="para" parents="336 639"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),691(a,2,2,1))].">
      <j1 rule="para" parents="8 691"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,461,a(flip),b,749,a)].">
      <j1 rule="hyper" parents="63 461 749"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,749,a(flip),b,461,a(flip))].">
      <j1 rule="hyper" parents="111 749 461"/>
    </justification>
  </clause>

  <clause id="752">
    <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(750(a,1),481(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="750 481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ L((y \ x) \ 1,y \ x,y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(293(a,1),751(a,1,1))].">
      <j1 rule="para" parents="293 751"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),692(a,2,2,1))].">
      <j1 rule="para" parents="8 692"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = (x \ 1) * R(T(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),692(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,466,a(flip),b,754,a)].">
      <j1 rule="hyper" parents="63 466 754"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * u) / ((x \ 1) * u) = R(R(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[para(756(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="756 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,460,a(flip),b,693,a),flip(a)].">
      <j1 rule="hyper" parents="257 460 693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(585,a,694,a)].">
      <j1 rule="hyper" parents="585 694"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,201,a(flip),b,697,a)].">
      <j1 rule="hyper" parents="115 201 697"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(111,a,293,a(flip),b,762,a),flip(a)].">
      <j1 rule="hyper" parents="111 293 762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),698(a,2,1))].">
      <j1 rule="para" parents="8 698"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (1 / x) * (((y * z) / (x * z)) * x) = R((1 / x) * y,x,z)
    ]]></literal>
    <justification jstring="[para(539(a,2),698(a,1,2))].">
      <j1 rule="para" parents="539 698"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(111,a,299,a(flip),b,764,a),flip(a)].">
      <j1 rule="hyper" parents="111 299 764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(481(a,2),764(a,1,2))].">
      <j1 rule="para" parents="481 764"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(318,a,189,a(flip),b,768,a),flip(a)].">
      <j1 rule="hyper" parents="318 189 768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,699,a),flip(a)].">
      <j1 rule="hyper" parents="118 699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(275(a,1),699(a,1,2)),flip(a)].">
      <j1 rule="para" parents="275 699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(257,a,587,a(flip),b,702,a),flip(a)].">
      <j1 rule="hyper" parents="257 587 702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(104(a,1),723(a,1,2,1))].">
      <j1 rule="para" parents="104 723"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(194(a,1),723(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="194 723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,78,a(flip),b,773,a),flip(a)].">
      <j1 rule="hyper" parents="257 78 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(111,a,78,a(flip),b,773,a)].">
      <j1 rule="hyper" parents="111 78 773"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ ((x / y) \ z)) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(111,a,72,a(flip),b,773,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 72 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(111,a,70,a(flip),b,773,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 70 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),775(a,1,2,1))].">
      <j1 rule="para" parents="79 775"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(220(a,2),775(a,1,2))].">
      <j1 rule="para" parents="220 775"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,220,a,b,776,a),flip(a)].">
      <j1 rule="hyper" parents="257 220 776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      a(1 / x,x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,509,a,b,781,a)].">
      <j1 rule="hyper" parents="63 509 781"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(781(a,1),546(a,1,3))].">
      <j1 rule="para" parents="781 546"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,92,a(flip),b,783,a)].">
      <j1 rule="hyper" parents="63 92 783"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(172,a,783,a(flip),b,94,a(flip))].">
      <j1 rule="hyper" parents="172 783 94"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(115,a,783,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 783 18"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(783(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="783 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      ((x / y) \ x) \ (x / (x / y)) = (x / (x / y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,79,a(flip),b,779,a),flip(a)].">
      <j1 rule="hyper" parents="257 79 779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(244(a,2),790(a,1,2))].">
      <j1 rule="para" parents="244 790"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(344(a,1),784(a,1,2))].">
      <j1 rule="para" parents="344 784"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(627(a,1),784(a,1,1))].">
      <j1 rule="para" parents="627 784"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,794,a)].">
      <j1 rule="hyper" parents="125 794"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(786(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="786 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(336(a,1),745(a,1,1))].">
      <j1 rule="para" parents="336 745"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(7(a,1),748(a,1,1,2))].">
      <j1 rule="para" parents="7 748"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(726(a,1),798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="726 798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),760(a,1,1,1,2))].">
      <j1 rule="para" parents="79 760"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),761(a,2,1,1))].">
      <j1 rule="para" parents="7 761"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),801(a,1,2,1))].">
      <j1 rule="para" parents="79 801"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      R(x,y,z) / x != R(x,y,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(802(a,1),204(a,2)),flip(a)].">
      <j1 rule="para" parents="802 204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,746,a,b,770,a)].">
      <j1 rule="hyper" parents="63 746 770"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),771(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,797,a)].">
      <j1 rule="hyper" parents="123 797"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(797(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="797 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(275(a,1),797(a,1,1))].">
      <j1 rule="para" parents="275 797"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(649(a,1),797(a,1,1))].">
      <j1 rule="para" parents="649 797"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(633,a,440,a),flip(a)].">
      <j1 rule="hyper" parents="633 440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,770,a(flip),b,810,a),flip(a)].">
      <j1 rule="hyper" parents="257 770 810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(257,a,656,a(flip),b,810,a),flip(a)].">
      <j1 rule="hyper" parents="257 656 810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,649,a(flip),b,810,a),flip(a)].">
      <j1 rule="hyper" parents="257 649 810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[hyper(115,a,810,a,b,770,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 810 770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,810,a,b,336,a)].">
      <j1 rule="hyper" parents="112 810 336"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(308(a,1),810(a,1,1))].">
      <j1 rule="para" parents="308 810"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(194(a,1),813(a,2,2))].">
      <j1 rule="para" parents="194 813"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(79(a,1),811(a,2,2,2,1))].">
      <j1 rule="para" parents="79 811"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,671,a(flip),b,814,a),flip(a)].">
      <j1 rule="hyper" parents="63 671 814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,650,a(flip),b,814,a),flip(a)].">
      <j1 rule="hyper" parents="63 650 814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),z) = (y * x) * K(z \ (z / K(x,y)),z)
    ]]></literal>
    <justification jstring="[para(16(a,2),814(a,2,2,1,2,2))].">
      <j1 rule="para" parents="16 814"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * K(u \ (u / L(z,y,x)),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),814(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 814"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) != z
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(817(a,2),313(a,1,2))].">
      <j1 rule="para" parents="817 313"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(371(a,1),499(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="371 499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(115,a,528,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="115 528 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(298(a,1),530(a,1,1,1))].">
      <j1 rule="para" parents="298 530"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,x,y)) = a(((x * y) * z) / (x * y),x,y)
    ]]></literal>
    <justification jstring="[para(575(a,1),84(a,1,2))].">
      <j1 rule="para" parents="575 84"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(112,a,591,a(flip),b,222,a),flip(a)].">
      <j1 rule="hyper" parents="112 591 222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(596(a,2),46(a,1))].">
      <j1 rule="para" parents="596 46"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ u)) / z)) = w
    ]]></literal>
    <justification jstring="[para(597(a,1),236(a,1,2))].">
      <j1 rule="para" parents="597 236"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(115,a,598,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="115 598 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[para(611(a,1),352(a,1,2))].">
      <j1 rule="para" parents="611 352"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(257,a,340,a(flip),b,636,a),flip(a)].">
      <j1 rule="hyper" parents="257 340 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(654(a,1),640(a,1))].">
      <j1 rule="para" parents="654 640"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      L(x,y,R((y * z) / y,y,x)) = (y * R(z,y,x)) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(465(a,1),690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="465 690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      (1 / x) * ((y * (x \ 1)) * x) = R((1 / x) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(149(a,1),765(a,1,2,1))].">
      <j1 rule="para" parents="149 765"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(103(a,2),415(a,1,1))].">
      <j1 rule="para" parents="103 415"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(490(a,2),43(a,1))].">
      <j1 rule="para" parents="490 43"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(92(a,1),557(a,1,2,1))].">
      <j1 rule="para" parents="92 557"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(241(a,1),557(a,1,2,1))].">
      <j1 rule="para" parents="241 557"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),565(a,2,2))].">
      <j1 rule="para" parents="10 565"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(604(a,1),750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="604 750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,336,a(flip),b,607,a),flip(a)].">
      <j1 rule="hyper" parents="257 336 607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z))
    ]]></literal>
    <justification jstring="[hyper(425,a,609,a)].">
      <j1 rule="hyper" parents="425 609"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(303,a,686,a),flip(a)].">
      <j1 rule="hyper" parents="303 686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      (x / y) * (y * L(T(x / y,y),z,u)) = L(x / y,z,u) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),851(a,2,2))].">
      <j1 rule="para" parents="12 851"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(201(a,1),851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="201 851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(268,a,853,a),flip(a)].">
      <j1 rule="hyper" parents="268 853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(118,a,853,a)].">
      <j1 rule="hyper" parents="118 853"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(111,a,131,a(flip),b,853,a)].">
      <j1 rule="hyper" parents="111 131 853"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(855(a,1),836(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="855 836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,193,a(flip),b,687,a)].">
      <j1 rule="hyper" parents="63 193 687"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      (x * (y * z)) * R(((x * y) * L(z,y,x)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(90(a,1),687(a,1,1))].">
      <j1 rule="para" parents="90 687"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(118,a,700,a)].">
      <j1 rule="hyper" parents="118 700"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = T(y / (x / z),u) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(112,a,336,a(flip),b,701,a)].">
      <j1 rule="hyper" parents="112 336 701"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      (T(1 / (x / y),z) * (x / y)) * y = T(y / x,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),701(a,2,1,1,1))].">
      <j1 rule="para" parents="7 701"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      (T(1 / (x / y),z) * (x / y)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,336,a(flip),b,864,a),flip(a)].">
      <j1 rule="hyper" parents="257 336 864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(336(a,1),865(a,1,1))].">
      <j1 rule="para" parents="336 865"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,866,a),flip(a)].">
      <j1 rule="hyper" parents="123 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(275(a,1),866(a,1,1))].">
      <j1 rule="para" parents="275 866"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,810,a,b,867,a)].">
      <j1 rule="hyper" parents="63 810 867"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,746,a,b,867,a)].">
      <j1 rule="hyper" parents="63 746 867"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * u) * T(((y * z) * u) \ (z * u),x)) / (z * u)
    ]]></literal>
    <justification jstring="[para(20(a,2),869(a,1,1,2,2))].">
      <j1 rule="para" parents="20 869"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(257,a,335,a(flip),b,868,a),flip(a)].">
      <j1 rule="hyper" parents="257 335 868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      (K((x / y) \ 1,x / y) * y) / x = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,868,a,b,336,a)].">
      <j1 rule="hyper" parents="112 868 336"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * (y / x) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,785,a(flip),b,873,a)].">
      <j1 rule="hyper" parents="63 785 873"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(268,a,875,a),flip(a)].">
      <j1 rule="hyper" parents="268 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(111,a,131,a(flip),b,875,a)].">
      <j1 rule="hyper" parents="111 131 875"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (((x * y) * x) / (x * y)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(203,a,12,a(flip),b,875,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 12 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(111,a,70,a(flip),b,875,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 70 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,879,a),flip(a)].">
      <j1 rule="hyper" parents="123 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = T(y * x,y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,624,a,b,881,a)].">
      <j1 rule="hyper" parents="63 624 881"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(881(a,1),194(a,1,1))].">
      <j1 rule="para" parents="881 194"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      T(T(x,x / y) / y,(x / y) * y) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),883(a,1,1,1,1))].">
      <j1 rule="para" parents="12 883"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),884(a,1,2))].">
      <j1 rule="para" parents="12 884"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(227,a,885,a),flip(a)].">
      <j1 rule="hyper" parents="227 885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(37,a,586,a,b,886,a)].">
      <j1 rule="hyper" parents="37 586 886"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(886(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="886 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(118,a,887,a)].">
      <j1 rule="hyper" parents="118 887"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),887(a,1,2,1,2))].">
      <j1 rule="para" parents="79 887"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(581(a,2),887(a,1,2))].">
      <j1 rule="para" parents="581 887"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[para(889(a,2),194(a,1,1))].">
      <j1 rule="para" parents="889 194"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),892(a,1,1,2,2))].">
      <j1 rule="para" parents="76 892"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(195(a,1),890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="195 890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      x * R(y,x,T(y,x)) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,576,a(flip),b,882,a(flip))].">
      <j1 rule="hyper" parents="37 576 882"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(118,a,896,a)].">
      <j1 rule="hyper" parents="118 896"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(897(a,1),356(a,1,1))].">
      <j1 rule="para" parents="897 356"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      R(L(x,y,x),y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a,b,898,a)].">
      <j1 rule="hyper" parents="63 29 898"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      R(z,y,T(z,y)) = x
    ]]></literal>
    <justification jstring="[para(898(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="898 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(203,a,12,a(flip),b,876,a)].">
      <j1 rule="hyper" parents="203 12 876"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(34,a,353,a,b,876,a),flip(a)].">
      <j1 rule="hyper" parents="34 353 876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      ((x * y) / x) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(876(a,1),43(a,1))].">
      <j1 rule="para" parents="876 43"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(112,a,901,a,b,xx)].">
      <j1 rule="hyper" parents="112 901"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[para(297(a,1),901(a,2,2)),flip(a)].">
      <j1 rule="para" parents="297 901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(310(a,1),901(a,2,2)),flip(a)].">
      <j1 rule="para" parents="310 901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(904(a,2),194(a,1,1))].">
      <j1 rule="para" parents="904 194"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(316(a,1),907(a,1,1,2))].">
      <j1 rule="para" parents="316 907"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(236,a,891,a)].">
      <j1 rule="hyper" parents="236 891"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(579,a,828,a),flip(a)].">
      <j1 rule="hyper" parents="579 828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(888,a,831,a),flip(a)].">
      <j1 rule="hyper" parents="888 831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(642,a,831,a)].">
      <j1 rule="hyper" parents="642 831"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),911(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),849(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),849(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a(flip),b,915,a)].">
      <j1 rule="hyper" parents="63 609 915"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,514,a(flip),b,915,a),flip(a)].">
      <j1 rule="hyper" parents="63 514 915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(614(a,1),916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="614 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(652(a,1),916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="652 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(808(a,2),916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="808 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(73(a,1),920(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="73 920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(425,a,921,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="425 921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(921(a,2),425(a,1))].">
      <j1 rule="para" parents="921 425"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,795,a,b,922,a),flip(a)].">
      <j1 rule="hyper" parents="34 795 922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      x / K(x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(172,a,148,a(flip),b,925,a(flip))].">
      <j1 rule="hyper" parents="172 148 925"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      R(x,x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(572,a,926,a)].">
      <j1 rule="hyper" parents="572 926"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a,b,929,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      (x / y) * (y * L(y \ x,z,u)) = L(x / y,z,u) * x
    ]]></literal>
    <justification jstring="[para(104(a,1),852(a,1,2,2,1))].">
      <j1 rule="para" parents="104 852"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),862(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,336,a(flip),b,863,a),flip(a)].">
      <j1 rule="hyper" parents="257 336 863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(460(a,1),910(a,1,1))].">
      <j1 rule="para" parents="460 910"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),912(a,2,1,1,2))].">
      <j1 rule="para" parents="7 912"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),937(a,1,2,1,2))].">
      <j1 rule="para" parents="79 937"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      ((x * (y \ 1)) / x) / (y \ 1) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(270,a,938,a),flip(a)].">
      <j1 rule="hyper" parents="270 938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),914(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(336(a,1),914(a,2,1))].">
      <j1 rule="para" parents="336 914"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(337(a,1),940(a,1,1))].">
      <j1 rule="para" parents="337 940"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(455,a,942,a)].">
      <j1 rule="hyper" parents="455 942"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      (x * T(T(y,x),z)) * T(y,x) = (y * x) * T(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(257,a,193,a(flip),b,942,a),flip(a)].">
      <j1 rule="hyper" parents="257 193 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,129,a(flip),b,942,a),flip(a)].">
      <j1 rule="hyper" parents="257 129 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      ((x * y) * T(y,z)) / y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,942,a)].">
      <j1 rule="hyper" parents="123 942"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(118,a,942,a)].">
      <j1 rule="hyper" parents="118 942"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(112,a,102,a(flip),b,942,a)].">
      <j1 rule="hyper" parents="112 102 942"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(454,a,942,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="454 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,77,a(flip),b,942,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 77 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(104(a,1),942(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="104 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      T(1 / T(x,y),x) = x \ (x / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(318,a,xx,b,952,a)].">
      <j1 rule="hyper" parents="318 952"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(118,a,952,a)].">
      <j1 rule="hyper" parents="118 952"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(955(a,1),672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="955 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(955(a,1),677(a,1,1)),flip(a)].">
      <j1 rule="para" parents="955 677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(114,a,895,a,b,943,a)].">
      <j1 rule="hyper" parents="114 895 943"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(112,a,102,a(flip),b,947,a),flip(a)].">
      <j1 rule="hyper" parents="112 102 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(270,a,959,a),flip(a)].">
      <j1 rule="hyper" parents="270 959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(111,a,195,a(flip),b,959,a)].">
      <j1 rule="hyper" parents="111 195 959"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      ((x \ y) / x) \ (y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(111,a,134,a(flip),b,959,a)].">
      <j1 rule="hyper" parents="111 134 959"/>
    </justification>
  </clause>

  <clause id="963">
    <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(291(a,1),959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="291 959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(959(a,1),818(a,2,2))].">
      <j1 rule="para" parents="959 818"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(949(a,1),707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="949 707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(173,a,957,a)].">
      <j1 rule="hyper" parents="173 957"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(958(a,1),720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="958 720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      T(x * T(x \ y,y),x \ y) = y
    ]]></literal>
    <justification jstring="[para(960(a,1),194(a,1,1))].">
      <j1 rule="para" parents="960 194"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      T(x,y * T(y \ x,x)) = x
    ]]></literal>
    <justification jstring="[para(960(a,1),343(a,1,2))].">
      <j1 rule="para" parents="960 343"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(514(a,1),969(a,1,2))].">
      <j1 rule="para" parents="514 969"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(668(a,2),970(a,1,2,2))].">
      <j1 rule="para" parents="668 970"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(770(a,1),970(a,1,2,2))].">
      <j1 rule="para" parents="770 970"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,971,a)].">
      <j1 rule="hyper" parents="54 971"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(893(a,1),972(a,1,2,2,2,2))].">
      <j1 rule="para" parents="893 972"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(123,a,967,a),flip(a)].">
      <j1 rule="hyper" parents="123 967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),974(a,1,2,2,2))].">
      <j1 rule="para" parents="10 974"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(976(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="976 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(172,a,977,a(flip),b,714,a(flip))].">
      <j1 rule="hyper" parents="172 977 714"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(203,a,943,a(flip),b,978,a(flip))].">
      <j1 rule="hyper" parents="203 943 978"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      T(((T(x,y) \ x) * x) / (T(x,y) \ x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(978(a,2),473(a,1,2))].">
      <j1 rule="para" parents="978 473"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,979,a(flip),b,339,a),flip(a)].">
      <j1 rule="hyper" parents="114 979 339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,895,a(flip),b,975,a),flip(a)].">
      <j1 rule="hyper" parents="63 895 975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,398,a,b,982,a)].">
      <j1 rule="hyper" parents="63 398 982"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(911(a,1),983(a,1,1))].">
      <j1 rule="para" parents="911 983"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(200(a,1),946(a,1,1))].">
      <j1 rule="para" parents="200 946"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(203,a,985,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="203 985 102"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(112,a,69,a(flip),b,985,a)].">
      <j1 rule="hyper" parents="112 69 985"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(104(a,1),953(a,1,2))].">
      <j1 rule="para" parents="104 953"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(194(a,1),953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="194 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(455,a,988,a)].">
      <j1 rule="hyper" parents="455 988"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      (x * (1 / x)) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(257,a,69,a(flip),b,988,a),flip(a)].">
      <j1 rule="hyper" parents="257 69 988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,77,a(flip),b,988,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 77 988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      K(x,1 / x) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(244(a,2),991(a,1,1))].">
      <j1 rule="para" parents="244 991"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(318,a,xx,b,992,a),flip(a)].">
      <j1 rule="hyper" parents="318 992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,651,a(flip),b,987,a),flip(a)].">
      <j1 rule="hyper" parents="257 651 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(994(a,1),812(a,1,1))].">
      <j1 rule="para" parents="994 812"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      T(x,y) * T((y \ (x * y)) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),934(a,1,1))].">
      <j1 rule="para" parents="22 934"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(102(a,1),935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[para(609(a,1),935(a,1,1))].">
      <j1 rule="para" parents="609 935"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a(flip),b,941,a)].">
      <j1 rule="hyper" parents="63 609 941"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(203,a,941,a(flip),b,609,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 941 609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),941(a,1,2,1,2))].">
      <j1 rule="para" parents="7 941"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1001(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      T(x * T(x \ y,x),x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(257,a,102,a(flip),b,1003,a),flip(a)].">
      <j1 rule="hyper" parents="257 102 1003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[para(102(a,1),1004(a,1,1))].">
      <j1 rule="para" parents="102 1004"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,1005,a,b,xx)].">
      <j1 rule="hyper" parents="112 1005"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1005(a,2),75(a,1,2,1))].">
      <j1 rule="para" parents="1005 75"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(1006(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1006 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(80(a,1),1006(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 1006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),1007(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 1007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(578(a,2),1009(a,1,2,1,2))].">
      <j1 rule="para" parents="578 1009"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a(flip),b,1002,a)].">
      <j1 rule="hyper" parents="63 609 1002"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(203,a,514,a(flip),b,1002,a(flip))].">
      <j1 rule="hyper" parents="203 514 1002"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(338(a,1),1015(a,1,2))].">
      <j1 rule="para" parents="338 1015"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(649(a,1),1015(a,1,2))].">
      <j1 rule="para" parents="649 1015"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(656(a,1),1015(a,1,2))].">
      <j1 rule="para" parents="656 1015"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,1017,a)].">
      <j1 rule="hyper" parents="54 1017"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1018(a,1),340(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1018 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1016(a,1),549(a,1,1))].">
      <j1 rule="para" parents="1016 549"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1019(a,1),521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1019 521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,520,a,b,1023,a)].">
      <j1 rule="hyper" parents="257 520 1023"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),1024(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(54,a,1025,a)].">
      <j1 rule="hyper" parents="54 1025"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,1025,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 1025 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      x * T(x \ 1,K(x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,1026,a,b,xx)].">
      <j1 rule="hyper" parents="115 1026"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(112,a,1028,a(flip),b,336,a),flip(a)].">
      <j1 rule="hyper" parents="112 1028 336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1029(a,1),533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1029 533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(111,a,993,a(flip),b,1027,a(flip))].">
      <j1 rule="hyper" parents="111 993 1027"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(257,a,244,a(flip),b,1031,a),flip(a)].">
      <j1 rule="hyper" parents="257 244 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(203,a,1032,a(flip),b,778,a)].">
      <j1 rule="hyper" parents="203 1032 778"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a,b,1034,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      R(x,1 / x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,553,a,b,1034,a)].">
      <j1 rule="hyper" parents="63 553 1034"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1035(a,1),340(a,1,1,2))].">
      <j1 rule="para" parents="1035 340"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(112,a,1036,a(flip),b,419,a)].">
      <j1 rule="hyper" parents="112 1036 419"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1036(a,1),417(a,1,1,1))].">
      <j1 rule="para" parents="1036 417"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1040(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(103(a,2),1040(a,1,1))].">
      <j1 rule="para" parents="103 1040"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      T(x,x \ 1) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(257,a,244,a(flip),b,1044,a),flip(a)].">
      <j1 rule="hyper" parents="257 244 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,654,a,b,1045,a(flip))].">
      <j1 rule="hyper" parents="35 654 1045"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(40,a,471,a,b,1046,a)].">
      <j1 rule="hyper" parents="40 471 1046"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,1046,a(flip),b,994,a),flip(a)].">
      <j1 rule="hyper" parents="115 1046 994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1046(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1046 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      T(1 / x,(x \ 1) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),1046(a,1,1,2))].">
      <j1 rule="para" parents="76 1046"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1046(a,1),996(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1046 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(571,a,1047,a)].">
      <j1 rule="hyper" parents="571 1047"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(114,a,220,a,b,1048,a)].">
      <j1 rule="hyper" parents="114 220 1048"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(36,a,291,a,b,1048,a)].">
      <j1 rule="hyper" parents="36 291 1048"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1048(a,2),280(a,1))].">
      <j1 rule="para" parents="1048 280"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1055(a,1),936(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1055 936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      T(1 / x,T(x,x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(103(a,2),1050(a,1,2))].">
      <j1 rule="para" parents="103 1050"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(124,a,1051,a)].">
      <j1 rule="hyper" parents="124 1051"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1045,a(flip),b,1051,a),flip(a)].">
      <j1 rule="hyper" parents="63 1045 1051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1044,a(flip),b,1051,a)].">
      <j1 rule="hyper" parents="63 1044 1051"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(111,a,1051,a(flip),b,1045,a(flip))].">
      <j1 rule="hyper" parents="111 1051 1045"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      K(x,x \ 1) * T((x * (1 / x)) \ y,z) = x * ((1 / x) * T((1 / x) \ (x \ y),z))
    ]]></literal>
    <justification jstring="[para(1060(a,2),609(a,1,1))].">
      <j1 rule="para" parents="1060 609"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(1060(a,2),991(a,1,1))].">
      <j1 rule="para" parents="1060 991"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(114,a,1061,a(flip),b,1040,a)].">
      <j1 rule="hyper" parents="114 1061 1040"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(172,a,1062,a(flip),b,793,a),flip(a)].">
      <j1 rule="hyper" parents="172 1062 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1062(a,1),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1062 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1054(a,1),786(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1054 786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      T(x / (y * x),T(y,y \ 1)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1058(a,1),300(a,2,1))].">
      <j1 rule="para" parents="1058 300"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (K(x,x \ 1) * (x * y)) = L(y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1066(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1066 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * x = (1 / (1 / (x / y))) * y
    ]]></literal>
    <justification jstring="[hyper(114,a,1068,a(flip),b,785,a),flip(a)].">
      <j1 rule="hyper" parents="114 1068 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(244(a,2),1069(a,1))].">
      <j1 rule="para" parents="244 1069"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1043(a,2),1056(a,1))].">
      <j1 rule="para" parents="1043 1056"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(847,a,1073,a)].">
      <j1 rule="hyper" parents="847 1073"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(565,a,1073,a),flip(a)].">
      <j1 rule="hyper" parents="565 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a(flip),b,1073,a),flip(a)].">
      <j1 rule="hyper" parents="34 10 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(1073(a,1),350(a,1,1))].">
      <j1 rule="para" parents="1073 350"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(1073(a,1),784(a,1,1))].">
      <j1 rule="para" parents="1073 784"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * ((1 / x) * (y * z))) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1073(a,1),359(a,1,1))].">
      <j1 rule="para" parents="1073 359"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1080(a,1,1))].">
      <j1 rule="para" parents="22 1080"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(118,a,1081,a)].">
      <j1 rule="hyper" parents="118 1081"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(1081(a,1),248(a,1,1))].">
      <j1 rule="para" parents="1081 248"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1086(a,1),201(a,1,2))].">
      <j1 rule="para" parents="1086 201"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1079,a,1061,a),flip(a)].">
      <j1 rule="hyper" parents="1079 1061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(342,a,1038,a),flip(a)].">
      <j1 rule="hyper" parents="342 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1041(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(195(a,1),1091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="195 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,1014,a),flip(a)].">
      <j1 rule="hyper" parents="63 192 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y
    ]]></literal>
    <justification jstring="[para(103(a,2),1095(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="103 1095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(195(a,1),1094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="195 1094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1098(a,1),956(a,1,1))].">
      <j1 rule="para" parents="1098 956"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1099(a,1),951(a,1,1,1))].">
      <j1 rule="para" parents="1099 951"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(257,a,299,a(flip),b,1030,a),flip(a)].">
      <j1 rule="hyper" parents="257 299 1030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1101(a,1,1,1))].">
      <j1 rule="para" parents="7 1101"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1102(a,1),208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1102 208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(257,a,104,a(flip),b,1103,a),flip(a)].">
      <j1 rule="hyper" parents="257 104 1103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1060(a,2),1057(a,2,1))].">
      <j1 rule="para" parents="1060 1057"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),989(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(455,a,1106,a)].">
      <j1 rule="hyper" parents="455 1106"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(112,a,77,a(flip),b,1106,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 77 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(890(a,1),1106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="890 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(261,a,1110,a),flip(a)].">
      <j1 rule="hyper" parents="261 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(732,a,1111,a)].">
      <j1 rule="hyper" parents="732 1111"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(123,a,1112,a)].">
      <j1 rule="hyper" parents="123 1112"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,913,a,b,1114,a)].">
      <j1 rule="hyper" parents="63 913 1114"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1115(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,1000,a)].">
      <j1 rule="hyper" parents="63 192 1000"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1000(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="10 1000"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),1000(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <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(273(a,2),1118(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="273 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(642,a,1100,a)].">
      <j1 rule="hyper" parents="642 1100"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / y = x * T(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(123,a,1120,a)].">
      <j1 rule="hyper" parents="123 1120"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y * T(y \ (z / x),u),x) = w
    ]]></literal>
    <justification jstring="[para(1120(a,1),238(a,1,2))].">
      <j1 rule="para" parents="1120 238"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(614(a,1),1120(a,1,1)),flip(a)].">
      <j1 rule="para" parents="614 1120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(744(a,2),1120(a,1,1))].">
      <j1 rule="para" parents="744 1120"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(719(a,1),1123(a,1,2,1))].">
      <j1 rule="para" parents="719 1123"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(66(a,1),1127(a,2,2,2,1,2))].">
      <j1 rule="para" parents="66 1127"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(257,a,192,a(flip),b,1129,a),flip(a)].">
      <j1 rule="hyper" parents="257 192 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(275(a,1),1129(a,2,2))].">
      <j1 rule="para" parents="275 1129"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,98,a(flip),b,1130,a),flip(a)].">
      <j1 rule="hyper" parents="35 98 1130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = ((a(x,y,z) * (u * w)) * v5) / (w * v5)
    ]]></literal>
    <justification jstring="[para(128(a,1),360(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="128 360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      R(x,y * ((x * y) \ z),a(x,y,(x * y) \ z)) \ z = (y * ((x * y) \ z)) * a(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(495(a,1),243(a,1,1))].">
      <j1 rule="para" parents="495 243"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(115,a,599,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="115 599 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <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(613(a,1),352(a,1,2))].">
      <j1 rule="para" parents="613 352"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(293(a,1),763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="293 763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,1138,a)].">
      <j1 rule="hyper" parents="125 1138"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(318,a,xx,b,1139,a)].">
      <j1 rule="hyper" parents="318 1139"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),859(a,2,1))].">
      <j1 rule="para" parents="11 859"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(114,a,1141,a(flip),b,340,a),flip(a)].">
      <j1 rule="hyper" parents="114 1141 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,201,a,b,1142,a)].">
      <j1 rule="hyper" parents="34 201 1142"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(593,a,905,a)].">
      <j1 rule="hyper" parents="593 905"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[para(587(a,1),1144(a,1,1))].">
      <j1 rule="para" parents="587 1144"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,R(1 / T(x,y),T(x,y),x))
    ]]></literal>
    <justification jstring="[para(719(a,1),1145(a,1,1,2,1))].">
      <j1 rule="para" parents="719 1145"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      (1 / (x / y)) \ (y / x) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(630,a,767,a),flip(a)].">
      <j1 rule="hyper" parents="630 767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = (1 / ((y \ x) / x)) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),1147(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      (1 / ((x \ y) / y)) * (x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,159,a(flip),b,1148,a(flip))].">
      <j1 rule="hyper" parents="115 159 1148"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = (x * ((x \ y) / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(318,a,xx,b,1149,a)].">
      <j1 rule="hyper" parents="318 1149"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(585,a,680,a)].">
      <j1 rule="hyper" parents="585 680"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(257,a,460,a(flip),b,682,a),flip(a)].">
      <j1 rule="hyper" parents="257 460 682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[hyper(425,a,685,a)].">
      <j1 rule="hyper" parents="425 685"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,464,a,b,688,a)].">
      <j1 rule="hyper" parents="63 464 688"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * R(a(x,y,z) \ ((x * (y * z)) \ u),w,v5)) = ((x * y) * z) * R(((x * (y * z)) * a(x,y,z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(111,a,887,a(flip),b,705,a(flip))].">
      <j1 rule="hyper" parents="111 887 705"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      (x * (y * z)) * ((u * (((x * y) * L(z,y,x)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u))
    ]]></literal>
    <justification jstring="[para(90(a,1),705(a,1,1))].">
      <j1 rule="para" parents="90 705"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(115,a,1123,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="115 1123 1156"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1156(a,2),1145(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1156 1145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,202,a(flip),b,755,a),flip(a)].">
      <j1 rule="hyper" parents="257 202 755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y) * (T(x,y) \ x),z,u) = R(x,z,u) * (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(719(a,1),1160(a,1,2,1,2))].">
      <j1 rule="para" parents="719 1160"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = z
    ]]></literal>
    <justification jstring="[para(769(a,1),309(a,1))].">
      <j1 rule="para" parents="769 309"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1163(a,2,1,1))].">
      <j1 rule="para" parents="7 1163"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1164(a,1,2,1))].">
      <j1 rule="para" parents="79 1164"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(123,a,1165,a)].">
      <j1 rule="hyper" parents="123 1165"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,159,a(flip),b,1165,a(flip))].">
      <j1 rule="hyper" parents="114 159 1165"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),1 / x) = (L(x,y,z) / x) \ ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(1165(a,1),92(a,2,1))].">
      <j1 rule="para" parents="1165 92"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      T((L(x,y,z) * (1 / x)) / L(x,y,z),L(x,y,z) / x) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1165(a,1),473(a,1,2))].">
      <j1 rule="para" parents="1165 473"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(187(a,1),1167(a,1,1,2))].">
      <j1 rule="para" parents="187 1167"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ L(x \ 1,x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(118,a,1170,a)].">
      <j1 rule="hyper" parents="118 1170"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1170(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1170 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ L((x \ y) \ 1,x \ y,x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1171(a,1,1,2,1))].">
      <j1 rule="para" parents="10 1171"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(293(a,1),1173(a,1,2))].">
      <j1 rule="para" parents="293 1173"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(173,a,1174,a)].">
      <j1 rule="hyper" parents="173 1174"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(118,a,826,a)].">
      <j1 rule="hyper" parents="118 826"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * ((x \ R(x,y,y \ 1)) * R((x \ R(x,y,y \ 1)) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(840(a,2),827(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="840 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,834,a)].">
      <j1 rule="hyper" parents="118 834"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(593,a,906,a)].">
      <j1 rule="hyper" parents="593 906"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(880(a,1),1184(a,1,1))].">
      <j1 rule="para" parents="880 1184"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1185,a)].">
      <j1 rule="hyper" parents="123 1185"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1186(a,1),664(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1186 664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      T(R(T(x,x * y),y,y \ 1) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(27(a,2),908(a,1,1,1))].">
      <j1 rule="para" parents="27 908"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(464(a,1),1151(a,2,1))].">
      <j1 rule="para" parents="464 1151"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(460(a,1),1152(a,1,1))].">
      <j1 rule="para" parents="460 1152"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(464(a,2),1154(a,2,2))].">
      <j1 rule="para" parents="464 1154"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1176(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <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),1193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1183(a,1,2,2,1))].">
      <j1 rule="para" parents="10 1183"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(348,a,1195,a)].">
      <j1 rule="hyper" parents="348 1195"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1195(a,1),348(a,1))].">
      <j1 rule="para" parents="1195 348"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1196(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(661(a,1),1196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="661 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(966(a,1),1196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="966 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1166(a,1),1196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1166 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(338(a,2),1199(a,1,2,1))].">
      <j1 rule="para" parents="338 1199"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(320(a,1),1188(a,1,1))].">
      <j1 rule="para" parents="320 1188"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1203(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1203 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      T(x * y,R(x,y,y \ 1)) = T(x * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(986(a,1),1204(a,1,1))].">
      <j1 rule="para" parents="986 1204"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),1205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(397(a,1),1206(a,2,2))].">
      <j1 rule="para" parents="397 1206"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),1207(a,1,1))].">
      <j1 rule="para" parents="12 1207"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(104(a,1),1208(a,1,2)),flip(a)].">
      <j1 rule="para" parents="104 1208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,689,a(flip),b,1190,a)].">
      <j1 rule="hyper" parents="63 689 1190"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(203,a,1190,a(flip),b,827,a),flip(a)].">
      <j1 rule="hyper" parents="203 1190 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(203,a,1190,a(flip),b,689,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 1190 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(111,a,1190,a(flip),b,827,a),flip(a)].">
      <j1 rule="hyper" parents="111 1190 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1190(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1190"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1190(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1216(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1216"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(261,a,1218,a),flip(a)].">
      <j1 rule="hyper" parents="261 1218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ y) = y * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,130,a(flip),b,1218,a),flip(a)].">
      <j1 rule="hyper" parents="257 130 1218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(118,a,1218,a)].">
      <j1 rule="hyper" parents="118 1218"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1219(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1219 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1221(a,1),707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1221 707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(115,a,1223,a(flip),b,463,a)].">
      <j1 rule="hyper" parents="115 1223 463"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      (x * R(T(y,x),z,u)) * (x \ (y * x)) = (y * x) * R(x \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1220(a,1,1,2,1))].">
      <j1 rule="para" parents="22 1220"/>
    </justification>
  </clause>

  <clause id="1226">
    <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),1213(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(538,a,1226,a)].">
      <j1 rule="hyper" parents="538 1226"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,1226,a,b,464,a)].">
      <j1 rule="hyper" parents="112 1226 464"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(176(a,1),1226(a,2,2,1,2))].">
      <j1 rule="para" parents="176 1226"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1229(a,1),1011(a,2,2,1))].">
      <j1 rule="para" parents="1229 1011"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = T(x * R(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),1228(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,689,a(flip),b,1215,a)].">
      <j1 rule="hyper" parents="63 689 1215"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1191(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(73(a,1),1191(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="73 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,685,a(flip),b,1239,a)].">
      <j1 rule="hyper" parents="63 685 1239"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(203,a,601,a(flip),b,1239,a(flip))].">
      <j1 rule="hyper" parents="203 601 1239"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(293(a,1),1243(a,1,2,2))].">
      <j1 rule="para" parents="293 1243"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(461(a,1),1243(a,1,2))].">
      <j1 rule="para" parents="461 1243"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1164(a,1),1243(a,1,2))].">
      <j1 rule="para" parents="1164 1243"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1246(a,1),340(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1246 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1245(a,1),549(a,1,1))].">
      <j1 rule="para" parents="1245 549"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1055(a,1),1241(a,2,1,2))].">
      <j1 rule="para" parents="1055 1241"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1105(a,1),1249(a,1,2))].">
      <j1 rule="para" parents="1105 1249"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1060(a,2),1250(a,2,1))].">
      <j1 rule="para" parents="1060 1250"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1253(a,1),1076(a,1,2))].">
      <j1 rule="para" parents="1253 1076"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      R((x * (y * z)) / (x * z),u,w) * (x * z) = x * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1192(a,2,2,1,1))].">
      <j1 rule="para" parents="11 1192"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = (x * (1 / y)) * (w * R(w \ ((x * (1 / y)) \ (x * w)),z,u))
    ]]></literal>
    <justification jstring="[para(190(a,2),1211(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="190 1211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,685,a(flip),b,1238,a)].">
      <j1 rule="hyper" parents="63 685 1238"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,601,a(flip),b,1238,a),flip(a)].">
      <j1 rule="hyper" parents="63 601 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(203,a,1238,a(flip),b,685,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 1238 685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      (x * L(x \ (x * y),z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1261(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1261"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(455,a,1263,a)].">
      <j1 rule="hyper" parents="455 1263"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,129,a(flip),b,1263,a),flip(a)].">
      <j1 rule="hyper" parents="257 129 1263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(111,a,129,a(flip),b,1263,a)].">
      <j1 rule="hyper" parents="111 129 1263"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      ((x * y) * z) * L(z,y,x) = (x * (y * z)) * z
    ]]></literal>
    <justification jstring="[para(90(a,1),1263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="90 1263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(112,a,90,a(flip),b,1265,a),flip(a)].">
      <j1 rule="hyper" parents="112 90 1265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      (x * (y * z)) / z != L(z,y,x) * u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / z,L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(1269(a,1),204(a,2)),flip(a)].">
      <j1 rule="para" parents="1269 204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1271">
    <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),1260(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(538,a,1271,a)].">
      <j1 rule="hyper" parents="538 1271"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      L(x \ T(x * y,x),z,u) = x \ T(x * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1272(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1009(a,1),1273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1009 1273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,1012,a(flip),b,1274,a),flip(a)].">
      <j1 rule="hyper" parents="63 1012 1274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1255(a,1,1,1))].">
      <j1 rule="para" parents="11 1255"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(484,a,1276,a),flip(a)].">
      <j1 rule="hyper" parents="484 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,131,a(flip),b,1276,a)].">
      <j1 rule="hyper" parents="112 131 1276"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(111,a,131,a(flip),b,1276,a)].">
      <j1 rule="hyper" parents="111 131 1276"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(111,a,70,a(flip),b,1276,a),flip(a)].">
      <j1 rule="hyper" parents="111 70 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,1276,a),flip(a)].">
      <j1 rule="hyper" parents="63 192 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(112,a,131,a(flip),b,1276,a(flip))].">
      <j1 rule="hyper" parents="112 131 1276"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(111,a,72,a(flip),b,1276,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 72 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      R(x,y,z) \ T(R(x,y,z) * (R(x,y,z) \ x),u) = T(x,u) * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1280(a,1),646(a,1,2,1,2))].">
      <j1 rule="para" parents="1280 646"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      ((1 / x) * y) / ((1 / x) * (x * y)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(297(a,1),1278(a,1,2,2))].">
      <j1 rule="para" parents="297 1278"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      (x * (y * (x * z))) / (x * (z * T(y,x * z))) = R(x,z,T(y,x * z))
    ]]></literal>
    <justification jstring="[para(381(a,1),1278(a,1,2,2))].">
      <j1 rule="para" parents="381 1278"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1282(a,1),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1282 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(203,a,98,a(flip),b,1281,a),flip(a)].">
      <j1 rule="hyper" parents="203 98 1281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,1288,a)].">
      <j1 rule="hyper" parents="118 1288"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      ((1 / x) * y) / L(y,x,x \ 1) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(1081(a,1),1285(a,1,2))].">
      <j1 rule="para" parents="1081 1285"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      ((a(x,y,z) * R(u,w,v5)) * (w * v5)) / ((u * w) * v5) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,560,a(flip),b,387,a),flip(a)].">
      <j1 rule="hyper" parents="257 560 387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      ((x * ((y * z) / (R(u,y,z) * (y * z)))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(114,a,590,a(flip),b,387,a)].">
      <j1 rule="hyper" parents="114 590 387"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      (x * R(x \ 1,x,y)) \ (x * R(1 / x,x,y)) = K(x,y / (x * y))
    ]]></literal>
    <justification jstring="[para(189(a,1),573(a,2,2))].">
      <j1 rule="para" parents="189 573"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) * K(x \ 1,x) = (R(x,y,z) * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(930(a,1),679(a,1,1,1))].">
      <j1 rule="para" parents="930 679"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(786(a,1),796(a,1,1))].">
      <j1 rule="para" parents="786 796"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(783(a,1),1083(a,1,2))].">
      <j1 rule="para" parents="783 1083"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(404(a,1),1146(a,2,2))].">
      <j1 rule="para" parents="404 1146"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(7(a,1),1299(a,2,2,1))].">
      <j1 rule="para" parents="7 1299"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1128(a,1),1300(a,1,1))].">
      <j1 rule="para" parents="1128 1300"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(1301(a,1),213(a,1)),flip(b)].">
      <j1 rule="para" parents="1301 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1302,a,1158,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1302 1158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1128(a,2),1303(a,1,2))].">
      <j1 rule="para" parents="1128 1303"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      (x * (y * (x * z))) / (L(y,z,x) * (x * z)) = R(x,z,T(y,x * z))
    ]]></literal>
    <justification jstring="[para(459(a,1),1286(a,1,2))].">
      <j1 rule="para" parents="459 1286"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,785,a(flip),b,1295,a)].">
      <j1 rule="hyper" parents="63 785 1295"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),1306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 1306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1054(a,1),1307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1054 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y))
    ]]></literal>
    <justification jstring="[para(1244(a,1),804(a,2,2,2))].">
      <j1 rule="para" parents="1244 804"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      (x * y) * K(z \ (z / K(y,x)),z) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16(a,2),822(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(810(a,1),1311(a,1,2))].">
      <j1 rule="para" parents="810 1311"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,1312,a)].">
      <j1 rule="hyper" parents="118 1312"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(203,a,941,a(flip),b,835,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 941 835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),835(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),x) = y * L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[para(739(a,1),835(a,2,2))].">
      <j1 rule="para" parents="739 835"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(203,a,1002,a(flip),b,1315,a),flip(a)].">
      <j1 rule="hyper" parents="203 1002 1315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(232,a,1317,a),flip(a)].">
      <j1 rule="hyper" parents="232 1317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,1317,a)].">
      <j1 rule="hyper" parents="118 1317"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,810,a,b,1317,a),flip(a)].">
      <j1 rule="hyper" parents="63 810 1317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1317(a,1),799(a,1,1))].">
      <j1 rule="para" parents="1317 799"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(115,a,1320,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 1320 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(275(a,1),1320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="275 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(667(a,1),1320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="667 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(816(a,2),1320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="816 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x)
    ]]></literal>
    <justification jstring="[para(103(a,1),1324(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="103 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1017(a,1),1319(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1017 1319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = ((1 / y) * T((1 / y) \ 1,(y \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(1297(a,1),1322(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1297 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      T((x \ 1) * x,y) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(102(a,1),1321(a,1,1,1))].">
      <j1 rule="para" parents="102 1321"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1327(a,2,2,1))].">
      <j1 rule="para" parents="10 1327"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(176(a,1),1330(a,2,2))].">
      <j1 rule="para" parents="176 1330"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(16(a,2),1316(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[para(667(a,1),1097(a,2,1))].">
      <j1 rule="para" parents="667 1097"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,1126,a),flip(a)].">
      <j1 rule="hyper" parents="63 192 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(809(a,2),1126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="809 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(1008,a,1338,a)].">
      <j1 rule="hyper" parents="1008 1338"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(80(a,1),1340(a,1,1))].">
      <j1 rule="para" parents="80 1340"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1341(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(1342(a,1),345(a,1,2))].">
      <j1 rule="para" parents="1342 345"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,1136,a)].">
      <j1 rule="hyper" parents="118 1136"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y)
    ]]></literal>
    <justification jstring="[para(1196(a,2),1136(a,1,2))].">
      <j1 rule="para" parents="1196 1136"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1348(a,2,2,1,2,2))].">
      <j1 rule="para" parents="8 1348"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1349(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1161(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(740(a,1),1200(a,1,2,1))].">
      <j1 rule="para" parents="740 1200"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      T(x,y) * R((y \ (x * y)) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1212(a,1,1))].">
      <j1 rule="para" parents="22 1212"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1353(a,1,2,1,1))].">
      <j1 rule="para" parents="22 1353"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      T(x,x * y) * R(T(x,x * y) \ (x * y),z,u) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1354(a,2,1,2,1))].">
      <j1 rule="para" parents="9 1354"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      (R(x,y,z) * u) * (u \ (x * u)) = (x * u) * R(u \ (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(202(a,1),1225(a,1,1))].">
      <j1 rule="para" parents="202 1225"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      (x * y) * R(y \ (x * y),z,u) = (R(x,z,u) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      (R(x,y,z) * u) * T(x,u) = (x * u) * R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(476(a,1),1231(a,2,2))].">
      <j1 rule="para" parents="476 1231"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(476(a,1),1359(a,1,1,2))].">
      <j1 rule="para" parents="476 1359"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(189(a,1),1360(a,1,1,2))].">
      <j1 rule="para" parents="189 1360"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(189(a,1),1361(a,2,2))].">
      <j1 rule="para" parents="189 1361"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,1362,a)].">
      <j1 rule="hyper" parents="54 1362"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      T(x,x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),1363(a,1,2,2,2))].">
      <j1 rule="para" parents="10 1363"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1363(a,1,2,2,2))].">
      <j1 rule="para" parents="12 1363"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      T((x \ y) \ y,x * ((x \ z) / z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1364(a,1),256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1364 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1365(a,1),208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1365 208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      ((x / y) * (y / x)) / (x / y) = L(y / x,x / y,y / x)
    ]]></literal>
    <justification jstring="[para(1365(a,1),472(a,1,1,2))].">
      <j1 rule="para" parents="1365 472"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(257,a,104,a(flip),b,1367,a),flip(a)].">
      <j1 rule="hyper" parents="257 104 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1369(a,1),870(a,2,1,2))].">
      <j1 rule="para" parents="1369 870"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = ((x \ y) * T(x,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(1366(a,1),870(a,2,1,2))].">
      <j1 rule="para" parents="1366 870"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      T(L(x / y,y / x,x / y),y) = ((y / x) * (y \ x)) / (y / x)
    ]]></literal>
    <justification jstring="[para(1368(a,1),493(a,1,1))].">
      <j1 rule="para" parents="1368 493"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      ((x / y) * (x \ y)) / (x / y) = L(x \ y,x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(580,a,1372,a),flip(a)].">
      <j1 rule="hyper" parents="580 1372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(601(a,1),1259(a,1,1))].">
      <j1 rule="para" parents="601 1259"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,216,a(flip),b,1310,a),flip(a)].">
      <j1 rule="hyper" parents="257 216 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(1376(a,1),747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1376 747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1140,a(flip),b,1378,a)].">
      <j1 rule="hyper" parents="63 1140 1378"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1379(a,1,1,2))].">
      <j1 rule="para" parents="9 1379"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1380(a,2,2))].">
      <j1 rule="para" parents="9 1380"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,1381,a)].">
      <j1 rule="hyper" parents="125 1381"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(187(a,2),1382(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="187 1382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(458,a,1383,a)].">
      <j1 rule="hyper" parents="458 1383"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * 1,y)) * z
    ]]></literal>
    <justification jstring="[para(73(a,1),1339(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="73 1339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8(a,1),1385(a,2,1,2,1))].">
      <j1 rule="para" parents="8 1385"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,10,a(flip),b,1386,a),flip(a)].">
      <j1 rule="hyper" parents="110 10 1386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1347(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      x \ (y * (((y / x) * (y \ x)) / (y / x))) = (x \ y) * (((x \ y) \ (y / x)) / (y / x))
    ]]></literal>
    <justification jstring="[para(778(a,1),1389(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="778 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(257,a,134,a(flip),b,1370,a),flip(a)].">
      <j1 rule="hyper" parents="257 134 1370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,73,a(flip),b,1391,a),flip(a)].">
      <j1 rule="hyper" parents="257 73 1391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1021,a(flip),b,663,a)].">
      <j1 rule="hyper" parents="63 1021 663"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1395(a,1),493(a,1,1))].">
      <j1 rule="para" parents="1395 493"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(580,a,1397,a),flip(a)].">
      <j1 rule="hyper" parents="580 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1398(a,1),1199(a,1,2))].">
      <j1 rule="para" parents="1398 1199"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ (x \ y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(293(a,1),753(a,1,2,2))].">
      <j1 rule="para" parents="293 753"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      (x \ y) * (((y \ x) \ 1) \ 1) = ((y \ x) \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,1400,a)].">
      <j1 rule="hyper" parents="125 1400"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (((y \ x) * (x \ y)) / (y \ x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1401(a,1),643(a,1,2,1))].">
      <j1 rule="para" parents="1401 643"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((y \ x) / ((x \ y) \ 1)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(1401(a,1),1196(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1401 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,333,a(flip),b,963,a),flip(a)].">
      <j1 rule="hyper" parents="257 333 963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)) = (x * (y * T(y \ 1,x))) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1404(a,1),880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1404 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = (1 / y) * (y * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[para(1404(a,1),938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1404 938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ (a(x,y,z) * (u * (w * v5))) = L(v5,w,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(331(a,1),562(a,1,2))].">
      <j1 rule="para" parents="331 562"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      R((x / (y * x)) \ 1,R(1 / y,y,x),y * x) = T(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),629(a,2,1))].">
      <j1 rule="para" parents="11 629"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),683(a,2,2))].">
      <j1 rule="para" parents="12 683"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = L((z * y) / x,u,w) * x
    ]]></literal>
    <justification jstring="[para(460(a,1),1409(a,1,1))].">
      <j1 rule="para" parents="460 1409"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(257,a,460,a(flip),b,1410,a),flip(a)].">
      <j1 rule="hyper" parents="257 460 1410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) * (1 / x) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(150(a,1),695(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="150 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      (1 / x) * L(T((1 / x) \ 1,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(704,a,1412,a)].">
      <j1 rule="hyper" parents="704 1412"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),1413(a,1,2,1,1))].">
      <j1 rule="para" parents="79 1413"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      (((x / y) * (1 / (x / y))) * y) / x = ((x / y) * (y / x)) / (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),703(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      (K(x / y,(x / y) \ 1) * y) / x = ((x / y) * (y / x)) / (x / y)
    ]]></literal>
    <justification jstring="[para(1060(a,2),1415(a,1,1,1))].">
      <j1 rule="para" parents="1060 1415"/>
    </justification>
  </clause>

  <clause id="1417">
    <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(102(a,1),860(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="102 860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(203,a,1215,a(flip),b,1417,a),flip(a)].">
      <j1 rule="hyper" parents="203 1215 1417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(482,a,1418,a),flip(a)].">
      <j1 rule="hyper" parents="482 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(651(a,1),1419(a,2,1,2))].">
      <j1 rule="para" parents="651 1419"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1022(a,1),1420(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1022 1420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,1318,a(flip),b,1421,a),flip(a)].">
      <j1 rule="hyper" parents="35 1318 1421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1422(a,1),104(a,1,1))].">
      <j1 rule="para" parents="1422 104"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1332,a(flip),b,1423,a),flip(a)].">
      <j1 rule="hyper" parents="63 1332 1423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1424(a,1),1388(a,1,2,2))].">
      <j1 rule="para" parents="1424 1388"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(118,a,1426,a),flip(a)].">
      <j1 rule="hyper" parents="118 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      x \ ((y * x) * T((y * x) \ z,u)) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),997(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(609(a,1),1428(a,1,2))].">
      <j1 rule="para" parents="609 1428"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y)
    ]]></literal>
    <justification jstring="[hyper(1125,a,1429,a),flip(a)].">
      <j1 rule="hyper" parents="1125 1429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1430(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(195(a,1),1431(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="195 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <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(203,a,1191,a,b,1137,a(flip))].">
      <j1 rule="hyper" parents="203 1191 1137"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(203,a,1238,a(flip),b,1137,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 1238 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <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(195(a,1),1433(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="195 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(176(a,1),1435(a,1,2,1,2))].">
      <j1 rule="para" parents="176 1435"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(187(a,1),1436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="187 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(526(a,1),1436(a,2,1,2))].">
      <j1 rule="para" parents="526 1436"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(658(a,1),1438(a,2,2,1))].">
      <j1 rule="para" parents="658 1438"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(727(a,1),1439(a,1,2))].">
      <j1 rule="para" parents="727 1439"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(174(a,1),1442(a,2,1,2))].">
      <j1 rule="para" parents="174 1442"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1399(a,1),1441(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1399 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1284(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(104(a,1),1445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(104(a,1),1446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="104 1446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      R((x * y) / x,z,u) \ (x \ (x * y)) = y * (R((x * y) / x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),1447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),1448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = y / y
    ]]></literal>
    <justification jstring="[para(191(a,1),1371(a,2,1))].">
      <j1 rule="para" parents="191 1371"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,73,a(flip),b,1450,a),flip(a)].">
      <j1 rule="hyper" parents="257 73 1450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(1451(a,1),747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1451 747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ x = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1150,a(flip),b,1453,a)].">
      <j1 rule="hyper" parents="63 1150 1453"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (((x / y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1454(a,1,1,2,1))].">
      <j1 rule="para" parents="79 1454"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1455(a,2,2,1))].">
      <j1 rule="para" parents="79 1455"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      L((x / y) \ 1,x / y,y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[hyper(309,a,1456,a)].">
      <j1 rule="hyper" parents="309 1456"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[para(1456(a,1),1393(a,1,1))].">
      <j1 rule="para" parents="1456 1393"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1458(a,1,1,2))].">
      <j1 rule="para" parents="11 1458"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1459(a,1,2,2))].">
      <j1 rule="para" parents="11 1459"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(56,a,1460,a)].">
      <j1 rule="hyper" parents="56 1460"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1162,a,1461,a)].">
      <j1 rule="hyper" parents="1162 1461"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(189(a,2),1462(a,1,3))].">
      <j1 rule="para" parents="189 1462"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(172,a,1463,a(flip),b,187,a(flip))].">
      <j1 rule="hyper" parents="172 1463 187"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y
    ]]></literal>
    <justification jstring="[para(1457(a,1),1411(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1457 1411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(803,a,1464,a)].">
      <j1 rule="hyper" parents="803 1464"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(189(a,1),1466(a,1,2))].">
      <j1 rule="para" parents="189 1466"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y / x) = x / y
    ]]></literal>
    <justification jstring="[para(299(a,1),1466(a,1,2))].">
      <j1 rule="para" parents="299 1466"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1467(a,1),1049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1467 1049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a(flip),b,1469,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 1469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(1469(a,1),872(a,2,1))].">
      <j1 rule="para" parents="1469 872"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),1470(a,1,2,2))].">
      <j1 rule="para" parents="12 1470"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      ((x / y) * (y / x)) / (x / y) = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(227,a,1468,a)].">
      <j1 rule="hyper" parents="227 1468"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(114,a,1472,a(flip),b,340,a)].">
      <j1 rule="hyper" parents="114 1472 340"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(841,a,1474,a)].">
      <j1 rule="hyper" parents="841 1474"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1060(a,2),1465(a,2,1))].">
      <j1 rule="para" parents="1060 1465"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1477(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1477"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,v5)) = L(x,y,a(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(567,a,1407,a)].">
      <j1 rule="hyper" parents="567 1407"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(212,a,1479,a),flip(a)].">
      <j1 rule="hyper" parents="212 1479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(593,a,644,a),flip(a)].">
      <j1 rule="hyper" parents="593 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1482(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(587(a,1),1482(a,2,1))].">
      <j1 rule="para" parents="587 1482"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(1483(a,1),261(a,1))].">
      <j1 rule="para" parents="1483 261"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(887(a,1),1485(a,1))].">
      <j1 rule="para" parents="887 1485"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(261,a,1484,a),flip(a)].">
      <j1 rule="hyper" parents="261 1484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(203,a,1484,a(flip),b,1136,a),flip(a)].">
      <j1 rule="hyper" parents="203 1484 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1484(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 1484"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(706,a,1489,a),flip(a)].">
      <j1 rule="hyper" parents="706 1489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(203,a,1489,a(flip),b,1350,a(flip))].">
      <j1 rule="hyper" parents="203 1489 1350"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1196,a(flip),b,1491,a)].">
      <j1 rule="hyper" parents="257 1196 1491"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1198(a,1),1491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1198 1491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1104(a,1),1494(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1104 1494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1495(a,2,2,1))].">
      <j1 rule="para" parents="76 1495"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1496(a,1,1,2))].">
      <j1 rule="para" parents="11 1496"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1497(a,1,2,1))].">
      <j1 rule="para" parents="11 1497"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1498(a,2,2))].">
      <j1 rule="para" parents="11 1498"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,1499,a)].">
      <j1 rule="hyper" parents="54 1499"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,1499,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 1499 22"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1499(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1499 232"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1500(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1500 232"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,344,a(flip),b,1501,a)].">
      <j1 rule="hyper" parents="111 344 1501"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(937(a,1),1490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="937 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1493(a,2,1,2,1))].">
      <j1 rule="para" parents="10 1493"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(338(a,2),1493(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="338 1493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(719(a,1),1510(a,1,2,1))].">
      <j1 rule="para" parents="719 1510"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(34,a,1443,a,b,1512,a)].">
      <j1 rule="hyper" parents="34 1443 1512"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1060(a,2),1512(a,2,1))].">
      <j1 rule="para" parents="1060 1512"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1513(a,1),731(a,1,1))].">
      <j1 rule="para" parents="1513 731"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1514(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="1514 1304"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(1516(a,1),43(a,1))].">
      <j1 rule="para" parents="1516 43"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(728,a,1515,a),flip(a)].">
      <j1 rule="hyper" parents="728 1515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      T(x,y) * ((z * ((y \ (x * y)) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1488(a,1,1))].">
      <j1 rule="para" parents="22 1488"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1519(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 1519"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(937(a,1),1509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="937 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(123,a,1521,a)].">
      <j1 rule="hyper" parents="123 1521"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1522(a,1),592(a,1,1))].">
      <j1 rule="para" parents="1522 592"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(444,a,1523,a),flip(a)].">
      <j1 rule="hyper" parents="444 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1524(a,1),493(a,1,1))].">
      <j1 rule="para" parents="1524 493"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(306,a,1525,a),flip(a)].">
      <j1 rule="hyper" parents="306 1525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(257,a,16,a,b,1526,a)].">
      <j1 rule="hyper" parents="257 16 1526"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),1527(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(792(a,1),1528(a,1,1))].">
      <j1 rule="para" parents="792 1528"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(114,a,1061,a(flip),b,1531,a)].">
      <j1 rule="hyper" parents="114 1061 1531"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ u))) / z)) = w
    ]]></literal>
    <justification jstring="[para(10(a,1),833(a,1,2,1,2,2))].">
      <j1 rule="para" parents="10 833"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      T(T(x,y) * T(T(x,y) \ x,x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(960(a,1),980(a,1,1))].">
      <j1 rule="para" parents="960 980"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      T(L(x,T(x,y) \ x,T(x,y)),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(739(a,1),1541(a,1,1))].">
      <j1 rule="para" parents="739 1541"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      T(L(x,T(x,y) \ x,T(x,y)),x * (T(x,y) \ x)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(978(a,1),1542(a,1,2))].">
      <j1 rule="para" parents="978 1542"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      L(T(x,x * (T(x,y) \ x)),T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,1543,a)].">
      <j1 rule="hyper" parents="63 25 1543"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(976(a,1),1544(a,1,1))].">
      <j1 rule="para" parents="976 1544"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,739,a,b,1545,a)].">
      <j1 rule="hyper" parents="63 739 1545"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1545(a,1),1334(a,1,2))].">
      <j1 rule="para" parents="1545 1334"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,981,a(flip),b,1546,a),flip(a)].">
      <j1 rule="hyper" parents="63 981 1546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = (a(x,y,z) * ((u * w) * v5)) / (w * v5)
    ]]></literal>
    <justification jstring="[para(331(a,1),1134(a,2,1))].">
      <j1 rule="para" parents="331 1134"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,856,a(flip),b,1172,a)].">
      <j1 rule="hyper" parents="63 856 1172"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(38,a,321,a,b,1172,a)].">
      <j1 rule="hyper" parents="38 321 1172"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ (u * y)))) / z)) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(1540,a,1484,a)].">
      <j1 rule="hyper" parents="1540 1484"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[hyper(1540,a,xx),flip(a)].">
      <j1 rule="hyper" parents="1540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) * y = x * (y * ((x \ (z * y)) / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),1553(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * z = (x * y) * (z * (L(y \ z,y,x) / z))
    ]]></literal>
    <justification jstring="[para(92(a,2),1555(a,2,2,2,1))].">
      <j1 rule="para" parents="92 1555"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(1485,a,1554,a),flip(a)].">
      <j1 rule="hyper" parents="1485 1554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x))
    ]]></literal>
    <justification jstring="[para(279(a,2),1557(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="279 1557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1489(a,1),1557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1489 1557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = a(x,y,z) * (((u * w) * v5) / (w * v5))
    ]]></literal>
    <justification jstring="[hyper(257,a,504,a(flip),b,1550,a),flip(a)].">
      <j1 rule="hyper" parents="257 504 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(513(a,1),1551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="513 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      R(a(x,y,z) * u,L(w,u,a(x,y,z)),v5) = a(x,y,z) * R(u,w,v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),1560(a,2,2))].">
      <j1 rule="para" parents="20 1560"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      R(a(x,y,z) * u,w,v5) = a(x,y,z) * R(u,w,v5)
    ]]></literal>
    <justification jstring="[para(128(a,1),1562(a,1,2))].">
      <j1 rule="para" parents="128 1562"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      (a(x,y,z) * (u * (w * v5))) \ ((a(x,y,z) * (u * w)) * v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(331(a,1),561(a,1,2,1))].">
      <j1 rule="para" parents="331 561"/>
    </justification>
  </clause>

  <clause id="1565">
    <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(220(a,2),850(a,1,2,1,1))].">
      <j1 rule="para" parents="220 850"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x
    ]]></literal>
    <justification jstring="[para(22(a,2),999(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * ((1 / x) * T((1 / x) \ (x \ y),z))
    ]]></literal>
    <justification jstring="[para(1060(a,2),1064(a,1,2,1,1))].">
      <j1 rule="para" parents="1060 1064"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (y * L(y \ x,y / x,x / y))
    ]]></literal>
    <justification jstring="[para(1373(a,1),1390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1373 1390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = x \ (K(y / x,(y / x) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1478(a,1),1572(a,2,2))].">
      <j1 rule="para" parents="1478 1572"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(1404(a,1),1405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1404 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,9,a(flip),b,1574,a),flip(a)].">
      <j1 rule="hyper" parents="257 9 1574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(649(a,1),1575(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="649 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,649,a(flip),b,1577,a),flip(a)].">
      <j1 rule="hyper" parents="63 649 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = L(x * T(x \ 1,y),y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(257,a,288,a(flip),b,1406,a),flip(a)].">
      <j1 rule="hyper" parents="257 288 1406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(1404(a,1),1579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1404 1579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(668(a,2),1580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="668 1580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(668(a,2),1581(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="668 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1487(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 1487"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(123,a,1583,a)].">
      <j1 rule="hyper" parents="123 1583"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1584(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      (a(x,y,z) * (u * (w * v5))) \ (a(x,y,z) * ((u * w) * v5)) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(331(a,1),1564(a,1,2))].">
      <j1 rule="para" parents="331 1564"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(257,a,1126,a(flip),b,1565,a),flip(a)].">
      <j1 rule="hyper" parents="257 1126 1565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(652(a,1),1567(a,2,2))].">
      <j1 rule="para" parents="652 1567"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(147(a,1),1588(a,2,2,1,1))].">
      <j1 rule="para" parents="147 1588"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(114,a,1589,a(flip),b,666,a)].">
      <j1 rule="hyper" parents="114 1589 666"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1508(a,1),1590(a,1,2))].">
      <j1 rule="para" parents="1508 1590"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1508(a,1),1591(a,2,1,2))].">
      <j1 rule="para" parents="1508 1591"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1052(a,1),1592(a,2,1))].">
      <j1 rule="para" parents="1052 1592"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(u,w,v5)) = a(a(u,w,v5) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(568,a,1586,a)].">
      <j1 rule="hyper" parents="568 1586"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(212,a,1594,a),flip(a)].">
      <j1 rule="hyper" parents="212 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,326,a(flip),b,511,a),flip(a)].">
      <j1 rule="hyper" parents="257 326 511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(709,a,1597,a)].">
      <j1 rule="hyper" parents="709 1597"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      (T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,1598,a),flip(a)].">
      <j1 rule="hyper" parents="63 192 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(709,a,823,a),flip(a)].">
      <j1 rule="hyper" parents="709 823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(514(a,1),1600(a,2,2))].">
      <j1 rule="para" parents="514 1600"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(361,a,1601,a)].">
      <j1 rule="hyper" parents="361 1601"/>
    </justification>
  </clause>

  <clause id="1603">
    <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(257,a,810,a(flip),b,1602,a)].">
      <j1 rule="hyper" parents="257 810 1602"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(73(a,1),1602(a,2,1,2))].">
      <j1 rule="para" parents="73 1602"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(649(a,1),1602(a,1,1))].">
      <j1 rule="para" parents="649 1602"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      L(x \ T(x,y * L(x \ 1,z,u)),z,u) = K((y * L(x \ 1,z,u)) \ y,y * L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),1605(a,2,1,2))].">
      <j1 rule="para" parents="11 1605"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(941(a,1),871(a,2,1))].">
      <j1 rule="para" parents="941 871"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1002(a,1),1607(a,2,1,1))].">
      <j1 rule="para" parents="1002 1607"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,20,a,b,1608,a)].">
      <j1 rule="hyper" parents="257 20 1608"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      R(x,y,z) * T(R(x,y,z) \ 1,u) = R(x * T(x \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,810,a(flip),b,1609,a)].">
      <j1 rule="hyper" parents="257 810 1609"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) = K(R(x,y,z) \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(73(a,1),1609(a,2,1,2))].">
      <j1 rule="para" parents="73 1609"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,1611,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="114 1611 20"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      (L(x,y,z) * (1 / x)) / L(x,y,z) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1247,a(flip),b,1169,a)].">
      <j1 rule="hyper" parents="63 1247 1169"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      L(1 / x,L(x,y,z),1 / x) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(1615(a,1),642(a,1,1))].">
      <j1 rule="para" parents="1615 642"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = x * L(x \ 1,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(1617,a,460,a)].">
      <j1 rule="hyper" parents="1617 460"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1201,a(flip),b,1618,a),flip(a)].">
      <j1 rule="hyper" parents="63 1201 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,668,a,b,678,a),flip(a)].">
      <j1 rule="hyper" parents="257 668 678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(1620(a,1),306(a,1,1))].">
      <j1 rule="para" parents="1620 306"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = (y \ x) \ L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(604(a,1),848(a,1,2)),flip(a)].">
      <j1 rule="para" parents="604 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(220(a,2),1153(a,1,2,1,1))].">
      <j1 rule="para" parents="220 1153"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(257,a,1258,a(flip),b,1623,a),flip(a)].">
      <j1 rule="hyper" parents="257 1258 1623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(691(a,1),1624(a,2,1))].">
      <j1 rule="para" parents="691 1624"/>
    </justification>
  </clause>

  <clause id="1626">
    <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(257,a,324,a(flip),b,574,a),flip(a)].">
      <j1 rule="hyper" parents="257 324 574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1627">
    <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(843,a,1626,a)].">
      <j1 rule="hyper" parents="843 1626"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,y \ 1,y)) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(930(a,1),1627(a,2,1,1))].">
      <j1 rule="para" parents="930 1627"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      L(((1 / x) \ (x \ 1)) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),635(a,1,1,1,2))].">
      <j1 rule="para" parents="7 635"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      L(K(x \ 1,x) \ y,a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(781(a,1),1629(a,1,1,1))].">
      <j1 rule="para" parents="781 1629"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      L(K(x \ 1,x) \ ((y * (x \ 1)) * x),a(1 / x,x,x \ 1),1 / x) = (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(839(a,1),1630(a,2,2))].">
      <j1 rule="para" parents="839 1630"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(x \ x,y,z)
    ]]></literal>
    <justification jstring="[para(1243(a,1),1606(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1243 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(66(a,1),1632(a,2,1))].">
      <j1 rule="para" parents="66 1632"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,365,a(flip),b,1633,a),flip(a)].">
      <j1 rule="hyper" parents="257 365 1633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x * 1
    ]]></literal>
    <justification jstring="[hyper(115,a,1634,a(flip),b,86,a),flip(a)].">
      <j1 rule="hyper" parents="115 1634 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,8,a(flip),b,1637,a),flip(a)].">
      <j1 rule="hyper" parents="257 8 1637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      x * (y * L(y \ 1,z,u)) != y
    ]]></literal>
    <literal><![CDATA[
      (y * L(y \ 1,z,u)) \ y = x
    ]]></literal>
    <justification jstring="[para(1638(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1638 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) = ((z \ 1) * y) \ ((z \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[para(1073(a,1),1085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1073 1085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(1640(a,2),362(a,1))].">
      <j1 rule="para" parents="1640 362"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(783(a,1),1641(a,1))].">
      <j1 rule="para" parents="783 1641"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1088(a,2),1642(a,1))].">
      <j1 rule="para" parents="1088 1642"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(582(a,1),1402(a,2,1))].">
      <j1 rule="para" parents="582 1402"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (x \ y) \ L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1622,a(flip),b,1645,a),flip(a)].">
      <j1 rule="hyper" parents="257 1622 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((x \ y) * (y \ x)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(1175(a,1),1403(a,2,2,1))].">
      <j1 rule="para" parents="1175 1403"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1647(a,2,2))].">
      <j1 rule="para" parents="11 1647"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,1648,a(flip),b,1646,a(flip))].">
      <j1 rule="hyper" parents="115 1648 1646"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(740(a,1),1511(a,2,2,1))].">
      <j1 rule="para" parents="740 1511"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = T(K(T(x,z),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1202(a,1),1651(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1202 1651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1352,a(flip),b,1652,a)].">
      <j1 rule="hyper" parents="63 1352 1652"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(1653(a,1),1078(a,1))].">
      <j1 rule="para" parents="1653 1078"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1654,a,1444,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1654 1444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1060,a(flip),b,1655,a),flip(a)].">
      <j1 rule="hyper" parents="34 1060 1655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      (T(T(x,x \ 1),y) / T(x,x \ 1)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(223(a,1),1656(a,1,2))].">
      <j1 rule="para" parents="223 1656"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(995(a,1),1657(a,1,1))].">
      <j1 rule="para" parents="995 1657"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1424,a(flip),b,1658,a),flip(a)].">
      <j1 rule="hyper" parents="63 1424 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      1 / T(x \ 1,y) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(467(a,1),1659(a,1,2,1))].">
      <j1 rule="para" parents="467 1659"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(165,a,1660,a)].">
      <j1 rule="hyper" parents="165 1660"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1660(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),1661(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(173,a,1662,a)].">
      <j1 rule="hyper" parents="173 1662"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,1663,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 1663 22"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1052,a,b,1664,a)].">
      <j1 rule="hyper" parents="63 1052 1664"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(104(a,1),1664(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="104 1664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(516,a,1665,a)].">
      <j1 rule="hyper" parents="516 1665"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(104(a,1),1665(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 1665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(115,a,1667,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 1667 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(841,a,1669,a)].">
      <j1 rule="hyper" parents="841 1669"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),1673(a,2,1,1))].">
      <j1 rule="para" parents="9 1673"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1475,a(flip),b,1674,a)].">
      <j1 rule="hyper" parents="63 1475 1674"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1675(a,1,2,2))].">
      <j1 rule="para" parents="10 1675"/>
    </justification>
  </clause>

  <clause id="1678">
    <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(514(a,1),1122(a,1,1)),flip(a)].">
      <j1 rule="para" parents="514 1122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <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(667(a,1),1678(a,2,1,2))].">
      <j1 rule="para" parents="667 1678"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      (x * (y * z)) * R((x * (y * z)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(90(a,1),861(a,1,2,1,1))].">
      <j1 rule="para" parents="90 861"/>
    </justification>
  </clause>

  <clause id="1683">
    <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(843,a,1682,a),flip(a)].">
      <j1 rule="hyper" parents="843 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1684">
    <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(687(a,1),1683(a,2,2))].">
      <j1 rule="para" parents="687 1683"/>
    </justification>
  </clause>

  <clause id="1685">
    <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(361,a,1684,a),flip(a)].">
      <j1 rule="hyper" parents="361 1684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1686">
    <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,752,a(flip),b,1685,a),flip(a)].">
      <j1 rule="hyper" parents="63 752 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1687">
    <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(1248(a,1),1686(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1248 1686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <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(257,a,1604,a(flip),b,1687,a),flip(a)].">
      <j1 rule="hyper" parents="257 1604 1687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,220,a(flip),b,1688,a),flip(a)].">
      <j1 rule="hyper" parents="35 220 1688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1689(a,1,1))].">
      <j1 rule="para" parents="79 1689"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(696(a,1),1690(a,1,2))].">
      <j1 rule="para" parents="696 1690"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(124,a,1691,a)].">
      <j1 rule="hyper" parents="124 1691"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(1639,a,1692,a)].">
      <j1 rule="hyper" parents="1639 1692"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1164(a,1),1693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1164 1693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      (x * (1 / y)) * (z * R(z \ L((1 / y) \ z,1 / y,x),u,w)) = ((x * (1 / y)) * R(L(y,1 / y,x),u,w)) * z
    ]]></literal>
    <justification jstring="[para(92(a,2),1257(a,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="92 1257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(257,a,1557,a(flip),b,1558,a),flip(a)].">
      <j1 rule="hyper" parents="257 1557 1558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      (x * (y * z)) * ((u * ((x * (y * z)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u))
    ]]></literal>
    <justification jstring="[para(90(a,1),1157(a,1,2,1,2,1))].">
      <j1 rule="para" parents="90 1157"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * ((y * z) * ((u * ((y * z) \ y)) / u))
    ]]></literal>
    <justification jstring="[hyper(833,a,1700,a),flip(a)].">
      <j1 rule="hyper" parents="833 1700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * (y * (z * ((u * (z \ 1)) / u)))
    ]]></literal>
    <justification jstring="[para(705(a,1),1701(a,2,2))].">
      <j1 rule="para" parents="705 1701"/>
    </justification>
  </clause>

  <clause id="1703">
    <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(361,a,1702,a),flip(a)].">
      <j1 rule="hyper" parents="361 1702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = L(x,y,z) * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1703(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,1060,a,b,1704,a),flip(a)].">
      <j1 rule="hyper" parents="257 1060 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      L(K(L(x,y,z),1 / x),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1201(a,1),1705(a,1,1))].">
      <j1 rule="para" parents="1201 1705"/>
    </justification>
  </clause>

  <clause id="1714">
    <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),1194(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1194"/>
    </justification>
  </clause>

  <clause id="1715">
    <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(684(a,1),1714(a,1,2))].">
      <j1 rule="para" parents="684 1714"/>
    </justification>
  </clause>

  <clause id="1716">
    <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(601(a,1),1715(a,1,2,2))].">
      <j1 rule="para" parents="601 1715"/>
    </justification>
  </clause>

  <clause id="1717">
    <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(362,a,1716,a),flip(a)].">
      <j1 rule="hyper" parents="362 1716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ ((1 / x) * 1)) = L(x * L(x \ 1,L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1168(a,1),1717(a,1,2))].">
      <j1 rule="para" parents="1168 1717"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      L(x * L(x \ 1,L(x,y,z),1 / x),y,z) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(8(a,1),1719(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 1719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = L(K(L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1619(a,1),1723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1619 1723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,1706,a(flip),b,1724,a),flip(a)].">
      <j1 rule="hyper" parents="257 1706 1724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,1060,a(flip),b,1725,a),flip(a)].">
      <j1 rule="hyper" parents="34 1060 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(172,a,1726,a(flip),b,1694,a),flip(a)].">
      <j1 rule="hyper" parents="172 1726 1694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),1727(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(187(a,1),1728(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(293(a,1),1728(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="293 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[para(76(a,1),1730(a,1,1))].">
      <j1 rule="para" parents="76 1730"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1649,a,b,1731,a)].">
      <j1 rule="hyper" parents="63 1649 1731"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,582,a,b,1731,a)].">
      <j1 rule="hyper" parents="63 582 1731"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1052,a,b,1733,a)].">
      <j1 rule="hyper" parents="34 1052 1733"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(257,a,675,a(flip),b,1735,a),flip(a)].">
      <j1 rule="hyper" parents="257 675 1735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(65(a,1),1735(a,2,1))].">
      <j1 rule="para" parents="65 1735"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1737(a,1),783(a,1,3))].">
      <j1 rule="para" parents="1737 783"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(832,a,1738,a),flip(a)].">
      <j1 rule="hyper" parents="832 1738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,92,a(flip),b,1738,a)].">
      <j1 rule="hyper" parents="63 92 1738"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[para(1734(a,1),194(a,1,1))].">
      <j1 rule="para" parents="1734 194"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(813(a,2),1742(a,1,1,2,2))].">
      <j1 rule="para" parents="813 1742"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1742(a,1),1662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1742 1662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(165,a,1744,a),flip(a)].">
      <j1 rule="hyper" parents="165 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1745(a,1,2))].">
      <j1 rule="para" parents="79 1745"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(813(a,2),1745(a,1,1))].">
      <j1 rule="para" parents="813 1745"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(1745(a,2),1326(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1745 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(388,a,1739,a)].">
      <j1 rule="hyper" parents="388 1739"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1059(a,1),1739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1059 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1065(a,1),1739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1065 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[para(1533(a,1),1739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1533 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = u
    ]]></literal>
    <justification jstring="[para(1749(a,1),231(a,1,1))].">
      <j1 rule="para" parents="1749 231"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1253,a(flip),b,1750,a)].">
      <j1 rule="hyper" parents="63 1253 1750"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,1750,a)].">
      <j1 rule="hyper" parents="63 192 1750"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x
    ]]></literal>
    <justification jstring="[hyper(112,a,1750,a(flip),b,1253,a(flip))].">
      <j1 rule="hyper" parents="112 1750 1253"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(219(a,1),1750(a,1,2))].">
      <j1 rule="para" parents="219 1750"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(268,a,1751,a),flip(a)].">
      <j1 rule="hyper" parents="268 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(34,a,1253,a,b,1752,a),flip(a)].">
      <j1 rule="hyper" parents="34 1253 1752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      (1 / (1 / x)) * z = y
    ]]></literal>
    <justification jstring="[para(1752(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1752 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(246(a,1),1752(a,1,2))].">
      <j1 rule="para" parents="246 1752"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(111,a,323,a(flip),b,1754,a),flip(a)].">
      <j1 rule="hyper" parents="111 323 1754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,32,a,b,1754,a(flip))].">
      <j1 rule="hyper" parents="35 32 1754"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1751(a,1),1754(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1751 1754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      x * K(x,x \ 1) = R(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,930,a,b,1763,a),flip(a)].">
      <j1 rule="hyper" parents="257 930 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a(flip),b,1763,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = R(x,K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1763(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1763 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,1668,a,b,1766,a)].">
      <j1 rule="hyper" parents="257 1668 1766"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x)
    ]]></literal>
    <justification jstring="[para(1766(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1766 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1517,a,1768,a)].">
      <j1 rule="hyper" parents="1517 1768"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(312,a,1770,a)].">
      <j1 rule="hyper" parents="312 1770"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,1770,a)].">
      <j1 rule="hyper" parents="54 1770"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(115,a,1770,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 1770 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1772(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1772 232"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1067(a,1),1772(a,1,2))].">
      <j1 rule="para" parents="1067 1772"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,1776,a)].">
      <j1 rule="hyper" parents="54 1776"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,1776,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 1776 22"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(1776(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1776 232"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1323,a,b,1777,a)].">
      <j1 rule="hyper" parents="63 1323 1777"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(220(a,1),1777(a,1,1))].">
      <j1 rule="para" parents="220 1777"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(1777(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1777 232"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1777(a,1),459(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1777 459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1782(a,1),1329(a,1,1))].">
      <j1 rule="para" parents="1782 1329"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ (y / x)) / (y / x)) = K(y / x,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1573,a,b,1771,a)].">
      <j1 rule="hyper" parents="63 1573 1771"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) \ (x * y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1752(a,1),1771(a,1,2))].">
      <j1 rule="para" parents="1752 1771"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1751,a(flip),b,1773,a),flip(a)].">
      <j1 rule="hyper" parents="63 1751 1773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1253,a(flip),b,1773,a),flip(a)].">
      <j1 rule="hyper" parents="63 1253 1773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1773(a,2),379(a,1,2))].">
      <j1 rule="para" parents="1773 379"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(1773(a,1),1739(a,1,1))].">
      <j1 rule="para" parents="1773 1739"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) * x = y * T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(257,a,771,a,b,1778,a),flip(a)].">
      <j1 rule="hyper" parents="257 771 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      R(x / y,y,K(z \ 1,z)) = (x * K(z \ 1,z)) / (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(172,a,1778,a,b,380,a),flip(a)].">
      <j1 rule="hyper" parents="172 1778 380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,392,a(flip),b,1778,a)].">
      <j1 rule="hyper" parents="111 392 1778"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      R(1 / x,y,z) * K(x \ 1,x) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1308,a(flip),b,1778,a),flip(a)].">
      <j1 rule="hyper" parents="63 1308 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1073,a(flip),b,1778,a),flip(a)].">
      <j1 rule="hyper" parents="63 1073 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      x / ((y \ x) * K(y \ 1,y)) = (y \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(172,a,1778,a(flip),b,925,a(flip))].">
      <j1 rule="hyper" parents="172 1778 925"/>
    </justification>
  </clause>

  <clause id="1800">
    <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(1778(a,2),463(a,1,1))].">
      <j1 rule="para" parents="1778 463"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,K(x \ 1,x)) = u
    ]]></literal>
    <justification jstring="[para(1778(a,1),523(a,1,2))].">
      <j1 rule="para" parents="1778 523"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(1778(a,1),785(a,1,1))].">
      <j1 rule="para" parents="1778 785"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(1778(a,1),786(a,1,1))].">
      <j1 rule="para" parents="1778 786"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((y * (x \ 1)) * x) = a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1778(a,2),278(a,1,1))].">
      <j1 rule="para" parents="1778 278"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1781(a,1),815(a,1,1))].">
      <j1 rule="para" parents="1781 815"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,1082,a(flip),b,1758,a),flip(a)].">
      <j1 rule="hyper" parents="63 1082 1758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,777,a(flip),b,1758,a),flip(a)].">
      <j1 rule="hyper" parents="63 777 1758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,1082,a(flip),b,1758,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 1082 1758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(268,a,1807,a),flip(a)].">
      <j1 rule="hyper" parents="268 1807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,1773,a,b,1807,a),flip(a)].">
      <j1 rule="hyper" parents="34 1773 1807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(786(a,2),1807(a,1,2))].">
      <j1 rule="para" parents="786 1807"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1307(a,2),1807(a,1,2))].">
      <j1 rule="para" parents="1307 1807"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1308(a,1),1807(a,1,2))].">
      <j1 rule="para" parents="1308 1807"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[para(1778(a,1),1807(a,1,2))].">
      <j1 rule="para" parents="1778 1807"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,1778,a(flip),b,1809,a)].">
      <j1 rule="hyper" parents="63 1778 1809"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      x / K(y \ 1,y) = K(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(112,a,1809,a(flip),b,1778,a(flip))].">
      <j1 rule="hyper" parents="112 1809 1778"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(1809(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1809 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * (1 / x)) * y) = y
    ]]></literal>
    <justification jstring="[para(1060(a,1),1809(a,1,2,1))].">
      <j1 rule="para" parents="1060 1809"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(1811(a,1),1587(a,1,2,1))].">
      <j1 rule="para" parents="1811 1587"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x,x \ 1) * (y * x),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1811(a,1),1625(a,1,2,1))].">
      <j1 rule="para" parents="1811 1625"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1778,a(flip),b,1812,a)].">
      <j1 rule="hyper" parents="63 1778 1812"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      R(x \ 1,y,z) * K(x,x \ 1) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,1308,a,b,1812,a),flip(a)].">
      <j1 rule="hyper" parents="34 1308 1812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1812(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1812 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,1752,a,b,1818,a),flip(a)].">
      <j1 rule="hyper" parents="34 1752 1818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1818(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1818 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(1819(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1819 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      (x * (1 / x)) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(34,a,1307,a(flip),b,1822,a),flip(a)].">
      <j1 rule="hyper" parents="34 1307 1822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      ((x * (y \ 1)) * y) * K(y,y \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,392,a,b,1825,a),flip(a)].">
      <j1 rule="hyper" parents="35 392 1825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1807(a,1),1759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1807 1759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1787(a,1),181(a,1)),flip(b)].">
      <j1 rule="para" parents="1787 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,1807,a,b,1808,a)].">
      <j1 rule="hyper" parents="34 1807 1808"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(115,a,132,a(flip),b,1808,a(flip))].">
      <j1 rule="hyper" parents="115 132 1808"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      (x * (1 / x)) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1060(a,1),1808(a,1,1))].">
      <j1 rule="para" parents="1060 1808"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(1735(a,1),1829(a,1,2))].">
      <j1 rule="para" parents="1735 1829"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(924,a,1837,a),flip(a)].">
      <j1 rule="hyper" parents="924 1837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(434,a,1839,a),flip(a)].">
      <j1 rule="hyper" parents="434 1839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(115,a,1840,a(flip),b,317,a),flip(a)].">
      <j1 rule="hyper" parents="115 1840 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      (x \ 1) * ((x * (1 / x)) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1060(a,1),1840(a,1,2,1))].">
      <j1 rule="para" parents="1060 1840"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = (1 / (1 / x)) * T(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),1843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * z) = ((1 / (1 / x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(1752(a,1),1740(a,1,1))].">
      <j1 rule="para" parents="1752 1740"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1818(a,1),1740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1818 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1818(a,1),1740(a,1,2))].">
      <j1 rule="para" parents="1818 1740"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(115,a,1785,a(flip),b,1844,a)].">
      <j1 rule="hyper" parents="115 1785 1844"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[hyper(111,a,1773,a(flip),b,1791,a)].">
      <j1 rule="hyper" parents="111 1773 1791"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,y * K(z \ 1,z),x) = w
    ]]></literal>
    <justification jstring="[para(1803(a,1),362(a,1,2,2))].">
      <j1 rule="para" parents="1803 362"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * K(x,x \ 1) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1817(a,1),1789(a,2,2))].">
      <j1 rule="para" parents="1817 1789"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      (R(x \ 1,y,z) * (K(x,x \ 1) * u)) \ (R(1 / x,y,z) * u) = a(R(x \ 1,y,z),K(x,x \ 1),u)
    ]]></literal>
    <justification jstring="[para(1826(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1826 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1857(a,1),707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1857 707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1736(a,1),805(a,1,2))].">
      <j1 rule="para" parents="1736 805"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1809(a,1),1816(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1809 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      R((x * (1 / x)) * y,z,u) = (x * (1 / x)) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1822(a,1),1832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1822 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(111,a,1518,a(flip),b,1853,a(flip))].">
      <j1 rule="hyper" parents="111 1518 1853"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1427,a(flip),b,1868,a)].">
      <j1 rule="hyper" parents="63 1427 1868"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(104(a,1),1869(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="104 1869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(104(a,1),1870(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 1870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),1871(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,1773,a(flip),b,1866,a),flip(a)].">
      <j1 rule="hyper" parents="257 1773 1866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x \ 1) * R((x * (1 / x)) * y,z,u) = (1 / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1867(a,2),1846(a,1,2))].">
      <j1 rule="para" parents="1867 1846"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) != z
    ]]></literal>
    <literal><![CDATA[
      ((y * x) / y) \ x = z
    ]]></literal>
    <justification jstring="[para(1875(a,1),233(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1875 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      R(x * K(y \ 1,y),z,u) * K(y,y \ 1) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1818(a,1),1873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1818 1873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1833,a,b,1877,a),flip(a)].">
      <j1 rule="hyper" parents="35 1833 1877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(917(a,1),1878(a,2,1))].">
      <j1 rule="para" parents="917 1878"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (z * y) = z * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(1778(a,2),1784(a,2,2))].">
      <j1 rule="para" parents="1778 1784"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ ((x * (y \ 1)) * y)),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(566,a,1804,a)].">
      <j1 rule="hyper" parents="566 1804"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,x \ (x / y)) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),1842(a,1,2,1))].">
      <j1 rule="para" parents="79 1842"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ (x * R(1 / x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,1861,a)].">
      <j1 rule="hyper" parents="118 1861"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = (x \ 1) * R((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1841(a,1),1874(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1841 1874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1293,a(flip),b,1884,a)].">
      <j1 rule="hyper" parents="63 1293 1884"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1886(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      (K(x / y,y / x) * y) / x = ((x / y) * (y / x)) / (x / y)
    ]]></literal>
    <justification jstring="[para(1888(a,1),1416(a,1,1,1))].">
      <j1 rule="para" parents="1888 1416"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      T(x,K(y / z,z / y)) = x
    ]]></literal>
    <justification jstring="[para(1888(a,1),1772(a,1,2))].">
      <j1 rule="para" parents="1888 1772"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      K(x / y,y / x) * z = z * K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(115,a,1890,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 1890 22"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      K(x / y,y / x) * y = (1 / (1 / (y / x))) * x
    ]]></literal>
    <justification jstring="[hyper(114,a,1473,a(flip),b,1889,a),flip(a)].">
      <j1 rule="hyper" parents="114 1473 1889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      K(x / y,y / x) * y = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(257,a,1671,a(flip),b,1892,a),flip(a)].">
      <j1 rule="hyper" parents="257 1671 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      x \ (K(x / y,y / x) * y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(111,a,1892,a,b,1671,a(flip))].">
      <j1 rule="hyper" parents="111 1892 1671"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1077,a,b,1892,a)].">
      <j1 rule="hyper" parents="35 1077 1892"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[para(1895(a,1),868(a,1,1))].">
      <j1 rule="para" parents="1895 868"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      K(x / y,y / x) * (x / y) = T(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(1895(a,1),874(a,1,1))].">
      <j1 rule="para" parents="1895 874"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      K((x * y) / y,y / (x * y)) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1895(a,1),1471(a,1,1))].">
      <j1 rule="para" parents="1895 1471"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) * z = K(y / x,x / y) \ z
    ]]></literal>
    <justification jstring="[para(1895(a,1),1811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1895 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      K((x / y) / x,x / (x / y)) * x = (x / y) * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),1893(a,2,2,2,2))].">
      <j1 rule="para" parents="79 1893"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1677(a,1),1896(a,2,2))].">
      <j1 rule="para" parents="1677 1896"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      T(x / y,y / x) != z * (x / y)
    ]]></literal>
    <literal><![CDATA[
      K(x / y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1897(a,1),44(a,1))].">
      <j1 rule="para" parents="1897 44"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(1745(a,2),1901(a,2,2))].">
      <j1 rule="para" parents="1745 1901"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1793,a,b,1903,a)].">
      <j1 rule="hyper" parents="35 1793 1903"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) * (x / y) = T(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(1904(a,2),1897(a,1,1))].">
      <j1 rule="para" parents="1904 1897"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      K(x / y,y / x) \ z = K(y / x,x / y) * z
    ]]></literal>
    <justification jstring="[para(1888(a,1),1899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1888 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      K(x \ 1,(y / x) \ y) * ((y / x) / y) = T((y / x) / y,y / (y / x))
    ]]></literal>
    <justification jstring="[para(79(a,1),1905(a,1,1,1,1))].">
      <j1 rule="para" parents="79 1905"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      K((x * y) / y,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1750,a,b,1898,a),flip(a)].">
      <j1 rule="hyper" parents="35 1750 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * y) = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(1908(a,1),1894(a,1,2,1))].">
      <j1 rule="para" parents="1908 1894"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1850,a(flip),b,1910,a),flip(a)].">
      <j1 rule="hyper" parents="63 1850 1910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(165,a,1911,a)].">
      <j1 rule="hyper" parents="165 1911"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(76(a,1),1912(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 1912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(165,a,1913,a)].">
      <j1 rule="hyper" parents="165 1913"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1081(a,1),1914(a,1,1,1,1))].">
      <j1 rule="para" parents="1081 1914"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1764,a(flip),b,1757,a),flip(a)].">
      <j1 rule="hyper" parents="257 1764 1757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      (1 / (1 / x)) * ((1 / x) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1760,a,1916,a)].">
      <j1 rule="hyper" parents="1760 1916"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      a(1 / (1 / x),1 / x,y) = L(y,x \ 1,x) \ y
    ]]></literal>
    <justification jstring="[para(1917(a,1),188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1917 188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      a(1 / (1 / x),1 / x,y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,508,a(flip),b,1918,a),flip(a)].">
      <j1 rule="hyper" parents="257 508 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1756,a(flip),b,1767,a),flip(a)].">
      <j1 rule="hyper" parents="63 1756 1767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      R(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1090(a,1),1920(a,1,2))].">
      <j1 rule="para" parents="1090 1920"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      (R(1 / x,y,z) * K(x \ 1,x)) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u
    ]]></literal>
    <justification jstring="[para(1922(a,1),531(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1922 531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,1254,a(flip),b,1769,a),flip(a)].">
      <j1 rule="hyper" parents="63 1254 1769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      L(x,K(y,y \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,1738,a(flip),b,1924,a),flip(a)].">
      <j1 rule="hyper" parents="257 1738 1924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      L(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[para(1090(a,1),1925(a,1,2))].">
      <j1 rule="para" parents="1090 1925"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1324,a(flip),b,1748,a),flip(a)].">
      <j1 rule="hyper" parents="63 1324 1748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      T(K(x \ (x * y),x),x \ (x * y)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),1928(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,692,a(flip),b,1885,a),flip(a)].">
      <j1 rule="hyper" parents="257 692 1885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      R(x * y,z,u) / y = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,761,a(flip),b,1931,a)].">
      <j1 rule="hyper" parents="63 761 1931"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(114,a,1931,a(flip),b,761,a(flip))].">
      <j1 rule="hyper" parents="114 1931 761"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      R((x \ y) * x,z,u) / x = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1932(a,2,2,1))].">
      <j1 rule="para" parents="10 1932"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1932(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),1933(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(147(a,1),1934(a,1,1,1))].">
      <j1 rule="para" parents="147 1934"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(124,a,1937,a)].">
      <j1 rule="hyper" parents="124 1937"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      (R(x,y,z) * (x \ 1)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,756,a,b,1937,a)].">
      <j1 rule="hyper" parents="114 756 1937"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,802,a,b,1937,a)].">
      <j1 rule="hyper" parents="63 802 1937"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,223,a,b,1937,a)].">
      <j1 rule="hyper" parents="36 223 1937"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(1937(a,1),405(a,1,1))].">
      <j1 rule="para" parents="1937 405"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      R(R(x,y,z) \ R(R(x,y,z),u,w),R(x,y,z),y * z) = (R(R(x,y,z),u,w) * (y * z)) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(1937(a,1),406(a,1,1))].">
      <j1 rule="para" parents="1937 406"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) * K(x \ 1,x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1294,a,b,1940,a)].">
      <j1 rule="hyper" parents="63 1294 1940"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,756,a,b,1941,a)].">
      <j1 rule="hyper" parents="257 756 1941"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x * R(x \ 1,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(172,a,159,a(flip),b,1941,a(flip))].">
      <j1 rule="hyper" parents="172 159 1941"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,1935,a),flip(a)].">
      <j1 rule="hyper" parents="125 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,147,a(flip),b,1936,a),flip(a)].">
      <j1 rule="hyper" parents="42 147 1936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(397(a,1),1936(a,2,1,2))].">
      <j1 rule="para" parents="397 1936"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      T(x,R(x \ 1,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(203,a,159,a(flip),b,1946,a)].">
      <j1 rule="hyper" parents="203 159 1946"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1951(a,2,1))].">
      <j1 rule="para" parents="79 1951"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      T(x / (y * x),T(y,x / (y * x))) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1408(a,1),1951(a,1,2))].">
      <j1 rule="para" parents="1408 1951"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1952(a,1),519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1952 519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u))
    ]]></literal>
    <justification jstring="[para(1948(a,2),1696(a,1,1))].">
      <j1 rule="para" parents="1948 1696"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * K(x \ 1,x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(103(a,1),1945(a,1,1,1))].">
      <j1 rule="para" parents="103 1945"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      (R(x \ 1,y,z) / (x * R(x \ 1,y,z))) \ 1 = K(x \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(1947(a,2),626(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1947 626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(112,a,1950,a(flip),b,221,a)].">
      <j1 rule="hyper" parents="112 1950 221"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,781,a(flip),b,1954,a),flip(a)].">
      <j1 rule="hyper" parents="257 781 1954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      x * T(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1960(a,1,2,2,1))].">
      <j1 rule="para" parents="79 1960"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,x) * y) * z
    ]]></literal>
    <justification jstring="[para(1961(a,1),1614(a,2,1,1))].">
      <j1 rule="para" parents="1961 1614"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      T(x / (y * x),T(y,y \ 1)) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1469(a,1),1953(a,1,2))].">
      <j1 rule="para" parents="1469 1953"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1074,a(flip),b,1963,a)].">
      <j1 rule="hyper" parents="63 1074 1963"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),1929(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1966(a,2,2))].">
      <j1 rule="para" parents="9 1966"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(1967(a,1),1621(a,1))].">
      <j1 rule="para" parents="1967 1621"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(x / y,y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(1904(a,1),1957(a,2,1))].">
      <j1 rule="para" parents="1904 1957"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,786,a(flip),b,1962,a),flip(a)].">
      <j1 rule="hyper" parents="35 786 1962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      x / ((R(y,z,u) \ x) * K(y \ 1,y)) = (R(y,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1971(a,1),1799(a,1,2,2))].">
      <j1 rule="para" parents="1971 1799"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      R(x / y,y,K(z \ 1,z)) = K(z \ 1,z) * (x / (K(z \ 1,z) * y))
    ]]></literal>
    <justification jstring="[hyper(257,a,1802,a(flip),b,1795,a),flip(a)].">
      <j1 rule="hyper" parents="257 1802 1795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      R((x * y) / y,y,K(z \ 1,z)) = K(z \ 1,z) * R(x / K(z \ 1,z),K(z \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(99(a,2),1975(a,2,2))].">
      <j1 rule="para" parents="99 1975"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      T((x / y) / x,x / (x / y)) = K(y \ 1,y) * ((x / y) / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1907(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      K((x / y) / x,x / (x / y)) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1902,a,1982,a)].">
      <j1 rule="hyper" parents="1902 1982"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      (x / y) * (1 / (1 / y)) = K(y \ 1,y) * x
    ]]></literal>
    <justification jstring="[para(1983(a,1),1900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1983 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(11(a,1),1984(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(203,a,1985,a(flip),b,1848,a(flip))].">
      <j1 rule="hyper" parents="203 1985 1848"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(76(a,1),1988(a,1,2,2))].">
      <j1 rule="para" parents="76 1988"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(166(a,1),1988(a,1,2)),flip(a)].">
      <j1 rule="para" parents="166 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,547,a(flip),b,1989,a),flip(a)].">
      <j1 rule="hyper" parents="63 547 1989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(103(a,2),1990(a,1,2))].">
      <j1 rule="para" parents="103 1990"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(115,a,1995,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 1995 22"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1755,a,b,1998,a)].">
      <j1 rule="hyper" parents="63 1755 1998"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(1830,a,2002,a)].">
      <j1 rule="hyper" parents="1830 2002"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1753,a,2002,a)].">
      <j1 rule="hyper" parents="1753 2002"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,254,a(flip),b,2002,a),flip(a)].">
      <j1 rule="hyper" parents="257 254 2002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(103(a,1),2006(a,1,1,2))].">
      <j1 rule="para" parents="103 2006"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(328(a,1),2006(a,1,1)),flip(a)].">
      <j1 rule="para" parents="328 2006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,254,a(flip),b,2007,a),flip(a)].">
      <j1 rule="hyper" parents="257 254 2007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1775,a,2008,a)].">
      <j1 rule="hyper" parents="1775 2008"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,392,a,b,2009,a),flip(a)].">
      <j1 rule="hyper" parents="35 392 2009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1132,a,b,2010,a)].">
      <j1 rule="hyper" parents="35 1132 2010"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(1762(a,1),2011(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1762 2011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      ((x * y) * ((z \ 1) \ 1)) / ((y * z) * K(z,z \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(2012(a,1),386(a,1,1))].">
      <j1 rule="para" parents="2012 386"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(111,a,2014,a(flip),b,744,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 2014 744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(172,a,2018,a(flip),b,1746,a(flip))].">
      <j1 rule="hyper" parents="172 2018 1746"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(171(a,1),2020(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="171 2020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(173,a,2023,a)].">
      <j1 rule="hyper" parents="173 2023"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(115,a,2024,a,b,xx)].">
      <j1 rule="hyper" parents="115 2024"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(76(a,1),2024(a,2,2,2,2))].">
      <j1 rule="para" parents="76 2024"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),2025(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 2025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2028(a,2,2,2,2))].">
      <j1 rule="para" parents="9 2028"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1732(a,2),2029(a,1,2))].">
      <j1 rule="para" parents="1732 2029"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2030(a,2,2,2))].">
      <j1 rule="para" parents="76 2030"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(2031(a,2),675(a,1,1,2))].">
      <j1 rule="para" parents="2031 675"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1602,a,b,2032,a)].">
      <j1 rule="hyper" parents="63 1602 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2033(a,1,2))].">
      <j1 rule="para" parents="79 2033"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(656(a,1),2034(a,1,1))].">
      <j1 rule="para" parents="656 2034"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,583,a(flip),b,2036,a),flip(a)].">
      <j1 rule="hyper" parents="63 583 2036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2037(a,2),194(a,1,1))].">
      <j1 rule="para" parents="2037 194"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x,x \ 1) * y,z,u) = (x \ L(x * (y / x),z,u)) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),1824(a,1,2,1,2))].">
      <j1 rule="para" parents="12 1824"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(1796(a,1),1882(a,1,1,2))].">
      <j1 rule="para" parents="1796 1882"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      x * a(x,y \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2041,a(flip),b,783,a(flip))].">
      <j1 rule="hyper" parents="115 2041 783"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      a(x,x \ 1,x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,1765,a,b,2043,a),flip(a)].">
      <j1 rule="hyper" parents="34 1765 2043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      R(x \ 1,y,z) * (K(x \ 1,x) \ u) = R(1 / x,y,z) * u
    ]]></literal>
    <justification jstring="[para(1797(a,1),1923(a,1,1))].">
      <j1 rule="para" parents="1797 1923"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      R(x \ 1,y,z) * (K(x,x \ 1) * u) = R(1 / x,y,z) * u
    ]]></literal>
    <justification jstring="[para(1811(a,1),2046(a,1,2))].">
      <j1 rule="para" parents="1811 2046"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = (x \ L(x * (y / x),z,u)) * x
    ]]></literal>
    <justification jstring="[para(1773(a,1),2040(a,1,2,1))].">
      <j1 rule="para" parents="1773 2040"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      K(x \ 1,x) * R(y / K(x \ 1,x),K(x \ 1,x),z) = R(y,z,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(11(a,1),1980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x,x \ 1) * y,K(x \ 1,x),z) = R(y,z,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1820(a,1),2057(a,1,2,1))].">
      <j1 rule="para" parents="1820 2057"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      R(K(x \ 1,x) * (K(x,x \ 1) * y),K(x \ 1,x),z) = R(y,z,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1307,a,b,2058,a)].">
      <j1 rule="hyper" parents="63 1307 2058"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(1809(a,1),2059(a,1,1))].">
      <j1 rule="para" parents="1809 2059"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,z \ 1)) = ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2012(a,1),2017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2012 2017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2062">
    <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(1801,a,1800,a),flip(a)].">
      <j1 rule="hyper" parents="1801 1800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,783,a(flip),b,2062,a),flip(a)].">
      <j1 rule="hyper" parents="257 783 2062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2062(a,2),787(a,1)),flip(b)].">
      <j1 rule="para" parents="2062 787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = K(y / x,x / y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1906,a(flip),b,1970,a),flip(a)].">
      <j1 rule="hyper" parents="257 1906 1970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      (R((x \ y) \ 1,z,u) / ((x \ y) * R((x \ y) \ 1,z,u))) \ 1 = (x \ y) * K(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1891,a(flip),b,2066,a),flip(a)].">
      <j1 rule="hyper" parents="257 1891 2066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      (x \ y) * K(y / x,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1947(a,1),2067(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1947 2067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1766,a,b,2068,a)].">
      <j1 rule="hyper" parents="34 1766 2068"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(1838,a,2069,a)].">
      <j1 rule="hyper" parents="1838 2069"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = (y \ x) * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(257,a,1888,a,b,2070,a)].">
      <j1 rule="hyper" parents="257 1888 2070"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      ((x \ y) \ (y / x)) / (y / x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1786,a,b,2071,a(flip))].">
      <j1 rule="hyper" parents="34 1786 2071"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      (1 / (x \ y)) * (y / x) = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(124,a,2072,a)].">
      <j1 rule="hyper" parents="124 2072"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      ((x / y) \ x) \ (x / (x / y)) = (1 / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),2073(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      T(1 / x,y / (y / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(203,a,2074,a(flip),b,789,a(flip))].">
      <j1 rule="hyper" parents="203 2074 789"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2075(a,1,2,2))].">
      <j1 rule="para" parents="11 2075"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(195(a,1),2076(a,1,2))].">
      <j1 rule="para" parents="195 2076"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      x \ (x / T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,954,a(flip),b,2077,a)].">
      <j1 rule="hyper" parents="63 954 2077"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,724,a,b,2077,a)].">
      <j1 rule="hyper" parents="40 724 2077"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(114,a,2077,a(flip),b,1806,a)].">
      <j1 rule="hyper" parents="114 2077 1806"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(38,a,726,a,b,2078,a),flip(a)].">
      <j1 rule="hyper" parents="38 726 2078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(165,a,2081,a)].">
      <j1 rule="hyper" parents="165 2081"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(124,a,2081,a)].">
      <j1 rule="hyper" parents="124 2081"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1548,a,b,2084,a)].">
      <j1 rule="hyper" parents="63 1548 2084"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2089(a,1),1547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2089 1547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) \ 1 = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,2079,a,b,134,a)].">
      <j1 rule="hyper" parents="113 2079 134"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(251,a,2091,a),flip(a)].">
      <j1 rule="hyper" parents="251 2091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2094,a)].">
      <j1 rule="hyper" parents="54 2094"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2094,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2094 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2094(a,1),234(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="2094 234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(127,a,2095,a)].">
      <j1 rule="hyper" parents="127 2095"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      K(x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2095,a)].">
      <j1 rule="hyper" parents="55 2095"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,2095,a(flip))].">
      <j1 rule="hyper" parents="41 25 2095"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2095(a,1),200(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2095 200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2095(a,1),302(a,1,2,1))].">
      <j1 rule="para" parents="2095 302"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(964(a,1),2095(a,1,2))].">
      <j1 rule="para" parents="964 2095"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2095(a,1),1599(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2095 1599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(115,a,2098,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 2098 22"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1337,a,b,2096,a)].">
      <j1 rule="hyper" parents="63 1337 2096"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(172,a,2103,a(flip),b,103,a(flip))].">
      <j1 rule="hyper" parents="172 2103 103"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2097,a,1582,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2097 1582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,2108,a(flip),b,288,a)].">
      <j1 rule="hyper" parents="111 2108 288"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      x \ K(y,z) != z * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      1 / z = x
    ]]></literal>
    <justification jstring="[para(2109(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="2109 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(280,a,2080,a)].">
      <j1 rule="hyper" parents="280 2080"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      K(K(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,2101,a,b,85,a),flip(a)].">
      <j1 rule="hyper" parents="110 2101 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      K(x \ T(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(813(a,1),2113(a,1,1))].">
      <j1 rule="para" parents="813 2113"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,2114,a)].">
      <j1 rule="hyper" parents="56 2114"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ z) = ((T(x,y) \ 1) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(2111(a,1),925(a,1,1))].">
      <j1 rule="para" parents="2111 925"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2111(a,1),1666(a,1,2))].">
      <j1 rule="para" parents="2111 1666"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1593,a,b,2117,a)].">
      <j1 rule="hyper" parents="35 1593 2117"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,2119,a),flip(a)].">
      <j1 rule="hyper" parents="118 2119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      K(x,T(x,y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,2119,a(flip),b,247,a),flip(a)].">
      <j1 rule="hyper" parents="110 2119 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(2119(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="2119 80"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,2122,a(flip),b,743,a),flip(a)].">
      <j1 rule="hyper" parents="111 2122 743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(662,a,2121,a),flip(a)].">
      <j1 rule="hyper" parents="662 2121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(657,a,2121,a)].">
      <j1 rule="hyper" parents="657 2121"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1186,a(flip),b,2121,a),flip(a)].">
      <j1 rule="hyper" parents="63 1186 2121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,223,a,b,2121,a)].">
      <j1 rule="hyper" parents="36 223 2121"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2121(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2121 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(2121(a,1),99(a,1,1))].">
      <j1 rule="para" parents="2121 99"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      K(x,y) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(2121(a,2),520(a,2,1))].">
      <j1 rule="para" parents="2121 520"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(2121(a,1),400(a,1,1))].">
      <j1 rule="para" parents="2121 400"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2121(a,1),837(a,1))].">
      <j1 rule="para" parents="2121 837"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(813(a,2),2128(a,1,2))].">
      <j1 rule="para" parents="813 2128"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1159,a,b,2123,a)].">
      <j1 rule="hyper" parents="63 1159 2123"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2123,a(flip),b,163,a)].">
      <j1 rule="hyper" parents="114 2123 163"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2123(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2123 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(2123(a,1),390(a,1,1,1))].">
      <j1 rule="para" parents="2123 390"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      L(x \ 1,x,y \ ((x * y) / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1187,a(flip),b,2124,a)].">
      <j1 rule="hyper" parents="63 1187 2124"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2124(a,1),300(a,2,1))].">
      <j1 rule="para" parents="2124 300"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2036,a(flip),b,2131,a)].">
      <j1 rule="hyper" parents="257 2036 2131"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2142(a,1,1,2))].">
      <j1 rule="para" parents="76 2142"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(166(a,1),2142(a,1,1)),flip(a)].">
      <j1 rule="para" parents="166 2142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2142(a,1),2038(a,1,1))].">
      <j1 rule="para" parents="2142 2038"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(1969,a,2145,a)].">
      <j1 rule="hyper" parents="1969 2145"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2145,a)].">
      <j1 rule="hyper" parents="54 2145"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2145(a,1),202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2145 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2147(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2147 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      T(R(x,y,z),K(x,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2147(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2147 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2147(a,1),201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2147 201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = K(T(x \ 1,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(1660(a,1),2143(a,1,1))].">
      <j1 rule="para" parents="1660 2143"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(1914(a,1),2144(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1914 2144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2149,a)].">
      <j1 rule="hyper" parents="54 2149"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2155(a,1),232(a,1,2))].">
      <j1 rule="para" parents="2155 232"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (K(x,z) * T(x,y)) / w = u
    ]]></literal>
    <justification jstring="[para(2155(a,1),429(a,1,2))].">
      <j1 rule="para" parents="2155 429"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(824,a,2134,a)].">
      <j1 rule="hyper" parents="824 2134"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2150,a)].">
      <j1 rule="hyper" parents="54 2150"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(173,a,2158,a)].">
      <j1 rule="hyper" parents="173 2158"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,2158,a)].">
      <j1 rule="hyper" parents="125 2158"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      (((x * y) / x) \ y) / y = 1 / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(112,a,2160,a(flip),b,1108,a)].">
      <j1 rule="hyper" parents="112 2160 1108"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      (((L(x,y,y \ 1) * y) / y) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(1089(a,1),2161(a,1,1,1,1))].">
      <j1 rule="para" parents="1089 2161"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(189(a,1),2135(a,1,2))].">
      <j1 rule="para" parents="189 2135"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      L(x \ 1,x,T(y,x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[para(195(a,1),2139(a,1,3,2))].">
      <j1 rule="para" parents="195 2139"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2125(a,1),522(a,1,1))].">
      <j1 rule="para" parents="2125 522"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2125(a,1),1869(a,1,1))].">
      <j1 rule="para" parents="2125 1869"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = (y \ T(y,(y \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(2126(a,1),1328(a,2,1))].">
      <j1 rule="para" parents="2126 1328"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(204,a,2152,a)].">
      <j1 rule="hyper" parents="204 2152"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(2172(a,1),232(a,1,2))].">
      <j1 rule="para" parents="2172 232"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,85,a(flip),b,2104,a),flip(a)].">
      <j1 rule="hyper" parents="34 85 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ x = z
    ]]></literal>
    <justification jstring="[para(2174(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2174 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(770(a,1),2169(a,1,1)),flip(a)].">
      <j1 rule="para" parents="770 2169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(816(a,2),2169(a,1,1)),flip(a)].">
      <j1 rule="para" parents="816 2169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ z) = T((x \ 1) \ 1,y) \ z
    ]]></literal>
    <justification jstring="[para(1663(a,2),2116(a,2,1))].">
      <j1 rule="para" parents="1663 2116"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2033(a,1),2168(a,1))].">
      <j1 rule="para" parents="2033 2168"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1660(a,1),2179(a,1,1))].">
      <j1 rule="para" parents="1660 2179"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      T(x * L(x \ ((y * z) / y),x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1433,a,b,2136,a)].">
      <j1 rule="hyper" parents="63 1433 2136"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(2137(a,1),734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2137 734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      x * L(x \ y,x,x \ T(x,z)) = L(y,x \ T(x,z),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(336(a,1),2132(a,2,1))].">
      <j1 rule="para" parents="336 2132"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      L(x \ 1,x,K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(2177(a,1),2166(a,1,3))].">
      <j1 rule="para" parents="2177 2166"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      T(L((x * y) / x,z \ T(z,x),z),x) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[para(2183(a,1),2181(a,1,1))].">
      <j1 rule="para" parents="2183 2181"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(580,a,2186,a)].">
      <j1 rule="hyper" parents="580 2186"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * (T(x,y) \ z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1084(a,1),2170(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1084 2170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2154(a,1),2189(a,2,2))].">
      <j1 rule="para" parents="2154 2189"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(257,a,246,a(flip),b,2190,a)].">
      <j1 rule="hyper" parents="257 246 2190"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      ((x * ((u / z) / x)) * z) * (u \ y) = w
    ]]></literal>
    <justification jstring="[para(1955(a,1),231(a,1))].">
      <j1 rule="para" parents="1955 231"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      a(R(x \ 1,y,z),K(x,x \ 1),u) = (R(1 / x,y,z) * u) \ (R(1 / x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2047(a,1),1863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2047 1863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      a(R(x \ 1,y,z),K(x,x \ 1),u) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,66,a(flip),b,2193,a),flip(a)].">
      <j1 rule="hyper" parents="257 66 2193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      a(R((x \ 1) \ 1,y,z),K(x \ 1,x),u) = 1
    ]]></literal>
    <justification jstring="[para(1067(a,1),2194(a,1,2))].">
      <j1 rule="para" parents="1067 2194"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      R(R(x,y,z) \ R(R(x,y,z),u,w),R(x,y,z),y * z) = ((R(x,u,w) * y) * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(324(a,1),1944(a,2,1))].">
      <j1 rule="para" parents="324 1944"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      (L(x,y,y \ 1) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2163(a,1,1,1))].">
      <j1 rule="para" parents="11 2163"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      x * ((y * ((1 / y) * (z * y))) / y) != (1 / y) * (z * y)
    ]]></literal>
    <literal><![CDATA[
      L(z,y,y \ 1) \ ((1 / y) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(2198(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2198 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((x * ((z * u) / ((y * z) * u))) / x) * ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(98(a,1),1292(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="98 1292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * u) * ((x * (((y * z) * u) \ (z * u))) / x)
    ]]></literal>
    <justification jstring="[hyper(257,a,587,a(flip),b,2206,a),flip(a)].">
      <j1 rule="hyper" parents="257 587 2206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[hyper(257,a,1484,a(flip),b,2207,a),flip(a)].">
      <j1 rule="hyper" parents="257 1484 2207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * y) * ((u * ((x * y) \ y)) / u)) * z
    ]]></literal>
    <justification jstring="[para(587(a,1),2208(a,1,1))].">
      <j1 rule="para" parents="587 2208"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * ((u * (x \ 1)) / u)) * y) * z
    ]]></literal>
    <justification jstring="[para(1489(a,1),2209(a,2,1))].">
      <j1 rule="para" parents="1489 2209"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u) = R(x * ((u * (x \ 1)) / u),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,98,a,b,2210,a),flip(a)].">
      <j1 rule="hyper" parents="35 98 2210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1197,a,2211,a),flip(a)].">
      <j1 rule="hyper" parents="1197 2211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      L(R(x,y \ 1,y),a(1 / y,y,y \ 1),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1796(a,1),1631(a,1,1))].">
      <j1 rule="para" parents="1796 1631"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      L(R(x,y \ 1,y),K(y \ 1,y),1 / y) = (1 * (y \ 1)) \ R((1 / y) * x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(782(a,1),2213(a,1,2))].">
      <j1 rule="para" parents="782 2213"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      (1 * (x \ 1)) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1927,a(flip),b,2214,a),flip(a)].">
      <j1 rule="hyper" parents="63 1927 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      (x \ 1) \ R((1 / x) * y,x,x \ 1) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2215(a,1,1))].">
      <j1 rule="para" parents="7 2215"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,412,a(flip),b,2217,a)].">
      <j1 rule="hyper" parents="63 412 2217"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1992,a(flip),b,2218,a)].">
      <j1 rule="hyper" parents="63 1992 2218"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,222,a,b,2219,a)].">
      <j1 rule="hyper" parents="63 222 2219"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,396,a(flip),b,2219,a),flip(a)].">
      <j1 rule="hyper" parents="63 396 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,2219,a(flip),b,222,a)].">
      <j1 rule="hyper" parents="112 2219 222"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1878,a(flip),b,2220,a),flip(a)].">
      <j1 rule="hyper" parents="35 1878 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2221(a,1),1936(a,2,1,2))].">
      <j1 rule="para" parents="2221 1936"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2223(a,1),1133(a,1,1))].">
      <j1 rule="para" parents="2223 1133"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(112,a,1170,a(flip),b,2225,a),flip(a)].">
      <j1 rule="hyper" parents="112 1170 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(112,a,12,a(flip),b,2225,a),flip(a)].">
      <j1 rule="hyper" parents="112 12 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1829(a,1),2225(a,1,1))].">
      <j1 rule="para" parents="1829 2225"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1831,a,2229,a)].">
      <j1 rule="hyper" parents="1831 2229"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      R(T(x,y / (1 / z)),y / (z \ 1),K(z \ 1,z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2232(a,1),2063(a,1,1,2))].">
      <j1 rule="para" parents="2232 2063"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(750(a,1),2237(a,1,2))].">
      <j1 rule="para" parents="750 2237"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(246(a,1),2234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="246 2234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(257,a,1092,a(flip),b,2239,a),flip(a)].">
      <j1 rule="hyper" parents="257 1092 2239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(112,a,2227,a(flip),b,2220,a),flip(a)].">
      <j1 rule="hyper" parents="112 2227 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,919,a(flip),b,2244,a)].">
      <j1 rule="hyper" parents="63 919 2244"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(257,a,1384,a(flip),b,2231,a),flip(a)].">
      <j1 rule="hyper" parents="257 1384 2231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,1 / y,(1 / y) \ 1) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,320,a,b,2241,a)].">
      <j1 rule="hyper" parents="257 320 2241"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1090(a,1),2242(a,1,1))].">
      <j1 rule="para" parents="1090 2242"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(696(a,1),2262(a,1,2))].">
      <j1 rule="para" parents="696 2262"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,2231,a,b,2263,a),flip(a)].">
      <j1 rule="hyper" parents="257 2231 2263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      ((x \ 1) * x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(220(a,1),2264(a,1,1))].">
      <j1 rule="para" parents="220 2264"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1375,a,b,2265,a)].">
      <j1 rule="hyper" parents="63 1375 2265"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2249,a(flip),b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="35 2249 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,187,a(flip),b,2267,a)].">
      <j1 rule="hyper" parents="257 187 2267"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(187(a,1),2268(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="187 2268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,2269,a(flip),b,1552,a),flip(a)].">
      <j1 rule="hyper" parents="110 2269 1552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,2271,a(flip),b,1561,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 2271 1561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a,b,2272,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(z * y) \ z)
    ]]></literal>
    <justification jstring="[para(2272(a,2),2012(a,2,2))].">
      <j1 rule="para" parents="2272 2012"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),2273(a,1,2,1))].">
      <j1 rule="para" parents="85 2273"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,1865,a,b,2274,a)].">
      <j1 rule="hyper" parents="34 1865 2274"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),2277(a,1,2,1))].">
      <j1 rule="para" parents="12 2277"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2278(a,1),1883(a,1,2))].">
      <j1 rule="para" parents="2278 1883"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),2275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(313,a,2281,a),flip(a)].">
      <j1 rule="hyper" parents="313 2281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1500,a(flip),b,2282,a),flip(a)].">
      <j1 rule="hyper" parents="63 1500 2282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2283(a,1),166(a,1,2,2))].">
      <j1 rule="para" parents="2283 166"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2286(a,1),1743(a,1,1))].">
      <j1 rule="para" parents="2286 1743"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(172,a,2287,a(flip),b,1747,a(flip))].">
      <j1 rule="hyper" parents="172 2287 1747"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,1869,a(flip),b,2288,a),flip(a)].">
      <j1 rule="hyper" parents="257 1869 2288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(2127(a,1),2289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2127 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(1876,a,2290,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1876 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1067(a,1),2280(a,1,2))].">
      <j1 rule="para" parents="1067 2280"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2026(a,1),2293(a,2,1))].">
      <j1 rule="para" parents="2026 2293"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(2295(a,1),1879(a,1,1))].">
      <j1 rule="para" parents="2295 1879"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(649(a,1),2296(a,2,1,2))].">
      <j1 rule="para" parents="649 2296"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2227,a(flip),b,2297,a)].">
      <j1 rule="hyper" parents="63 2227 2297"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),2298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(123,a,2299,a),flip(a)].">
      <j1 rule="hyper" parents="123 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,2299,a),flip(a)].">
      <j1 rule="hyper" parents="112 10 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,2300,a)].">
      <j1 rule="hyper" parents="118 2300"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(111,a,195,a(flip),b,2300,a)].">
      <j1 rule="hyper" parents="111 195 2300"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(111,a,133,a(flip),b,2300,a),flip(a)].">
      <j1 rule="hyper" parents="111 133 2300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2300(a,1),1578(a,1,1))].">
      <j1 rule="para" parents="2300 1578"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2107,a,b,2302,a)].">
      <j1 rule="hyper" parents="63 2107 2302"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(114,a,2302,a(flip),b,2107,a)].">
      <j1 rule="hyper" parents="114 2302 2107"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2127,a,b,2302,a(flip))].">
      <j1 rule="hyper" parents="38 2127 2302"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(2302(a,1),369(a,1,1))].">
      <j1 rule="para" parents="2302 369"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2308(a,1),2291(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2308 2291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      x * (T(y,x) \ y) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(115,a,2303,a,b,xx)].">
      <j1 rule="hyper" parents="115 2303"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(2303(a,2),2128(a,1,2))].">
      <j1 rule="para" parents="2303 2128"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(2303(a,2),2130(a,1,1))].">
      <j1 rule="para" parents="2303 2130"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      T(x,K(y,x) \ 1) = x
    ]]></literal>
    <justification jstring="[para(2177(a,1),2312(a,1,2))].">
      <j1 rule="para" parents="2177 2312"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      (K(x,y) \ 1) * y = y * (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(115,a,2314,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 2314 22"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,938,a,b,2306,a)].">
      <j1 rule="hyper" parents="63 938 2306"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,939,a(flip),b,2306,a)].">
      <j1 rule="hyper" parents="63 939 2306"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2306(a,1),380(a,1,1,1))].">
      <j1 rule="para" parents="2306 380"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(2306(a,1),378(a,1,1,1))].">
      <j1 rule="para" parents="2306 378"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      T((x \ T(x,y)) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2307(a,2),194(a,1,1))].">
      <j1 rule="para" parents="2307 194"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(114,a,2310,a(flip),b,2160,a)].">
      <j1 rule="hyper" parents="114 2310 2160"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2310(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(195(a,1),2310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="195 2310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      (((x * y) / x) * T(((x * y) / x) \ z,y)) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(2310(a,1),748(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2310 748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(2310(a,1),902(a,1,2,2,1))].">
      <j1 rule="para" parents="2310 902"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(2200,a,2321,a)].">
      <j1 rule="hyper" parents="2200 2321"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(2323(a,1),2083(a,1,1))].">
      <j1 rule="para" parents="2323 2083"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2311(a,2),2323(a,1,1))].">
      <j1 rule="para" parents="2311 2323"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2125(a,1),2327(a,1,1))].">
      <j1 rule="para" parents="2125 2327"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      (x \ y) * (x \ ((x \ y) \ y)) = y / x
    ]]></literal>
    <justification jstring="[para(103(a,1),2301(a,1,2,2))].">
      <j1 rule="para" parents="103 2301"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(2315(a,1),187(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2315 187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(173,a,2328,a)].">
      <j1 rule="hyper" parents="173 2328"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,2330,a)].">
      <j1 rule="hyper" parents="118 2330"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      x / ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x))) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(674(a,1),2332(a,1,2,2))].">
      <j1 rule="para" parents="674 2332"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(195(a,1),2309(a,2,2)),flip(a)].">
      <j1 rule="para" parents="195 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(104(a,1),2304(a,1,2))].">
      <j1 rule="para" parents="104 2304"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2322,a,b,2336,a)].">
      <j1 rule="hyper" parents="63 2322 2336"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1197,a,2317,a)].">
      <j1 rule="hyper" parents="1197 2317"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,772,a,b,2317,a)].">
      <j1 rule="hyper" parents="63 772 2317"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1703,a(flip),b,2317,a)].">
      <j1 rule="hyper" parents="63 1703 2317"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(115,a,1196,a,b,2317,a(flip))].">
      <j1 rule="hyper" parents="115 1196 2317"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,1156,a,b,2317,a(flip))].">
      <j1 rule="hyper" parents="38 1156 2317"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(2317(a,1),1491(a,1,1))].">
      <j1 rule="para" parents="2317 1491"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(2317(a,1),1559(a,2,2,1))].">
      <j1 rule="para" parents="2317 1559"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(2317(a,1),2212(a,1,1))].">
      <j1 rule="para" parents="2317 2212"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1486,a,2343,a)].">
      <j1 rule="hyper" parents="1486 2343"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      T(x,x / (x * y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(2343(a,2),538(a,1))].">
      <j1 rule="para" parents="2343 538"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(223(a,1),2342(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="223 2342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2338,a(flip),b,2344,a),flip(a)].">
      <j1 rule="hyper" parents="257 2338 2344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(2351(a,2),43(a,1))].">
      <j1 rule="para" parents="2351 43"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = x \ T(x,R(z \ 1,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2141(a,1),2352(a,2,2,2,1))].">
      <j1 rule="para" parents="2141 2352"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R((y * x) \ (x * y),x,z)
    ]]></literal>
    <justification jstring="[para(2313(a,1),612(a,1,1))].">
      <j1 rule="para" parents="2313 612"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      T(x,x / (y * x)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(2164(a,2),2350(a,1))].">
      <j1 rule="para" parents="2164 2350"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(2356,a,909,a(flip))].">
      <j1 rule="hyper" parents="2356 909"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,2357,a)].">
      <j1 rule="hyper" parents="125 2357"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2357(a,2,2,1))].">
      <j1 rule="para" parents="79 2357"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),2358(a,1,2,2,1))].">
      <j1 rule="para" parents="9 2358"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(34,a,648,a,b,2360,a)].">
      <j1 rule="hyper" parents="34 648 2360"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,2015,a(flip),b,2361,a),flip(a)].">
      <j1 rule="hyper" parents="63 2015 2361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(186(a,2),2362(a,1,2))].">
      <j1 rule="para" parents="186 2362"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(112,a,2363,a(flip),b,575,a),flip(a)].">
      <j1 rule="hyper" parents="112 2363 575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2338,a(flip),b,2346,a),flip(a)].">
      <j1 rule="hyper" parents="257 2338 2346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2317(a,1),2341(a,1,1))].">
      <j1 rule="para" parents="2317 2341"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,2185,a(flip),b,2331,a),flip(a)].">
      <j1 rule="hyper" parents="257 2185 2331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,2305,a(flip),b,2364,a)].">
      <j1 rule="hyper" parents="63 2305 2364"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,1344,a(flip),b,2369,a)].">
      <j1 rule="hyper" parents="63 1344 2369"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),2370(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2371(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(1644,a,2326,a)].">
      <j1 rule="hyper" parents="1644 2326"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R(K(x,y),x,z)
    ]]></literal>
    <justification jstring="[para(16(a,2),2355(a,2,1))].">
      <j1 rule="para" parents="16 2355"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,(z \ 1) \ 1),z,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2365,a,b,2354,a),flip(a)].">
      <j1 rule="hyper" parents="257 2365 2354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(1990(a,1),2375(a,2,1,2))].">
      <j1 rule="para" parents="1990 2375"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(2310(a,1),2325(a,2,2))].">
      <j1 rule="para" parents="2310 2325"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(2192,a,2345,a)].">
      <j1 rule="hyper" parents="2192 2345"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2347(a,1),2378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2347 2378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(1990(a,1),2379(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1990 2379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1990(a,1),2380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1990 2380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2381(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(434,a,2382,a),flip(a)].">
      <j1 rule="hyper" parents="434 2382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(525,a,2383,a)].">
      <j1 rule="hyper" parents="525 2383"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(34,a,715,a,b,2383,a),flip(a)].">
      <j1 rule="hyper" parents="34 715 2383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,712,a(flip),b,2383,a),flip(a)].">
      <j1 rule="hyper" parents="34 712 2383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2307(a,1),2383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2307 2383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(111,a,2384,a(flip),b,2188,a)].">
      <j1 rule="hyper" parents="111 2384 2188"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(2323(a,2),2384(a,1,2))].">
      <j1 rule="para" parents="2323 2384"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(194(a,1),2393(a,1,2,1,2))].">
      <j1 rule="para" parents="194 2393"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(732,a,2390,a)].">
      <j1 rule="hyper" parents="732 2390"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1111,a,b,2390,a)].">
      <j1 rule="hyper" parents="35 1111 2390"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2390(a,2,2,1))].">
      <j1 rule="para" parents="10 2390"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1116,a(flip),b,2396,a)].">
      <j1 rule="hyper" parents="63 1116 2396"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,895,a(flip),b,2396,a)].">
      <j1 rule="hyper" parents="63 895 2396"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(76(a,1),2396(a,1,2,2))].">
      <j1 rule="para" parents="76 2396"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(203,a,950,a(flip),b,2395,a)].">
      <j1 rule="hyper" parents="203 950 2395"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(2398(a,1),984(a,1,1))].">
      <j1 rule="para" parents="2398 984"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,22,a,b,2401,a),flip(a)].">
      <j1 rule="hyper" parents="257 22 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(111,a,2394,a(flip),b,2377,a),flip(a)].">
      <j1 rule="hyper" parents="111 2394 2377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,132,a(flip),b,2386,a)].">
      <j1 rule="hyper" parents="112 132 2386"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(2387(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2387 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(2392(a,2),738(a,1))].">
      <j1 rule="para" parents="2392 738"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(111,a,2357,a,b,2397,a)].">
      <j1 rule="hyper" parents="111 2357 2397"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2386,a,b,2397,a)].">
      <j1 rule="hyper" parents="63 2386 2397"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2138,a,2405,a)].">
      <j1 rule="hyper" parents="2138 2405"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(2405(a,1),2374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2405 2374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2184,a(flip),b,2410,a)].">
      <j1 rule="hyper" parents="63 2184 2410"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,2399,a(flip),b,2402,a),flip(a)].">
      <j1 rule="hyper" parents="257 2399 2402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(2414(a,1),637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2414 637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,2404,a)].">
      <j1 rule="hyper" parents="125 2404"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(115,a,79,a(flip),b,2404,a),flip(a)].">
      <j1 rule="hyper" parents="115 79 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(203,a,2417,a,b,85,a),flip(a)].">
      <j1 rule="hyper" parents="203 2417 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(123,a,2417,a)].">
      <j1 rule="hyper" parents="123 2417"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),2419(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(2419(a,1),305(a,1))].">
      <j1 rule="para" parents="2419 305"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2319,a,b,2416,a)].">
      <j1 rule="hyper" parents="63 2319 2416"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(104(a,1),2420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 2420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2333,a(flip),b,2423,a),flip(a)].">
      <j1 rule="hyper" parents="257 2333 2423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2340,a(flip),b,2424,a),flip(a)].">
      <j1 rule="hyper" parents="63 2340 2424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),2406(a,1,2))].">
      <j1 rule="para" parents="10 2406"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2335,a,b,2411,a),flip(a)].">
      <j1 rule="hyper" parents="257 2335 2411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      L(x \ T(x,T(y,x)),T(y,x),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2411(a,1),395(a,1)),flip(b)].">
      <j1 rule="para" parents="2411 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2427,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 2427 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(361,a,2430,a)].">
      <j1 rule="hyper" parents="361 2430"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2431(a,1),50(a,2))].">
      <j1 rule="para" parents="2431 50"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(807,a,2413,a),flip(a)].">
      <j1 rule="hyper" parents="807 2413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,253,a,b,2425,a(flip))].">
      <j1 rule="hyper" parents="38 253 2425"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2436(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 2436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2436(a,1),2337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2436 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2437(a,1),2359(a,1,2))].">
      <j1 rule="para" parents="2437 2359"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),2440(a,2,2))].">
      <j1 rule="para" parents="11 2440"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),2441(a,1,2,2))].">
      <j1 rule="para" parents="22 2441"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2411(a,2),2428(a,1))].">
      <j1 rule="para" parents="2411 2428"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(2436(a,1),2408(a,1,1))].">
      <j1 rule="para" parents="2436 2408"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      T(L(x,y,y \ 1),(1 / y) \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1087(a,1),2444(a,2,2))].">
      <j1 rule="para" parents="1087 2444"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2304,a(flip),b,2434,a)].">
      <j1 rule="hyper" parents="63 2304 2434"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(2434(a,1),2327(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2434 2327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2439,a(flip),b,2446,a)].">
      <j1 rule="hyper" parents="63 2439 2446"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,649,a(flip),b,2448,a),flip(a)].">
      <j1 rule="hyper" parents="257 649 2448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1990(a,1),2449(a,1,1))].">
      <j1 rule="para" parents="1990 2449"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      x \ ((y * x) / y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,2302,a,b,2450,a)].">
      <j1 rule="hyper" parents="257 2302 2450"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(257,a,2304,a(flip),b,2450,a),flip(a)].">
      <j1 rule="hyper" parents="257 2304 2450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2450,a,b,2302,a),flip(a)].">
      <j1 rule="hyper" parents="115 2450 2302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(114,a,2450,a,b,2413,a)].">
      <j1 rule="hyper" parents="114 2450 2413"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2323,a,b,2450,a)].">
      <j1 rule="hyper" parents="39 2323 2450"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      (x \ T(x,y)) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(114,a,2450,a(flip),b,2081,a)].">
      <j1 rule="hyper" parents="114 2450 2081"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      x \ (y \ T(y,x)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,2450,a(flip),b,719,a)].">
      <j1 rule="hyper" parents="111 2450 719"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2450(a,2),2383(a,1,2,1))].">
      <j1 rule="para" parents="2450 2383"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(2450(a,2),2386(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2450 2386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(2450(a,1),2418(a,2,1))].">
      <j1 rule="para" parents="2450 2418"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(341,a,2455,a)].">
      <j1 rule="hyper" parents="341 2455"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      x * T(y,T(x,y)) = y * x
    ]]></literal>
    <justification jstring="[hyper(115,a,2455,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="115 2455 22"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2414,a,b,2455,a)].">
      <j1 rule="hyper" parents="63 2414 2455"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2399,a,b,2455,a)].">
      <j1 rule="hyper" parents="63 2399 2455"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,2455,a(flip),b,961,a),flip(a)].">
      <j1 rule="hyper" parents="172 2455 961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(115,a,2455,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="115 2455 199"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,2455,a(flip),b,733,a),flip(a)].">
      <j1 rule="hyper" parents="111 2455 733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),2455(a,1,2))].">
      <j1 rule="para" parents="25 2455"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(104(a,1),2455(a,1,2)),flip(a)].">
      <j1 rule="para" parents="104 2455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2455(a,1),201(a,1,2,1))].">
      <j1 rule="para" parents="2455 201"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(2455(a,1),2442(a,1,2))].">
      <j1 rule="para" parents="2455 2442"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,2415,a,b,2462,a(flip))].">
      <j1 rule="hyper" parents="35 2415 2462"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(900,a,2473,a)].">
      <j1 rule="hyper" parents="900 2473"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(367,a,2473,a)].">
      <j1 rule="hyper" parents="367 2473"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a,b,2473,a)].">
      <j1 rule="hyper" parents="63 29 2473"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,638,a,b,2476,a),flip(a)].">
      <j1 rule="hyper" parents="42 638 2476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,452,a,b,2476,a)].">
      <j1 rule="hyper" parents="42 452 2476"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[para(2476(a,1),377(a,1,1,1))].">
      <j1 rule="para" parents="2476 377"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      (T(x,y) * T(y,x)) / y = x
    ]]></literal>
    <justification jstring="[hyper(428,a,2466,a)].">
      <j1 rule="hyper" parents="428 2466"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(2467(a,1),1434(a,1,2,1))].">
      <j1 rule="para" parents="2467 1434"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      T(x,x * y) * R(x \ T(x * y,x),z,u) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(2467(a,1),1355(a,1,2,1))].">
      <j1 rule="para" parents="2467 1355"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(257,a,103,a(flip),b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="257 103 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      L(T(x,x \ y),y / x,x) = T(x,x * (y / x))
    ]]></literal>
    <justification jstring="[para(2470(a,1),468(a,1,1))].">
      <j1 rule="para" parents="2470 468"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2474,a(flip),b,897,a)].">
      <j1 rule="hyper" parents="115 2474 897"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2484(a,1,2))].">
      <j1 rule="para" parents="11 2484"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),2484(a,1,2))].">
      <j1 rule="para" parents="76 2484"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(552,a,2463,a),flip(a)].">
      <j1 rule="hyper" parents="552 2463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(551,a,2463,a)].">
      <j1 rule="hyper" parents="551 2463"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a(flip),b,2463,a)].">
      <j1 rule="hyper" parents="63 27 2463"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),2492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 2492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),z,u) = T(R(x,z,u),R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,2493,a)].">
      <j1 rule="hyper" parents="63 27 2493"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2493(a,1),2403(a,1,2))].">
      <j1 rule="para" parents="2493 2403"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(2495(a,1),232(a,1,2))].">
      <j1 rule="para" parents="2495 232"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(2495(a,1),2464(a,1,1,2))].">
      <j1 rule="para" parents="2495 2464"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(2497(a,1),303(a,1,2,1))].">
      <j1 rule="para" parents="2497 303"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(2497(a,1),304(a,1,2,1))].">
      <j1 rule="para" parents="2497 304"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(38,a,2337,a(flip),b,2451,a),flip(a)].">
      <j1 rule="hyper" parents="38 2337 2451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(2453(a,1),194(a,1,1))].">
      <j1 rule="para" parents="2453 194"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2352,a(flip),b,2460,a)].">
      <j1 rule="hyper" parents="257 2352 2460"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2461(a,1),494(a,1,1))].">
      <j1 rule="para" parents="2461 494"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(189(a,2),2472(a,1,1))].">
      <j1 rule="para" parents="189 2472"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      ((x * y) / x) / (y / x) = L(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2478(a,1,1,1,2))].">
      <j1 rule="para" parents="12 2478"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1270,a,2479,a)].">
      <j1 rule="hyper" parents="1270 2479"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2509(a,1),226(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2509 226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,2510,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 2510 22"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(173,a,2507,a)].">
      <j1 rule="hyper" parents="173 2507"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(488,a,2512,a)].">
      <j1 rule="hyper" parents="488 2512"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(2421,a,2452,a)].">
      <j1 rule="hyper" parents="2421 2452"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(257,a,2416,a,b,2459,a)].">
      <j1 rule="hyper" parents="257 2416 2459"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(124,a,2503,a)].">
      <j1 rule="hyper" parents="124 2503"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(2503(a,1),194(a,1,1))].">
      <j1 rule="para" parents="2503 194"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(2503(a,1),474(a,1,1))].">
      <j1 rule="para" parents="2503 474"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(79(a,1),2518(a,1,2))].">
      <j1 rule="para" parents="79 2518"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(227,a,2522,a)].">
      <j1 rule="hyper" parents="227 2522"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y)
    ]]></literal>
    <justification jstring="[para(2522(a,1),533(a,1,1))].">
      <j1 rule="para" parents="2522 533"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2520,a,b,91,a)].">
      <j1 rule="hyper" parents="115 2520 91"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(104(a,1),2513(a,1,3)),flip(a)].">
      <j1 rule="para" parents="104 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      ((x \ y) * x) * (y / x) = y * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(114,a,2517,a(flip),b,990,a)].">
      <j1 rule="hyper" parents="114 2517 990"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * ((y / x) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2527(a,1,1,1))].">
      <j1 rule="para" parents="79 2527"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      ((x * (x \ y)) / x) / ((x \ y) / x) = (x * ((x \ y) / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(257,a,421,a(flip),b,2508,a),flip(a)].">
      <j1 rule="hyper" parents="257 421 2508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,877,a,b,2515,a)].">
      <j1 rule="hyper" parents="63 877 2515"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      R(1 / x,x,x \ y) \ (y / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2526(a,1),297(a,1,1))].">
      <j1 rule="para" parents="2526 297"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      L(T(x,x \ y),y / x,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2492,a(flip),b,2485,a),flip(a)].">
      <j1 rule="hyper" parents="257 2492 2485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(2531(a,1),441(a,1,2))].">
      <j1 rule="para" parents="2531 441"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,2329,a(flip),b,2447,a),flip(a)].">
      <j1 rule="hyper" parents="257 2329 2447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(2506,a,2534,a),flip(a)].">
      <j1 rule="hyper" parents="2506 2534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2506,a,2535,a),flip(a)].">
      <j1 rule="hyper" parents="2506 2535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2536(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(2538(a,1),2376(a,1,1,2))].">
      <j1 rule="para" parents="2538 2376"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(468(a,1),2471(a,1,2))].">
      <j1 rule="para" parents="468 2471"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2511,a(flip),b,2540,a),flip(a)].">
      <j1 rule="hyper" parents="257 2511 2540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1005,a(flip),b,2499,a),flip(a)].">
      <j1 rule="hyper" parents="35 1005 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(124,a,2542,a)].">
      <j1 rule="hyper" parents="124 2542"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * x
    ]]></literal>
    <justification jstring="[para(79(a,1),2528(a,2,2))].">
      <j1 rule="para" parents="79 2528"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      (x * y) * ((y * x) / ((y * x) / x)) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),2545(a,1,1,2))].">
      <j1 rule="para" parents="11 2545"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      (x * y) * ((y * x) / y) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),2546(a,1,2,2))].">
      <j1 rule="para" parents="11 2546"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      x * (((y \ x) * y) / (y \ x)) = ((y \ x) * y) * y
    ]]></literal>
    <justification jstring="[hyper(424,a,2547,a)].">
      <j1 rule="hyper" parents="424 2547"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(2503(a,1),2548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2503 2548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(2467(a,1),2549(a,1,1,1))].">
      <j1 rule="para" parents="2467 2549"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x
    ]]></literal>
    <justification jstring="[hyper(257,a,493,a(flip),b,2524,a),flip(a)].">
      <j1 rule="hyper" parents="257 493 2524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x
    ]]></literal>
    <justification jstring="[para(2523(a,2),2551(a,1,2))].">
      <j1 rule="para" parents="2523 2551"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),2539(a,1,1,2,2))].">
      <j1 rule="para" parents="11 2539"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2115,a(flip),b,2553,a),flip(a)].">
      <j1 rule="hyper" parents="63 2115 2553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2554(a,1),2318(a,1,1))].">
      <j1 rule="para" parents="2554 2318"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(81(a,1),2555(a,1,2))].">
      <j1 rule="para" parents="81 2555"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(103(a,1),2556(a,1,1,2))].">
      <j1 rule="para" parents="103 2556"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(173,a,2558,a)].">
      <j1 rule="hyper" parents="173 2558"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(257,a,2424,a,b,2559,a)].">
      <j1 rule="hyper" parents="257 2424 2559"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,u * R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,27,a,b,2496,a)].">
      <j1 rule="hyper" parents="257 27 2496"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      (x / y) / ((y \ x) / y) = (y * ((y \ x) / y)) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),2529(a,1,1,1))].">
      <j1 rule="para" parents="10 2529"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(2543(a,1),2550(a,1,1))].">
      <j1 rule="para" parents="2543 2550"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(2498,a,2564,a),flip(a)].">
      <j1 rule="hyper" parents="2498 2564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,2525,a,b,2565,a),flip(a)].">
      <j1 rule="hyper" parents="34 2525 2565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(165,a,2566,a)].">
      <j1 rule="hyper" parents="165 2566"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),2567(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      R(T(x,(x \ (R(x,y,z) \ u)) * R(x,y,z)),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1283(a,1),2561(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1283 2561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(2554(a,1),2422(a,1,1))].">
      <j1 rule="para" parents="2554 2422"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(2426,a,2570,a),flip(a)].">
      <j1 rule="hyper" parents="2426 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(2406,a,2570,a),flip(a)].">
      <j1 rule="hyper" parents="2406 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2454,a(flip),b,2571,a)].">
      <j1 rule="hyper" parents="63 2454 2571"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(2572(a,1),2458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2572 2458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(669,a,2574,a)].">
      <j1 rule="hyper" parents="669 2574"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,671,a(flip),b,2574,a),flip(a)].">
      <j1 rule="hyper" parents="63 671 2574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      x * (T(x,y / (z \ 1)) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ T(z * y,x) = u
    ]]></literal>
    <justification jstring="[para(2574(a,1),669(a,1))].">
      <j1 rule="para" parents="2574 669"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),2552(a,2,1,2))].">
      <j1 rule="para" parents="79 2552"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      ((x * (y * T(y \ T(z,x),y))) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(1566(a,1),2324(a,1,1))].">
      <j1 rule="para" parents="1566 2324"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(102(a,1),2580(a,1,1,1,2))].">
      <j1 rule="para" parents="102 2580"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(2310(a,1),2581(a,1,2))].">
      <j1 rule="para" parents="2310 2581"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(2146(a,1),2334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2146 2334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(2176(a,1),2583(a,1,2))].">
      <j1 rule="para" parents="2176 2583"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2584(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="9 2584"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),2585(a,1,2,1,2))].">
      <j1 rule="para" parents="102 2585"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),2586(a,1,2,1))].">
      <j1 rule="para" parents="16 2586"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(2175,a,2587,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2175 2587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      (K(x,y) \ 1) \ (K(x,y) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(111,a,2588,a(flip),b,2315,a)].">
      <j1 rule="hyper" parents="111 2588 2315"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(2588(a,1),2367(a,1,1))].">
      <j1 rule="para" parents="2588 2367"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(2589(a,1),650(a,1,2,1))].">
      <j1 rule="para" parents="2589 650"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,2590,a)].">
      <j1 rule="hyper" parents="125 2590"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2592(a,1),2013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2592 2013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,254,a(flip),b,2591,a),flip(a)].">
      <j1 rule="hyper" parents="63 254 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,253,a(flip),b,2594,a),flip(a)].">
      <j1 rule="hyper" parents="63 253 2594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2595,a(flip),b,2593,a),flip(a)].">
      <j1 rule="hyper" parents="257 2595 2593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2596(a,1),1628(a,1,2,2))].">
      <j1 rule="para" parents="2596 1628"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(483,a,2597,a),flip(a)].">
      <j1 rule="hyper" parents="483 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(486,a,2598,a(flip))].">
      <j1 rule="hyper" parents="486 2598"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,1 / y,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),2250(a,1,1,3))].">
      <j1 rule="para" parents="79 2250"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,y \ 1,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2219(a,1),2602(a,1,1))].">
      <j1 rule="para" parents="2219 2602"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2227(a,1),2603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2227 2603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2604(a,2,1,1,2))].">
      <j1 rule="para" parents="7 2604"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),2605(a,2,2))].">
      <j1 rule="para" parents="79 2605"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      T(L(x,y,y \ 1),y) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2445(a,1,1,2))].">
      <j1 rule="para" parents="79 2445"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(25(a,2),2607(a,1,1))].">
      <j1 rule="para" parents="25 2607"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),(1 / x) \ 1)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1086(a,1),2608(a,1,1))].">
      <j1 rule="para" parents="1086 2608"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),x)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2609(a,1,2,2,2))].">
      <j1 rule="para" parents="79 2609"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ L(T(y,x),x,x \ 1)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),2610(a,1,2,2))].">
      <j1 rule="para" parents="25 2610"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1086(a,1),2611(a,1,2,2))].">
      <j1 rule="para" parents="1086 2611"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2612(a,1,2))].">
      <j1 rule="para" parents="9 2612"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * (a(x,y,y \ 1) * R((x \ R(x,y,y \ 1)) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(544(a,1),1177(a,2,2,1))].">
      <j1 rule="para" parents="544 1177"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * (a(x,y,y \ 1) * R(a(x,y,y \ 1) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(544(a,1),2623(a,2,2,2,1,1))].">
      <j1 rule="para" parents="544 2623"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * R(a(x,y,y \ 1) * (a(x,y,y \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1563(a,2),2624(a,2,2))].">
      <j1 rule="para" parents="1563 2624"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      R(x,y,y \ 1) * R(L(T(y,y \ 1),y \ 1,x * y),z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2625(a,2,2,1))].">
      <j1 rule="para" parents="10 2625"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      R(x,y,y \ 1) * L(R(T(y,y \ 1),z,u),y \ 1,x * y) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),2626(a,1,2))].">
      <j1 rule="para" parents="29 2626"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * R(T(y,y \ 1),z,u)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,414,a(flip),b,2627,a)].">
      <j1 rule="hyper" parents="63 414 2627"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      (x * y) * (R(y,z,u) * (y \ 1)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(202(a,1),2628(a,1,2))].">
      <j1 rule="para" parents="202 2628"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      (x * y) * (y \ R(y,z,u)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(756(a,1),2629(a,1,2))].">
      <j1 rule="para" parents="756 2629"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      (x / y) * R(y,z,u) = x * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(261,a,2630,a),flip(a)].">
      <j1 rule="hyper" parents="261 2630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(118,a,2630,a)].">
      <j1 rule="hyper" parents="118 2630"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      (x * y) \ (y * R(T(x,y),z,u)) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(111,a,2630,a(flip),b,193,a(flip))].">
      <j1 rule="hyper" parents="111 2630 193"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(111,a,2630,a(flip),b,130,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 2630 130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      T(x,y * z) \ R(T(x,y * z),y,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(462(a,1),2633(a,1,2)),flip(a)].">
      <j1 rule="para" parents="462 2633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      a(x,y,z) = T(x,y * z) \ R(T(x,y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,14,a,b,2635,a)].">
      <j1 rule="hyper" parents="257 14 2635"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * R(a(x,y,z) \ ((x * (y * z)) \ u),w,v5)) = ((x * y) * z) * R(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),1155(a,2,2,1,1))].">
      <j1 rule="para" parents="82 1155"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * R(a(x,y,z) \ ((x * (y * z)) \ u),w,v5)) = (x * y) * (z * R(z \ ((x * y) \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(257,a,689,a(flip),b,2637,a),flip(a)].">
      <j1 rule="hyper" parents="257 689 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      (x * (y * z)) * R(a(x,y,z) * (a(x,y,z) \ ((x * (y * z)) \ u)),w,v5) = (x * y) * (z * R(z \ ((x * y) \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(1563(a,2),2638(a,1,2))].">
      <j1 rule="para" parents="1563 2638"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      (x * (y * z)) * R((x * (y * z)) \ u,w,v5) = (x * y) * (z * R(z \ ((x * y) \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),2639(a,1,2,1))].">
      <j1 rule="para" parents="10 2639"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      (x * y) * (z * R(z \ ((x * y) \ u),w,v5)) = x * ((y * z) * R((y * z) \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(844,a,2640,a),flip(a)].">
      <j1 rule="hyper" parents="844 2640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      (x * y) * (z * R(z \ ((x * y) \ u),w,v5)) = x * (y * (z * R(z \ (y \ (x \ u)),w,v5)))
    ]]></literal>
    <justification jstring="[para(689(a,1),2641(a,2,2))].">
      <j1 rule="para" parents="689 2641"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      (x * y) * (z * R(z \ L(y \ u,y,x),w,v5)) = x * (y * (z * R(z \ (y \ (x \ (x * u))),w,v5)))
    ]]></literal>
    <justification jstring="[para(92(a,2),2643(a,1,2,2,1,2))].">
      <j1 rule="para" parents="92 2643"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      (x * y) * (z * R(z \ L(y \ u,y,x),w,v5)) = x * (y * (z * R(z \ (y \ u),w,v5)))
    ]]></literal>
    <justification jstring="[para(9(a,1),2644(a,2,2,2,2,1,2,2))].">
      <j1 rule="para" parents="9 2644"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * ((1 / y) * (w * R(w \ ((1 / y) \ w),z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1695,a(flip),b,2645,a)].">
      <j1 rule="hyper" parents="63 1695 2645"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * (((1 / y) * R((1 / y) \ 1,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1237(a,1),2646(a,2,2))].">
      <j1 rule="para" parents="1237 2646"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * (((1 / y) * R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(79(a,1),2647(a,2,2,1,2,1))].">
      <j1 rule="para" parents="79 2647"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      ((x * (1 / y)) * R(L(y,1 / y,x),z,u)) * w = x * ((y \ R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1941(a,1),2648(a,2,2,1))].">
      <j1 rule="para" parents="1941 2648"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      (x * ((1 / y) * R(y,z,u))) * w = x * ((y \ R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(330(a,1),2649(a,1,1))].">
      <j1 rule="para" parents="330 2649"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * w = x * ((y \ R(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1941(a,1),2650(a,1,1,2))].">
      <j1 rule="para" parents="1941 2650"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,2651,a)].">
      <j1 rule="hyper" parents="388 2651"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(361,a,2651,a)].">
      <j1 rule="hyper" parents="361 2651"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ w = (y \ R(y,z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(111,a,72,a(flip),b,2651,a)].">
      <j1 rule="hyper" parents="111 72 2651"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      R(x,a(y,z,z \ 1),u) = x
    ]]></literal>
    <justification jstring="[para(544(a,1),2652(a,1,2))].">
      <j1 rule="para" parents="544 2652"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(2636(a,2),2653(a,1,2))].">
      <j1 rule="para" parents="2636 2653"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      (x * a(y,z,u)) * w = x * (a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(832,a,2658,a),flip(a)].">
      <j1 rule="hyper" parents="832 2658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      (x * a(y,z,u)) \ w = a(y,z,u) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,241,a(flip),b,2658,a)].">
      <j1 rule="hyper" parents="63 241 2658"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) \ y) = x * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(172,a,2658,a(flip),b,92,a(flip))].">
      <j1 rule="hyper" parents="172 2658 92"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / w = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(172,a,2658,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="172 2658 18"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) = x / a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(115,a,2658,a(flip),b,294,a(flip))].">
      <j1 rule="hyper" parents="115 2658 294"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(782(a,1),2656(a,1,2))].">
      <j1 rule="para" parents="782 2656"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2060,a(flip),b,2673,a)].">
      <j1 rule="hyper" parents="63 2060 2673"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      R(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(1737(a,1),2673(a,1,2))].">
      <j1 rule="para" parents="1737 2673"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2064,a,2674,a),flip(a)].">
      <j1 rule="hyper" parents="2064 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2238,a(flip),b,2674,a),flip(a)].">
      <j1 rule="hyper" parents="63 2238 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,2674,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 2674 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2674(a,1,3,1))].">
      <j1 rule="para" parents="79 2674"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(2674(a,1),379(a,1,1))].">
      <j1 rule="para" parents="2674 379"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1737(a,1),2674(a,1,3))].">
      <j1 rule="para" parents="1737 2674"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2676,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 2676 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      (x * ((K(y,y \ 1) * z) * u)) \ (((x * K(y,y \ 1)) * z) * u) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(2676(a,1),385(a,1,1,1))].">
      <j1 rule="para" parents="2676 385"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      x * K(y,1 / y) != z * (u * K(y,1 / y))
    ]]></literal>
    <literal><![CDATA[
      z * u = x
    ]]></literal>
    <justification jstring="[para(2681(a,1),389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2681 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1864,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="63 1864 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(114,a,2683,a(flip),b,2061,a(flip))].">
      <j1 rule="hyper" parents="114 2683 2061"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(114,a,2683,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 2683 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2683(a,1),379(a,1,1))].">
      <j1 rule="para" parents="2683 379"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2683(a,1),1790(a,1,1))].">
      <j1 rule="para" parents="2683 1790"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1798(a,1),2677(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1798 2677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(2679(a,1),2577(a,1,2,1))].">
      <j1 rule="para" parents="2679 2577"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(2694(a,1),2373(a,2,1))].">
      <j1 rule="para" parents="2694 2373"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      (x / a(y,z,u)) \ w = a(y,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(111,a,258,a(flip),b,2659,a(flip))].">
      <j1 rule="hyper" parents="111 258 2659"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ ((x * a(y,z,u)) * (w * v5)) = L(v5,w,x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2659(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2659 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * u) = ((x * y) * z) * u
    ]]></literal>
    <justification jstring="[para(82(a,1),2659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      T((x * y) \ (x * (a(z,u,w) * y)),x) = R(T(a(z,u,w),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(2659(a,1),707(a,1,1,2))].">
      <j1 rule="para" parents="2659 707"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(1783,a,2680,a)].">
      <j1 rule="hyper" parents="1783 2680"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(361,a,2680,a)].">
      <j1 rule="hyper" parents="361 2680"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(2680(a,1),1803(a,1,1))].">
      <j1 rule="para" parents="2680 1803"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2680(a,1),1851(a,1,1))].">
      <j1 rule="para" parents="2680 1851"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2704(a,1),1881(a,1,1))].">
      <j1 rule="para" parents="2704 1881"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      R(x,y,L(K(z \ 1,z),u,w)) = x
    ]]></literal>
    <justification jstring="[para(2704(a,2),2674(a,1,3))].">
      <j1 rule="para" parents="2704 2674"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1852,a,b,2682,a)].">
      <j1 rule="hyper" parents="63 1852 2682"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(1778(a,2),2682(a,1,2))].">
      <j1 rule="para" parents="1778 2682"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1791,a(flip),b,2685,a)].">
      <j1 rule="hyper" parents="63 1791 2685"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      (x * (y * (K(z,z \ 1) * u))) \ ((x * (y * K(z,z \ 1))) * u) = a(x,y * K(z,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2685(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2685 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (x * (y * K(z,z \ 1))) * u = (x * y) * (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2690(a,1),2685(a,1,1))].">
      <j1 rule="para" parents="2690 2685"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1766(a,1),2691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1766 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2723(a,1),1791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2723 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u * K(z \ 1,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(2703(a,2),362(a,1,2,2))].">
      <j1 rule="para" parents="2703 362"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(1821,a,2708,a)].">
      <j1 rule="hyper" parents="1821 2708"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(483,a,2708,a)].">
      <j1 rule="hyper" parents="483 2708"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(172,a,169,a(flip),b,2710,a)].">
      <j1 rule="hyper" parents="172 169 2710"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(2708(a,1),2711(a,1,2))].">
      <j1 rule="para" parents="2708 2711"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2713(a,1),2710(a,1,1))].">
      <j1 rule="para" parents="2713 2710"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1068(a,1),2731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1068 2731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(2738(a,1),1815(a,1,2,1))].">
      <j1 rule="para" parents="2738 1815"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(1778(a,2),2735(a,1,2))].">
      <j1 rule="para" parents="1778 2735"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,1268,a(flip),b,2701,a),flip(a)].">
      <j1 rule="hyper" parents="34 1268 2701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      a(x,y,z) = z / L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,2741,a),flip(a)].">
      <j1 rule="hyper" parents="123 2741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(118,a,2741,a),flip(a)].">
      <j1 rule="hyper" parents="118 2741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      L(x,y,z) != u \ x
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(2741(a,1),126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2741 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      a(x,y,z) * (L(z,y,x) * u) = z * u
    ]]></literal>
    <justification jstring="[para(2741(a,1),331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2741 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2741(a,1),1480(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2741 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(2741(a,1),1595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2741 1595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = x * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(2741(a,1),2665(a,1,1,2))].">
      <j1 rule="para" parents="2741 2665"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      R(a(x,y,R(z,u,w)),L(R(z,u,w),y,x),u * w) = ((z * u) * w) / (L(R(z,u,w),y,x) * (u * w))
    ]]></literal>
    <justification jstring="[para(2742(a,2),405(a,1,1))].">
      <j1 rule="para" parents="2742 405"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      (a(x,y,z) * u) \ z = u \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(2743(a,2),420(a,2,2))].">
      <j1 rule="para" parents="2743 420"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2473(a,1),2746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2473 2746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(290(a,1),2747(a,1,1))].">
      <j1 rule="para" parents="290 2747"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2473(a,1),2747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2473 2747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,2473,a(flip),b,2754,a),flip(a)].">
      <j1 rule="hyper" parents="257 2473 2754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(929(a,1),2756(a,1,1))].">
      <j1 rule="para" parents="929 2756"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(111,a,10,a(flip),b,2745,a),flip(a)].">
      <j1 rule="hyper" parents="111 10 2745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      R(a(x,y,z),L(z,y,x) * u,w) = ((z * u) * w) / ((L(z,y,x) * u) * w)
    ]]></literal>
    <justification jstring="[para(2745(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="2745 20"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      (x * (y * z)) / (L(y,u,w) * z) = x * a(w,u,y)
    ]]></literal>
    <justification jstring="[para(2745(a,1),2665(a,1,1,2))].">
      <j1 rule="para" parents="2745 2665"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (x * u) = L(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(165,a,2748,a)].">
      <j1 rule="hyper" parents="165 2748"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      (1 / x) * a(x \ 1,x,y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1290,a(flip),b,2748,a),flip(a)].">
      <j1 rule="hyper" parents="63 1290 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = x * a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1264,a(flip),b,2748,a)].">
      <j1 rule="hyper" parents="63 1264 2748"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      (L(x,y,z) * u) \ L(x,y,z) = (x * u) \ x
    ]]></literal>
    <justification jstring="[para(2745(a,1),2750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2745 2750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = a(u,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,461,a,b,2760,a)].">
      <j1 rule="hyper" parents="63 461 2760"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      a(x,y,z) \ 1 = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,750,a(flip),b,2760,a),flip(a)].">
      <j1 rule="hyper" parents="63 750 2760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      x * (a(y,z,x) \ u) = L(x,z,y) * u
    ]]></literal>
    <justification jstring="[para(2760(a,1),854(a,1,2))].">
      <j1 rule="para" parents="2760 854"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) = x / a(u,z,y)
    ]]></literal>
    <justification jstring="[para(2769(a,1),2667(a,1,2))].">
      <j1 rule="para" parents="2769 2667"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (x * L(y,z,u)) * a(u,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),2765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 2765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(179,a,2770,a),flip(a)].">
      <j1 rule="hyper" parents="179 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      a(x,y,z / u) \ z = u * L(u \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,933,a,b,2770,a),flip(a)].">
      <j1 rule="hyper" parents="34 933 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      L(x,y,z) = x / a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,148,a(flip),b,2770,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="112 148 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(111,a,148,a(flip),b,2770,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 148 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = a(z,y,x) * u
    ]]></literal>
    <justification jstring="[hyper(111,a,132,a(flip),b,2770,a(flip))].">
      <j1 rule="hyper" parents="111 132 2770"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      L(a(x,y,z),L(z,y,x),u) = (u * L(z,y,x)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(2774(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="2774 18"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      x * a(y,z,u) != u
    ]]></literal>
    <literal><![CDATA[
      L(u,z,y) = x
    ]]></literal>
    <justification jstring="[para(2774(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2774 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      a(x,y,z) * (z \ u) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(2776(a,2),2699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2776 2699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(114,a,2777,a(flip),b,2742,a(flip))].">
      <j1 rule="hyper" parents="114 2777 2742"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(L(z,u,w),y,x),w * u) = ((w * u) * L(L(z,u,w),y,x)) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(2777(a,2),376(a,1,1))].">
      <j1 rule="para" parents="2777 376"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(274,a,2782,a)].">
      <j1 rule="hyper" parents="274 2782"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * y) = a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,2772,a)].">
      <j1 rule="hyper" parents="118 2772"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) \ y = a(u,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(111,a,10,a(flip),b,2772,a)].">
      <j1 rule="hyper" parents="111 10 2772"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      L(a(x,y,z),u * L(z,y,x),w) = (w * (u * L(z,y,x))) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(2772(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="2772 18"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      T(L(x,y,z) \ u,a(z,y,x)) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(2781(a,1),366(a,1,1))].">
      <j1 rule="para" parents="2781 366"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,2785,a(flip))].">
      <j1 rule="hyper" parents="41 25 2785"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      T(x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(2777(a,2),2790(a,1,2))].">
      <j1 rule="para" parents="2777 2790"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (1 / x) * a(1 / x,x,y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(2755(a,2),2764(a,1,2))].">
      <j1 rule="para" parents="2755 2764"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      ((x * (y * x)) / x) \ L(x,y,x) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(2479(a,2),2766(a,1,1))].">
      <j1 rule="para" parents="2479 2766"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      a(x,y,z / (u \ 1)) \ z = u \ L(u * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,691,a(flip),b,2775,a),flip(a)].">
      <j1 rule="hyper" parents="257 691 2775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) \ y = a(u,z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(691(a,1),2787(a,1,1))].">
      <j1 rule="para" parents="691 2787"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      (x / (y * x)) * y = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,768,a,b,2793,a)].">
      <j1 rule="hyper" parents="34 768 2793"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      a(1 / (1 / x),1 / x,y) = (1 / x) * R(x,1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,542,a,b,2797,a),flip(a)].">
      <j1 rule="hyper" parents="63 542 2797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1305,a(flip),b,2762,a)].">
      <j1 rule="hyper" parents="63 1305 2762"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = (a(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[para(2768(a,1),2787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2768 2787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(257,a,588,a(flip),b,2801,a),flip(a)].">
      <j1 rule="hyper" parents="257 588 2801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,174,a(flip),b,2802,a),flip(a)].">
      <j1 rule="hyper" parents="257 174 2802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      T(a(x,y,z / u),z) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),2802(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="79 2802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      a(x,y,R(z \ 1,z,u)) = a(x,y,u / (z * u))
    ]]></literal>
    <justification jstring="[para(1964(a,2),2803(a,1,3))].">
      <j1 rule="para" parents="1964 2803"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ (z \ u)) = (z \ L(u,y,x)) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2796(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(2578,a,2697,a)].">
      <j1 rule="hyper" parents="2578 2697"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2576,a,b,2697,a(flip))].">
      <j1 rule="hyper" parents="114 2576 2697"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2808(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),2808(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(2808(a,1),196(a,1,2,2))].">
      <j1 rule="para" parents="2808 196"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1823,a,b,2810,a)].">
      <j1 rule="hyper" parents="63 1823 2810"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2810(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 2810"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),2810(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(257,a,614,a,b,2811,a)].">
      <j1 rule="hyper" parents="257 614 2811"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(2811(a,1),2248(a,1,2))].">
      <j1 rule="para" parents="2811 2248"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1949(a,1),2812(a,1,1,1))].">
      <j1 rule="para" parents="1949 2812"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(2816(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2816 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(101(a,1),2817(a,2,1,2))].">
      <j1 rule="para" parents="101 2817"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(104(a,1),2817(a,2,1,2))].">
      <j1 rule="para" parents="104 2817"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      T((x \ y) * x,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(2817(a,2),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2817 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(2817(a,2),2582(a,1,1,1,2))].">
      <j1 rule="para" parents="2817 2582"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(113,a,2827,a,b,2480,a)].">
      <j1 rule="hyper" parents="113 2827 2480"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),2832(a,1,2))].">
      <j1 rule="para" parents="80 2832"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(2833(a,2),2560(a,1,1))].">
      <j1 rule="para" parents="2833 2560"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(104(a,1),2813(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="104 2813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(227,a,2829,a)].">
      <j1 rule="hyper" parents="227 2829"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(115,a,2829,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2829 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(2362(a,1),2834(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2362 2834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      T(x,y) / (z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (z \ x) \ T((z \ x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),2826(a,1,1,1))].">
      <j1 rule="para" parents="10 2826"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1827,a,2815,a),flip(a)].">
      <j1 rule="hyper" parents="1827 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(2818(a,2),2830(a,1))].">
      <j1 rule="para" parents="2818 2830"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(2192,a,2835,a),flip(a)].">
      <j1 rule="hyper" parents="2192 2835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(2836(a,1),213(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2836 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1959,a,b,2837,a)].">
      <j1 rule="hyper" parents="63 1959 2837"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      (x \ y) * ((z \ ((x \ y) \ y)) * z) = ((z \ x) * z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2837(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(189(a,2),2837(a,1,1,1,2))].">
      <j1 rule="para" parents="189 2837"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ y,z) * K(x,x \ 1) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1762(a,1),2840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1762 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(2724(a,1),1840(a,1,2))].">
      <j1 rule="para" parents="2724 1840"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(2724(a,1),1845(a,1,1))].">
      <j1 rule="para" parents="2724 1845"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1761,a(flip),b,2739,a)].">
      <j1 rule="hyper" parents="63 1761 2739"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(2852(a,1),2606(a,1,1))].">
      <j1 rule="para" parents="2852 2606"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      L(a(x,y,z),L(z,y,x),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,2786,a(flip),b,2779,a),flip(a)].">
      <j1 rule="hyper" parents="257 2786 2779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      (1 / x) * R(x,1 / x,y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1919,a(flip),b,2798,a),flip(a)].">
      <j1 rule="hyper" parents="63 1919 2798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      a(x,x \ 1,y) * x = R(x,1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,2856,a(flip),b,802,a(flip))].">
      <j1 rule="hyper" parents="114 2856 802"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,918,a,b,2822,a)].">
      <j1 rule="hyper" parents="63 918 2822"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      T(x,T(((y \ 1) \ 1) \ z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(2848(a,1),2688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2848 2688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      T(x,T((1 / y) \ z,u)) = T(x,T((y \ 1) \ z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),2859(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2689(a,1),44(a,1))].">
      <j1 rule="para" parents="2689 44"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2372,a(flip),b,2698,a),flip(a)].">
      <j1 rule="hyper" parents="63 2372 2698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2419,a(flip),b,2862,a),flip(a)].">
      <j1 rule="hyper" parents="39 2419 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1342(a,1),2863(a,1,2))].">
      <j1 rule="para" parents="1342 2863"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(2506,a,2864,a)].">
      <j1 rule="hyper" parents="2506 2864"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(2865(a,1),2191(a,2,1,2))].">
      <j1 rule="para" parents="2865 2191"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(2865(a,1),2505(a,1,2,2,1))].">
      <j1 rule="para" parents="2865 2505"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,2867,a),flip(a)].">
      <j1 rule="hyper" parents="125 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2353,a,2868,a)].">
      <j1 rule="hyper" parents="2353 2868"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(2839,a,904,a)].">
      <j1 rule="hyper" parents="2839 904"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / ((z * K(x \ 1,x)) * u) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[hyper(112,a,2706,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="112 2706 98"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      (x * y) \ (K(z,z \ 1) * (x * (K(z \ 1,z) * (y * u)))) = L(u,y * K(z \ 1,z),x)
    ]]></literal>
    <justification jstring="[hyper(1860,a,2707,a),flip(a)].">
      <j1 rule="hyper" parents="1860 2707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(18(a,2),2736(a,2,1))].">
      <j1 rule="para" parents="18 2736"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2846,a(flip),b,2849,a)].">
      <j1 rule="hyper" parents="63 2846 2849"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,2853,a(flip),b,2874,a),flip(a)].">
      <j1 rule="hyper" parents="63 2853 2874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(2844,a,2858,a)].">
      <j1 rule="hyper" parents="2844 2858"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(257,a,2409,a(flip),b,2866,a),flip(a)].">
      <j1 rule="hyper" parents="257 2409 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(2877(a,1),2838(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2877 2838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(2827(a,1),2880(a,1,1))].">
      <j1 rule="para" parents="2827 2880"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(257,a,2514,a(flip),b,2881,a),flip(a)].">
      <j1 rule="hyper" parents="257 2514 2881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2875,a,b,2882,a)].">
      <j1 rule="hyper" parents="63 2875 2882"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      R(T(a(x,y,z),u * w),u,w) = T(L(T(a(x,y,z),w),w,u),u)
    ]]></literal>
    <justification jstring="[para(197(a,1),2702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="197 2702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      R(T(a(x,y,z),u * w),u,w) = L(T(T(a(x,y,z),w),u),w,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,25,a,b,2884,a),flip(a)].">
      <j1 rule="hyper" parents="257 25 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(2883(a,1),2850(a,2,2))].">
      <j1 rule="para" parents="2883 2850"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(1936(a,2),2847(a,1,1))].">
      <j1 rule="para" parents="1936 2847"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(231,a,2888,a),flip(a)].">
      <j1 rule="hyper" parents="231 2888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (x * (a(y,z,u) * (w * v5))) = L(v5,w,x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2659(a,1),2700(a,1,2))].">
      <j1 rule="para" parents="2659 2700"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2727,a,2873,a)].">
      <j1 rule="hyper" parents="2727 2873"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = K(y \ 1,y) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,1778,a,b,2891,a),flip(a)].">
      <j1 rule="hyper" parents="257 1778 2891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1825(a,1),2892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1825 2892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2048,a(flip),b,2893,a)].">
      <j1 rule="hyper" parents="63 2048 2893"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(2895(a,1),75(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2895 75"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),2895(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(115,a,2898,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 2898 18"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(147(a,1),2898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="147 2898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(368(a,1),2898(a,2,1,2))].">
      <j1 rule="para" parents="368 2898"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(371(a,1),2898(a,2,1,2))].">
      <j1 rule="para" parents="371 2898"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,2900,a)].">
      <j1 rule="hyper" parents="123 2900"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(118,a,2900,a)].">
      <j1 rule="hyper" parents="118 2900"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2904(a,1),338(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2904 338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(111,a,2906,a(flip),b,715,a)].">
      <j1 rule="hyper" parents="111 2906 715"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,1679,a(flip),b,2899,a),flip(a)].">
      <j1 rule="hyper" parents="63 1679 2899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(241(a,1),2899(a,1,2,1,2))].">
      <j1 rule="para" parents="241 2899"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(111,a,2901,a(flip),b,219,a),flip(a)].">
      <j1 rule="hyper" parents="111 2901 219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2876,a(flip),b,2913,a)].">
      <j1 rule="hyper" parents="63 2876 2913"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,2886,a(flip),b,2902,a),flip(a)].">
      <j1 rule="hyper" parents="63 2886 2902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(143(a,1),2915(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="143 2915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,246,a,b,2916,a),flip(a)].">
      <j1 rule="hyper" parents="34 246 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2917,a),flip(a)].">
      <j1 rule="hyper" parents="125 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(114,a,2917,a(flip),b,2882,a)].">
      <j1 rule="hyper" parents="114 2917 2882"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(114,a,2917,a(flip),b,2514,a)].">
      <j1 rule="hyper" parents="114 2917 2514"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,2921,a)].">
      <j1 rule="hyper" parents="347 2921"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),2924(a,1,2,1))].">
      <j1 rule="para" parents="9 2924"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      T(K(x,y),y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,2925,a,b,2480,a)].">
      <j1 rule="hyper" parents="113 2925 2480"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(115,a,2925,a(flip),b,250,a(flip))].">
      <j1 rule="hyper" parents="115 2925 250"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,2460,a(flip),b,2926,a),flip(a)].">
      <j1 rule="hyper" parents="40 2460 2926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,2418,a(flip),b,2926,a),flip(a)].">
      <j1 rule="hyper" parents="40 2418 2926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,2413,a,b,2929,a)].">
      <j1 rule="hyper" parents="257 2413 2929"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2405,a,b,2929,a)].">
      <j1 rule="hyper" parents="257 2405 2929"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2366,a,b,2929,a)].">
      <j1 rule="hyper" parents="257 2366 2929"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      K(x,y) = T(y,T(x,y)) \ y
    ]]></literal>
    <justification jstring="[hyper(257,a,2323,a,b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="257 2323 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2317,a,b,2929,a)].">
      <j1 rule="hyper" parents="257 2317 2929"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(257,a,2121,a,b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="257 2121 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,651,a,b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="257 651 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2125,a(flip),b,2929,a)].">
      <j1 rule="hyper" parents="257 2125 2929"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,2929,a,b,2450,a),flip(a)].">
      <j1 rule="hyper" parents="172 2929 2450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      T(x,y) / K(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(172,a,2929,a,b,xx)].">
      <j1 rule="hyper" parents="172 2929"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,2929,a,b,2450,a)].">
      <j1 rule="hyper" parents="115 2929 2450"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(115,a,2929,a,b,2303,a)].">
      <j1 rule="hyper" parents="115 2929 2303"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2929,a,b,2302,a),flip(a)].">
      <j1 rule="hyper" parents="115 2929 2302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      a(x,y,z) \ T(a(x,y,z) * u,w) = u * K(a(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(115,a,2929,a,b,420,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2929 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2929,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="115 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2929,a,b,2413,a)].">
      <j1 rule="hyper" parents="114 2929 2413"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,2929,a,b,2405,a)].">
      <j1 rule="hyper" parents="114 2929 2405"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(114,a,2929,a,b,2306,a),flip(a)].">
      <j1 rule="hyper" parents="114 2929 2306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(114,a,2929,a,b,2121,a),flip(a)].">
      <j1 rule="hyper" parents="114 2929 2121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,2929,a,b,651,a)].">
      <j1 rule="hyper" parents="111 2929 651"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2133,a,2929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2133 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),2929(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),2929(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2929(a,2),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2929 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2929(a,2),2129(a,1,1))].">
      <j1 rule="para" parents="2929 2129"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(2929(a,2),2299(a,1,1,2))].">
      <j1 rule="para" parents="2929 2299"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2929(a,2),2320(a,1,1,1))].">
      <j1 rule="para" parents="2929 2320"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(2929(a,2),2301(a,1,2))].">
      <j1 rule="para" parents="2929 2301"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2929(a,2),2383(a,1,2,1))].">
      <j1 rule="para" parents="2929 2383"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      x \ T(x,y \ x) = K(x,x / y)
    ]]></literal>
    <justification jstring="[para(2400(a,1),2929(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2400 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2929(a,2),2386(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2929 2386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(2929(a,2),2407(a,1,1))].">
      <j1 rule="para" parents="2929 2407"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[para(2929(a,2),2456(a,1,1))].">
      <j1 rule="para" parents="2929 2456"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[para(2929(a,2),2457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2929 2457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      K(x,(y \ z) / z) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(2536(a,1),2929(a,2,2))].">
      <j1 rule="para" parents="2536 2929"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,2310,a,b,2930,a),flip(a)].">
      <j1 rule="hyper" parents="257 2310 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,2081,a,b,2930,a),flip(a)].">
      <j1 rule="hyper" parents="257 2081 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,719,a,b,2930,a),flip(a)].">
      <j1 rule="hyper" parents="257 719 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,322,a,b,2930,a(flip))].">
      <j1 rule="hyper" parents="38 322 2930"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2930(a,2),233(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2930 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(2930(a,2),2083(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2930 2083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2930(a,2),2092(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2930 2092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      T(x,x * y) \ x = K(y * x,x)
    ]]></literal>
    <justification jstring="[para(2493(a,1),2930(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2493 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(2930(a,2),2504(a,1,1,2))].">
      <j1 rule="para" parents="2930 2504"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(2930(a,2),2571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2930 2571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2930(a,2),2572(a,1,1))].">
      <j1 rule="para" parents="2930 2572"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2941(a,2),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2941 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2942(a,1),224(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2942 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(2943(a,1),2575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2943 2575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (x * y) * K(y,z) != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2948(a,2),388(a,2,2))].">
      <j1 rule="para" parents="2948 388"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (x * K(x,y)) \ x = K(y,x)
    ]]></literal>
    <justification jstring="[para(2948(a,1),2930(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2948 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,K(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(2952(a,2),362(a,1,2,2))].">
      <j1 rule="para" parents="2952 362"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      (x * K(y,z)) * y != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(2952(a,2),388(a,2,2))].">
      <j1 rule="para" parents="2952 388"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(2952(a,2),1222(a,1,1))].">
      <j1 rule="para" parents="2952 1222"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(211,a,2960,a),flip(a)].">
      <j1 rule="hyper" parents="211 2960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2967(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2967 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      R(x,y,z) / R(T(x,u),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),2971(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 2971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      T(x,y) * K(x * y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,2494,a,b,2981,a),flip(a)].">
      <j1 rule="hyper" parents="40 2494 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2981(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2981 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2981(a,1),202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2981 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (1 / (x * K(y,x))) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2981(a,1),1414(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2981 1414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2981(a,1),2469(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2981 2469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z * K(x * y,z))
    ]]></literal>
    <justification jstring="[para(2981(a,1),2799(a,1,3))].">
      <j1 rule="para" parents="2981 2799"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (x * y) * L(z,y * x,K(x,y)) = K(x,y) * ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2928,a(flip),b,163,a)].">
      <j1 rule="hyper" parents="114 2928 163"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2930,a,b,2935,a)].">
      <j1 rule="hyper" parents="257 2930 2935"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),3015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 3015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2981(a,1),3015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2981 3015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      K(x,y) = x * (((y * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2515,a,b,2939,a),flip(a)].">
      <j1 rule="hyper" parents="257 2515 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      T(x,y * x) * (x \ 1) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(2493(a,2),2939(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2493 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2943,a,b,2944,a),flip(a)].">
      <j1 rule="hyper" parents="34 2943 2944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(104(a,1),3024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="104 3024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(210(a,1),3024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="210 3024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2945(a,1),239(a,1,1))].">
      <j1 rule="para" parents="2945 239"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(2945(a,1),99(a,1,1))].">
      <j1 rule="para" parents="2945 99"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(2945(a,2),380(a,1,2))].">
      <j1 rule="para" parents="2945 380"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(2945(a,1),576(a,1,1))].">
      <j1 rule="para" parents="2945 576"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(2945(a,1),578(a,1,1))].">
      <j1 rule="para" parents="2945 578"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(2945(a,1),596(a,1,1))].">
      <j1 rule="para" parents="2945 596"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(2945(a,1),1107(a,2,1,2))].">
      <j1 rule="para" parents="2945 1107"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (x * L(y,z,u)) = y * K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1263(a,1),2945(a,1,1))].">
      <j1 rule="para" parents="1263 2945"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,x,y)) = a(z * K(x * y,z),x,y)
    ]]></literal>
    <justification jstring="[para(2945(a,1),830(a,2,1))].">
      <j1 rule="para" parents="2945 830"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[hyper(112,a,641,a,b,2951,a(flip))].">
      <j1 rule="hyper" parents="112 641 2951"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2953(a,1),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2953 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2968(a,2),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2968 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(2970(a,2),2162(a,1,1))].">
      <j1 rule="para" parents="2970 2162"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      (x * K(y,x)) \ x = K(x,y)
    ]]></literal>
    <justification jstring="[para(2945(a,1),2970(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2945 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2869,a(flip),b,3025,a),flip(a)].">
      <j1 rule="hyper" parents="63 2869 3025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(115,a,3025,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="115 3025 88"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2448(a,1),2989(a,1))].">
      <j1 rule="para" parents="2448 2989"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2316(a,2),2990(a,1))].">
      <j1 rule="para" parents="2316 2990"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(710,a,2940,a)].">
      <j1 rule="hyper" parents="710 2940"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1610,a(flip),b,2940,a)].">
      <j1 rule="hyper" parents="63 1610 2940"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,915,a(flip),b,2940,a)].">
      <j1 rule="hyper" parents="63 915 2940"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,770,a(flip),b,2940,a)].">
      <j1 rule="hyper" parents="63 770 2940"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,2940,a(flip),b,770,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 2940 770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(114,a,2940,a(flip),b,806,a)].">
      <j1 rule="hyper" parents="114 2940 806"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(114,a,2940,a(flip),b,867,a(flip))].">
      <j1 rule="hyper" parents="114 2940 867"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(2940(a,1),1014(a,2,1))].">
      <j1 rule="para" parents="2940 1014"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = y * K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(2940(a,1),1315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2940 1315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,2943,a(flip),b,2950,a)].">
      <j1 rule="hyper" parents="111 2943 2950"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(111,a,102,a(flip),b,2950,a)].">
      <j1 rule="hyper" parents="111 102 2950"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,2950,a)].">
      <j1 rule="hyper" parents="63 192 2950"/>
    </justification>
  </clause>

  <clause id="3069">
    <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),2950(a,2,1))].">
      <j1 rule="para" parents="27 2950"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(2950(a,1),268(a,1))].">
      <j1 rule="para" parents="2950 268"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(201(a,1),2950(a,1,2))].">
      <j1 rule="para" parents="201 2950"/>
    </justification>
  </clause>

  <clause id="3073">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(202(a,1),2950(a,1,2))].">
      <j1 rule="para" parents="202 2950"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2948(a,2),2950(a,1,2))].">
      <j1 rule="para" parents="2948 2950"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      L(x * K(y,x),K(x,y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(3066(a,1),92(a,1,1))].">
      <j1 rule="para" parents="3066 92"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(118,a,2962,a)].">
      <j1 rule="hyper" parents="118 2962"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(111,a,10,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="111 10 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,2943,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="110 2943 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(34,a,2515,a,b,2962,a)].">
      <j1 rule="hyper" parents="34 2515 2962"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2541,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="34 2541 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(1501(a,1),2962(a,1,2))].">
      <j1 rule="para" parents="1501 2962"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3083,a)].">
      <j1 rule="hyper" parents="123 3083"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,3083,a)].">
      <j1 rule="hyper" parents="118 3083"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3083(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3083 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3083(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3083 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3083(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3083 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      K(x,y) != 1 / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3087(a,1),45(a,1))].">
      <j1 rule="para" parents="3087 45"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(3087(a,1),2954(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3087 2954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(115,a,3088,a(flip),b,2953,a)].">
      <j1 rule="hyper" parents="115 3088 2953"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3088(a,1),1313(a,2,2,1))].">
      <j1 rule="para" parents="3088 1313"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2990,a,2964,a),flip(a)].">
      <j1 rule="hyper" parents="2990 2964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),3100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      K(x,T(y,y \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(103(a,2),3101(a,1,2))].">
      <j1 rule="para" parents="103 3101"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      K(x * y,T(x,y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3102(a,1,2,2))].">
      <j1 rule="para" parents="9 3102"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2530,a,b,2965,a)].">
      <j1 rule="hyper" parents="63 2530 2965"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,338,a,b,2965,a)].">
      <j1 rule="hyper" parents="63 338 2965"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2906,a(flip),b,2965,a)].">
      <j1 rule="hyper" parents="63 2906 2965"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(2989,a,2980,a),flip(a)].">
      <j1 rule="hyper" parents="2989 2980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(738,a,2982,a),flip(a)].">
      <j1 rule="hyper" parents="738 2982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(172,a,2982,a(flip),b,717,a)].">
      <j1 rule="hyper" parents="172 2982 717"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(115,a,2982,a(flip),b,717,a)].">
      <j1 rule="hyper" parents="115 2982 717"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(2983(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2983 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (K(u,z) * (T(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(2983(a,1),359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2983 359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(172,a,2992,a(flip),b,160,a)].">
      <j1 rule="hyper" parents="172 2992 160"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(40,a,2981,a,b,3009,a)].">
      <j1 rule="hyper" parents="40 2981 3009"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,2494,a,b,3009,a),flip(a)].">
      <j1 rule="hyper" parents="40 2494 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      R(x,y,z) * (x * (((u * R(x,y,z)) / u) \ 1)) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3022(a,2),1276(a,2,2))].">
      <j1 rule="para" parents="3022 1276"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(2945(a,1),3042(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2945 3042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      x * (y / x) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(3048(a,1),43(a,1))].">
      <j1 rule="para" parents="3048 43"/>
    </justification>
  </clause>

  <clause id="3124">
    <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),3082(a,1,2,1))].">
      <j1 rule="para" parents="27 3082"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,2953,a(flip),b,3110,a),flip(a)].">
      <j1 rule="hyper" parents="257 2953 3110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(112,a,2953,a(flip),b,3110,a)].">
      <j1 rule="hyper" parents="112 2953 3110"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,2962,a(flip),b,3112,a),flip(a)].">
      <j1 rule="hyper" parents="34 2962 3112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,742,a(flip),b,3112,a),flip(a)].">
      <j1 rule="hyper" parents="34 742 3112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3112(a,1),2983(a,1,2))].">
      <j1 rule="para" parents="3112 2983"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(268,a,3132,a),flip(a)].">
      <j1 rule="hyper" parents="268 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(204,a,3132,a),flip(a)].">
      <j1 rule="hyper" parents="204 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,3132,a)].">
      <j1 rule="hyper" parents="123 3132"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,x)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1501,a,b,3132,a),flip(a)].">
      <j1 rule="hyper" parents="34 1501 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,1501,a(flip),b,3132,a),flip(a)].">
      <j1 rule="hyper" parents="34 1501 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(318,a,3132,a(flip),b,131,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="318 3132 131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(115,a,3132,a(flip),b,160,a)].">
      <j1 rule="hyper" parents="115 3132 160"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(3132(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3132 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(3132(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3132 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(3132(a,1),92(a,2,2))].">
      <j1 rule="para" parents="3132 92"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(3135(a,1),218(a,1,2))].">
      <j1 rule="para" parents="3135 218"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3135(a,1),382(a,1,1,3))].">
      <j1 rule="para" parents="3135 382"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3137(a,1),182(a,1)),flip(b)].">
      <j1 rule="para" parents="3137 182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3125(a,1),214(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3125 214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2102,a,3085,a)].">
      <j1 rule="hyper" parents="2102 3085"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(3120(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3120 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      T(x,y \ x) * K(y \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(1209(a,1),3155(a,1,1))].">
      <j1 rule="para" parents="1209 3155"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2931(a,1,1,2,1))].">
      <j1 rule="para" parents="9 2931"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1585,a(flip),b,2936,a)].">
      <j1 rule="hyper" parents="63 1585 2936"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(115,a,2936,a(flip),b,1389,a(flip))].">
      <j1 rule="hyper" parents="115 2936 1389"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(114,a,2936,a(flip),b,1585,a(flip))].">
      <j1 rule="hyper" parents="114 2936 1585"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(2936(a,1),705(a,2,2))].">
      <j1 rule="para" parents="2936 705"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2936(a,1),1489(a,2,1))].">
      <j1 rule="para" parents="2936 1489"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(2936(a,1),2209(a,1,1))].">
      <j1 rule="para" parents="2936 2209"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(172,a,2949,a(flip),b,3135,a)].">
      <j1 rule="hyper" parents="172 2949 3135"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,2929,a,b,2969,a),flip(a)].">
      <j1 rule="hyper" parents="257 2929 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3168(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y) * 1
    ]]></literal>
    <justification jstring="[hyper(257,a,8,a,b,3171,a),flip(a)].">
      <j1 rule="hyper" parents="257 8 3171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(3039,a,3023,a)].">
      <j1 rule="hyper" parents="3039 3023"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2157,a,3074,a(flip))].">
      <j1 rule="hyper" parents="2157 3074"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2156,a,3074,a(flip))].">
      <j1 rule="hyper" parents="2156 3074"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3074(a,2),2156(a,1))].">
      <j1 rule="para" parents="3074 2156"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      (x \ y) / (((z * x) / z) \ y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,3084,a,b,3135,a)].">
      <j1 rule="hyper" parents="172 3084 3135"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(115,a,3132,a(flip),b,3105,a)].">
      <j1 rule="hyper" parents="115 3132 3105"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * ((y * (u \ z)) * T(L(T(u,u \ z),u \ z,y),x)) = y * z
    ]]></literal>
    <justification jstring="[para(273(a,2),3133(a,1,2,2,1))].">
      <j1 rule="para" parents="273 3133"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      x / (y * (z * T(z \ (y \ x),u))) = K(u,x / (y * z))
    ]]></literal>
    <justification jstring="[para(609(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="609 3167"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      x / (((y \ (x / z)) * y) * z) = K(y,x / (y * z))
    ]]></literal>
    <justification jstring="[para(915(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="915 3167"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(998(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="998 3167"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(3172(a,2),119(a,1)),flip(b)].">
      <j1 rule="para" parents="3172 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      (T(x,y) \ z) / ((((x * y) * R(T(x,y),u,w)) / (R(x,u,w) * y)) \ z) = K(R(x,u,w) * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1358(a,1),3178(a,1,2,1,1))].">
      <j1 rule="para" parents="1358 3178"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(903,a,3181,a)].">
      <j1 rule="hyper" parents="903 3181"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(257,a,3134,a,b,3181,a)].">
      <j1 rule="hyper" parents="257 3134 3181"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3181(a,1),575(a,1,1))].">
      <j1 rule="para" parents="3181 575"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(2951(a,1),3191(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2951 3191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2861,a,3199,a)].">
      <j1 rule="hyper" parents="2861 3199"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(79(a,1),2966(a,1,2))].">
      <j1 rule="para" parents="79 2966"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(3103(a,1),3008(a,1,2))].">
      <j1 rule="para" parents="3103 3008"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,3205,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="111 3205 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(3205(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3205 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(770(a,1),3049(a,1))].">
      <j1 rule="para" parents="770 3049"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(1603(a,1),3049(a,1))].">
      <j1 rule="para" parents="1603 3049"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / (y * u)) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),3188(a,1,2,1))].">
      <j1 rule="para" parents="99 3188"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1503,a,3206,a)].">
      <j1 rule="hyper" parents="1503 3206"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(3109(a,2),3212(a,1,1))].">
      <j1 rule="para" parents="3109 3212"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2959,a,b,3010,a)].">
      <j1 rule="hyper" parents="35 2959 3010"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      a(x,y,z * K(x * y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,3013,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="111 3013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(111,a,3032,a,b,2945,a(flip))].">
      <j1 rule="hyper" parents="111 3032 2945"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3032(a,2),2970(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3032 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,2945,a(flip),b,3033,a)].">
      <j1 rule="hyper" parents="257 2945 3033"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(2842,a,3057,a),flip(a)].">
      <j1 rule="hyper" parents="2842 3057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,915,a(flip),b,3057,a)].">
      <j1 rule="hyper" parents="63 915 3057"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,3057,a(flip),b,614,a(flip))].">
      <j1 rule="hyper" parents="115 3057 614"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K(((x * y) / (x * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(112,a,608,a(flip),b,3059,a)].">
      <j1 rule="hyper" parents="112 608 3059"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2949,a,b,3059,a),flip(a)].">
      <j1 rule="hyper" parents="35 2949 3059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),3230(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 3230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(3106(a,2),204(a,2)),flip(a)].">
      <j1 rule="para" parents="3106 204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,3119,a)].">
      <j1 rule="hyper" parents="118 3119"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = a(x,y,z * K(x * y,z))
    ]]></literal>
    <justification jstring="[para(3217(a,1),560(a,1,1))].">
      <j1 rule="para" parents="3217 560"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * K(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(3236(a,1),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3236 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(3057(a,2),3236(a,1,2,1))].">
      <j1 rule="para" parents="3057 3236"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1942(a,1),2956(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1942 2956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,x,R(y,z,u))) = R(y,x,R(y,z,u)) / T(y,x)
    ]]></literal>
    <justification jstring="[para(1223(a,1),3007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1223 3007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,27,a,b,3156,a),flip(a)].">
      <j1 rule="hyper" parents="257 27 3156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ x) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2153(a,1),3158(a,1,2))].">
      <j1 rule="para" parents="2153 3158"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2929(a,2),2933(a,1,1))].">
      <j1 rule="para" parents="2929 2933"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2599(a,1),3244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2599 3244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,(z * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      ((z * y) / z) \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(3035(a,1),306(a,1,1))].">
      <j1 rule="para" parents="3035 306"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1119,a(flip),b,3052,a)].">
      <j1 rule="hyper" parents="63 1119 3052"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(614(a,1),3052(a,1,2))].">
      <j1 rule="para" parents="614 3052"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2940(a,1),3053(a,1,1))].">
      <j1 rule="para" parents="2940 3053"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3254(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2144(a,1),3254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2144 3254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      K(R(R(1 / x,y,z),u,w) \ 1,v5) = R(R(K(x,v5),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3255(a,1),3254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3255 3254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(3256(a,1),3135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3256 3135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3058(a,2),3061(a,1,2))].">
      <j1 rule="para" parents="3058 3061"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1520(a,1),3160(a,1,1))].">
      <j1 rule="para" parents="1520 3160"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1554(a,1),3160(a,1,1))].">
      <j1 rule="para" parents="1554 3160"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,3162,a,b,3163,a),flip(a)].">
      <j1 rule="hyper" parents="257 3162 3163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[para(2837(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="2837 3186"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(2845(a,1),3187(a,1,2))].">
      <j1 rule="para" parents="2845 3187"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(3088(a,1),3224(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="3088 3224"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),3259(a,1,2,1,1))].">
      <j1 rule="para" parents="79 3259"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(3171(a,1),3263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3171 3263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(204,a,3269,a)].">
      <j1 rule="hyper" parents="204 3269"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      L(x * K(y,x),K(x * K(y,x),y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(3018(a,2),3075(a,1,2))].">
      <j1 rule="para" parents="3018 3075"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,u) = w
    ]]></literal>
    <justification jstring="[para(1432(a,1),3208(a,1,2))].">
      <j1 rule="para" parents="1432 3208"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,3217,a(flip),b,3237,a),flip(a)].">
      <j1 rule="hyper" parents="257 3217 3237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      ((R(x,y,z) * u) * w) / ((x * u) * w) = R(x,u,w) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2197,a(flip),b,3273,a)].">
      <j1 rule="hyper" parents="63 2197 3273"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1943,a(flip),b,3273,a)].">
      <j1 rule="hyper" parents="63 1943 3273"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2500,a,3072,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2500 3072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2501,a,3073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2501 3073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ z,y,x) / z)) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3164(a,1),1556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3164 1556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      ((x * y) * z) / (x * (z * T(z \ (x \ ((x * y) * z)),u))) = K(u,R(y * K(x,y),x,z))
    ]]></literal>
    <justification jstring="[para(3030(a,2),3185(a,2,2))].">
      <j1 rule="para" parents="3030 3185"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      (x \ R(y,z,u)) * K(((x \ R(y,z,u)) \ (x \ 1)) \ 1,w) = x \ R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),3221(a,2,2))].">
      <j1 rule="para" parents="27 3221"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(2844,a,3222,a),flip(a)].">
      <j1 rule="hyper" parents="2844 3222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,66,a(flip),b,3240,a),flip(a)].">
      <j1 rule="hyper" parents="257 66 3240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,3286,a,b,3083,a),flip(a)].">
      <j1 rule="hyper" parents="110 3286 3083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) = v5 \ v5
    ]]></literal>
    <justification jstring="[hyper(257,a,66,a,b,3288,a),flip(a)].">
      <j1 rule="hyper" parents="257 66 3288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(3289(a,2),145(a,1)),flip(b)].">
      <j1 rule="para" parents="3289 145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),3252(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3265,a(flip),b,3266,a),flip(a)].">
      <j1 rule="hyper" parents="63 3265 3266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3000,a,2825,a)].">
      <j1 rule="hyper" parents="3000 2825"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),y * R(x,z,u)) * (T(x,y) \ w) = R(x,y,R(x,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(1223(a,1),3124(a,1,2,1))].">
      <j1 rule="para" parents="1223 3124"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(2940(a,1),3209(a,1,1))].">
      <j1 rule="para" parents="2940 3209"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3296,a,xx),flip(a)].">
      <j1 rule="hyper" parents="3296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,3297,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 3297 18"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2144(a,1),3297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2144 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(3299(a,1),3135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3299 3135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(3247(a,1),3300(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3247 3300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2110,a,3301,a)].">
      <j1 rule="hyper" parents="2110 3301"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,8,a(flip),b,3301,a),flip(a)].">
      <j1 rule="hyper" parents="257 8 3301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(3301(a,2),119(a,1)),flip(b)].">
      <j1 rule="para" parents="3301 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      L(K(x,y),z,u) != w \ 1
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(3303(a,1),48(a,1))].">
      <j1 rule="para" parents="3303 48"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      R(R(K(x,y),x,x \ z),z,u) = K((((x \ z) * u) / (z * u)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(443(a,1),3257(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="443 3257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(643(a,1),3261(a,1,1,1))].">
      <j1 rule="para" parents="643 3261"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(3057(a,2),3267(a,1,2))].">
      <j1 rule="para" parents="3057 3267"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),3268(a,2,1,1))].">
      <j1 rule="para" parents="79 3268"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3309(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      (K(x,y) * ((1 / x) * z)) / (K(x,y) * z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(428,a,3310,a)].">
      <j1 rule="hyper" parents="428 3310"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      K(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y)
    ]]></literal>
    <justification jstring="[para(2489(a,1),3279(a,1,2))].">
      <j1 rule="para" parents="2489 3279"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      K(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y) * T(x * R(y,z,u),x) = R(y,z,u) * T(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y)
    ]]></literal>
    <justification jstring="[para(2489(a,1),3280(a,1,2))].">
      <j1 rule="para" parents="2489 3280"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3251,a,b,3291,a)].">
      <j1 rule="hyper" parents="63 3251 3291"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(118,a,3308,a)].">
      <j1 rule="hyper" parents="118 3308"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(114,a,3316,a(flip),b,2811,a)].">
      <j1 rule="hyper" parents="114 3316 2811"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      a(x,y,z) \ T(a(x,y,z) * u,w) != u * v5
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(2946(a,2),43(a,1))].">
      <j1 rule="para" parents="2946 43"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ z) / z),y,x) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2897(a,2),3282(a,1,2))].">
      <j1 rule="para" parents="2897 3282"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      x * (y * (z * ((y \ z) / z))) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(236,a,3320,a)].">
      <j1 rule="hyper" parents="236 3320"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * y = x * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(2358(a,1),3321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2358 3321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2599(a,1),3322(a,1,1,2))].">
      <j1 rule="para" parents="2599 3322"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(1990(a,1),3324(a,2,2))].">
      <j1 rule="para" parents="1990 3324"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(2998,a,3325,a)].">
      <j1 rule="hyper" parents="2998 3325"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,3325,a)].">
      <j1 rule="hyper" parents="123 3325"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(118,a,3325,a)].">
      <j1 rule="hyper" parents="118 3325"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(112,a,12,a(flip),b,3325,a),flip(a)].">
      <j1 rule="hyper" parents="112 12 3325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,947,a,b,3325,a)].">
      <j1 rule="hyper" parents="35 947 3325"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,942,a,b,3325,a),flip(a)].">
      <j1 rule="hyper" parents="35 942 3325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(318,a,948,a(flip),b,3328,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="318 948 3328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,948,a(flip),b,3328,a(flip))].">
      <j1 rule="hyper" parents="111 948 3328"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(2997,a,3329,a)].">
      <j1 rule="hyper" parents="2997 3329"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3271,a(flip),b,3338,a)].">
      <j1 rule="hyper" parents="63 3271 3338"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(z,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(115,a,3338,a(flip),b,3271,a(flip))].">
      <j1 rule="hyper" parents="115 3338 3271"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(3338(a,1),329(a,1,2,1))].">
      <j1 rule="para" parents="3338 329"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(270,a,3331,a)].">
      <j1 rule="hyper" parents="270 3331"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,159,a(flip),b,3331,a(flip))].">
      <j1 rule="hyper" parents="111 159 3331"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(111,a,3331,a(flip),b,3325,a)].">
      <j1 rule="hyper" parents="111 3331 3325"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2993,a,3332,a)].">
      <j1 rule="hyper" parents="2993 3332"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,3325,a,b,3332,a)].">
      <j1 rule="hyper" parents="257 3325 3332"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      ((x / T(y,z)) * y) \ x = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,12,a(flip),b,3332,a)].">
      <j1 rule="hyper" parents="111 12 3332"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      R(x * y,K(y,x),K(x,z)) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(3332(a,1),408(a,1,2))].">
      <j1 rule="para" parents="3332 408"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      ((x * y) * T(z,u)) / ((y * z) * K(z,u)) = R(R(x,y,z),y * z,K(z,u))
    ]]></literal>
    <justification jstring="[para(3332(a,1),386(a,1,1))].">
      <j1 rule="para" parents="3332 386"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      L(x \ T(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(448,a,3337,a)].">
      <j1 rule="hyper" parents="448 3337"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(3337(a,1),217(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3337 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2929(a,2),3354(a,1,1))].">
      <j1 rule="para" parents="2929 3354"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(257,a,3088,a,b,3359,a),flip(a)].">
      <j1 rule="hyper" parents="257 3088 3359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      (x * y) * T(K(y,z),u) = x * (y * T(K(y,z),u))
    ]]></literal>
    <justification jstring="[para(3359(a,1),333(a,1,2,1))].">
      <j1 rule="para" parents="3359 333"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      (x / y) * (y * R(K(y,z),u,w)) = x * R(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3359(a,1),502(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3359 502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3305,a,3360,a)].">
      <j1 rule="hyper" parents="3305 3360"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3360(a,2),3091(a,1))].">
      <j1 rule="para" parents="3360 3091"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3363,a,b,3363,a)].">
      <j1 rule="hyper" parents="257 3363 3363"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,3363,a,b,2774,a),flip(a)].">
      <j1 rule="hyper" parents="110 3363 2774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,3363,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="115 3363 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(115,a,3363,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 3363 18"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3365(a,1),212(a,1))].">
      <j1 rule="para" parents="3365 212"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(172,a,2945,a,b,3339,a)].">
      <j1 rule="hyper" parents="172 2945 3339"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * R(x \ (x * K(y,z)),u,w)) * y) = (y * K(z,y)) * R(((x * K(y,z)) \ (x * y)) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(3339(a,1),1214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3339 1214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(3235,a,3342,a),flip(a)].">
      <j1 rule="hyper" parents="3235 3342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(669,a,3342,a)].">
      <j1 rule="hyper" parents="669 3342"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2949,a,b,3342,a)].">
      <j1 rule="hyper" parents="63 2949 3342"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(203,a,2949,a,b,3342,a(flip))].">
      <j1 rule="hyper" parents="203 2949 3342"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,3057,a(flip),b,3342,a(flip))].">
      <j1 rule="hyper" parents="34 3057 3342"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(3342(a,2),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3342 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(3342(a,1),1314(a,2,1))].">
      <j1 rule="para" parents="3342 1314"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2094,a(flip),b,3380,a),flip(a)].">
      <j1 rule="hyper" parents="257 2094 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(103(a,2),3380(a,1,1))].">
      <j1 rule="para" parents="103 3380"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),3390(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      K(T(x,x \ y) \ 1,z) = K(y \ (x \ y),z)
    ]]></literal>
    <justification jstring="[para(103(a,2),3386(a,1,1,1))].">
      <j1 rule="para" parents="103 3386"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(z \ y,x) \ 1
    ]]></literal>
    <justification jstring="[para(3386(a,1),3088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3386 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(3386(a,1),3285(a,1,2))].">
      <j1 rule="para" parents="3386 3285"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(3386(a,1),3297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3386 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      (x / y) * (z / (z / y)) = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(2918(a,2),3367(a,1,2))].">
      <j1 rule="para" parents="2918 3367"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3368,a(flip),b,3328,a)].">
      <j1 rule="hyper" parents="114 3368 3328"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(305,a,3377,a)].">
      <j1 rule="hyper" parents="305 3377"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3035,a(flip),b,3377,a)].">
      <j1 rule="hyper" parents="63 3035 3377"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1107,a(flip),b,3377,a)].">
      <j1 rule="hyper" parents="63 1107 3377"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      K(x / (x / y),z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3382(a,2,2,1))].">
      <j1 rule="para" parents="79 3382"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3088,a(flip),b,3396,a),flip(a)].">
      <j1 rule="hyper" parents="257 3088 3396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3396(a,2),3091(a,1))].">
      <j1 rule="para" parents="3396 3091"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(113,a,3405,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 3405 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3270,a,b,3405,a)].">
      <j1 rule="hyper" parents="63 3270 3405"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(3405(a,1),3244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3405 3244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3407(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(76(a,1),3408(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(313,a,3415,a),flip(a)].">
      <j1 rule="hyper" parents="313 3415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(103(a,2),3418(a,1,2))].">
      <j1 rule="para" parents="103 3418"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2490(a,2),3418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2490 3418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),3422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(257,a,3424,a,b,3425,a)].">
      <j1 rule="hyper" parents="257 3424 3425"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3401(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      (x * ((y * z) / y)) * K(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(11(a,1),3403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(3426(a,2),3095(a,1,1))].">
      <j1 rule="para" parents="3426 3095"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3429(a,1,1,2,1))].">
      <j1 rule="para" parents="10 3429"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      ((x * y) / x) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(2951(a,2),3355(a,1,1))].">
      <j1 rule="para" parents="2951 3355"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) \ (u * y)) = w
    ]]></literal>
    <justification jstring="[para(92(a,2),3406(a,1,2,1))].">
      <j1 rule="para" parents="92 3406"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3270(a,2),3406(a,1))].">
      <j1 rule="para" parents="3270 3406"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      K(x,R(x,y,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ R(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(2159(a,1),3435(a,1))].">
      <j1 rule="para" parents="2159 3435"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3067,a(flip),b,3336,a),flip(a)].">
      <j1 rule="hyper" parents="63 3067 3336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      K(x / y,(x / y) \ x) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(3123,a,3399,a)].">
      <j1 rule="hyper" parents="3123 3399"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(112,a,3400,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="112 3400 98"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(3056(a,1),3388(a,1))].">
      <j1 rule="para" parents="3056 3388"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),3442(a,1,1,1))].">
      <j1 rule="para" parents="22 3442"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      K(L(x \ y,x,z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * y) \ (z * x),u) = w
    ]]></literal>
    <justification jstring="[para(92(a,2),3442(a,1,1,1))].">
      <j1 rule="para" parents="92 3442"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(3135(a,1),3442(a,1,1,1))].">
      <j1 rule="para" parents="3135 3442"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3361(a,1),3097(a,1,2))].">
      <j1 rule="para" parents="3361 3097"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(111,a,3389,a(flip),b,3342,a(flip))].">
      <j1 rule="hyper" parents="111 3389 3342"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),3449(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(3434,a,3413,a),flip(a)].">
      <j1 rule="hyper" parents="3434 3413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3452(a,2,2,1))].">
      <j1 rule="para" parents="10 3452"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3452(a,2,2,2))].">
      <j1 rule="para" parents="10 3452"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(92(a,2),3452(a,2,2))].">
      <j1 rule="para" parents="92 3452"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(3364,a,3453,a)].">
      <j1 rule="hyper" parents="3364 3453"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(3453(a,1),25(a,2,1))].">
      <j1 rule="para" parents="3453 25"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(3444,a,3398,a),flip(a)].">
      <j1 rule="hyper" parents="3444 3398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3458(a,2,1,1))].">
      <j1 rule="para" parents="10 3458"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3458(a,2,1,2))].">
      <j1 rule="para" parents="10 3458"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),3458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(3374,a,3459,a)].">
      <j1 rule="hyper" parents="3374 3459"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3453,a(flip),b,3459,a)].">
      <j1 rule="hyper" parents="63 3453 3459"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(3459(a,1),3374(a,1))].">
      <j1 rule="para" parents="3459 3374"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      K((x * ((x \ y) / z)) \ y,u) = L(K(z,u),x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3461(a,1,1,2))].">
      <j1 rule="para" parents="10 3461"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(94(a,2),3461(a,1,1))].">
      <j1 rule="para" parents="94 3461"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(257,a,18,a(flip),b,3466,a),flip(a)].">
      <j1 rule="hyper" parents="257 18 3466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3466(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(3466(a,1),3088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3466 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3303,a(flip),b,3469,a),flip(a)].">
      <j1 rule="hyper" parents="257 3303 3469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(3469(a,2),3304(a,1))].">
      <j1 rule="para" parents="3469 3304"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),3470(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 3470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(115,a,3460,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="115 3460 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(3467(a,2),362(a,1))].">
      <j1 rule="para" parents="3467 362"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      K(L(x \ y,x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x \ y,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(76(a,1),3475(a,1,1,2))].">
      <j1 rule="para" parents="76 3475"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(1080(a,1),3476(a,1,1))].">
      <j1 rule="para" parents="1080 3476"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      K((R(x,y,z) \ (R(x,y,z) * (x \ u))) \ u,w \ (R(x,y,z) * u)) = K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u)
    ]]></literal>
    <justification jstring="[para(1277(a,1),3463(a,2,1))].">
      <j1 rule="para" parents="1277 3463"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(246(a,1),3474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="246 3474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,3397,a,b,3479,a),flip(a)].">
      <j1 rule="hyper" parents="34 3397 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(172,a,3480,a(flip),b,3088,a)].">
      <j1 rule="hyper" parents="172 3480 3088"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(3090,a,3481,a),flip(a)].">
      <j1 rule="hyper" parents="3090 3481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(3325(a,1),3440(a,1,2))].">
      <j1 rule="para" parents="3325 3440"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(390,a,3483,a),flip(a)].">
      <j1 rule="hyper" parents="390 3483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(2961(a,1),3484(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2961 3484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      (x * K(y \ z,y)) * y = x * (y * K(y \ z,y))
    ]]></literal>
    <justification jstring="[para(2106(a,1),2911(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2106 2911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3489(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),3492(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (z * K(y,z))) = z
    ]]></literal>
    <justification jstring="[hyper(118,a,3493,a)].">
      <j1 rule="hyper" parents="118 3493"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,3340,a(flip),b,3493,a),flip(a)].">
      <j1 rule="hyper" parents="35 3340 3493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(3332(a,1),3493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3332 3493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(261,a,3496,a),flip(a)].">
      <j1 rule="hyper" parents="261 3496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,3496,a)].">
      <j1 rule="hyper" parents="118 3496"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,3332,a,b,3496,a),flip(a)].">
      <j1 rule="hyper" parents="35 3332 3496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,3330,a,b,3496,a),flip(a)].">
      <j1 rule="hyper" parents="35 3330 3496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(3496(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="3496 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(3496(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3496 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(3499(a,1),398(a,1,1))].">
      <j1 rule="para" parents="3499 398"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3247,a(flip),b,3500,a),flip(a)].">
      <j1 rule="hyper" parents="257 3247 3500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,3348,a,b,3500,a)].">
      <j1 rule="hyper" parents="39 3348 3500"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(3342(a,2),3500(a,1,1))].">
      <j1 rule="para" parents="3342 3500"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,3501,a(flip),b,3328,a),flip(a)].">
      <j1 rule="hyper" parents="114 3501 3328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(270,a,3502,a),flip(a)].">
      <j1 rule="hyper" parents="270 3502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3181,a(flip),b,3502,a)].">
      <j1 rule="hyper" parents="63 3181 3502"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(3216(a,1),3504(a,1,1))].">
      <j1 rule="para" parents="3216 3504"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(3342(a,2),3504(a,1,1))].">
      <j1 rule="para" parents="3342 3504"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      (x * ((x \ y) * K(z \ (x \ y),u))) \ y != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * z) \ y) = w
    ]]></literal>
    <justification jstring="[para(3474(a,2),3504(a,1,1))].">
      <j1 rule="para" parents="3474 3504"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(523,a,3495,a)].">
      <j1 rule="hyper" parents="523 3495"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[para(2095(a,1),3523(a,1,1))].">
      <j1 rule="para" parents="2095 3523"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(3524(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="3524 330"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(609(a,1),3510(a,1,1))].">
      <j1 rule="para" parents="609 3510"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(941(a,1),3510(a,1,1))].">
      <j1 rule="para" parents="941 3510"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(111,a,90,a(flip),b,3511,a)].">
      <j1 rule="hyper" parents="111 90 3511"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(3498(a,1),3118(a,1,1))].">
      <j1 rule="para" parents="3498 3118"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(257,a,2465,a,b,3515,a),flip(a)].">
      <j1 rule="hyper" parents="257 2465 3515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(609(a,1),3521(a,1,1))].">
      <j1 rule="para" parents="609 3521"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(3206(a,1),3533(a,1,2))].">
      <j1 rule="para" parents="3206 3533"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(3299(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="3299 3508"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(39,a,2743,a(flip),b,3537,a),flip(a)].">
      <j1 rule="hyper" parents="39 2743 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(39,a,18,a(flip),b,3537,a),flip(a)].">
      <j1 rule="hyper" parents="39 18 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),3537(a,1,1))].">
      <j1 rule="para" parents="90 3537"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(353(a,1),3537(a,1,1))].">
      <j1 rule="para" parents="353 3537"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(3540(a,1),237(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3540 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) = L(K(u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(3332(a,1),3541(a,1,1,2))].">
      <j1 rule="para" parents="3332 3541"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      R(x,K(y,z),R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,3525,a)].">
      <j1 rule="hyper" parents="388 3525"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3505,a(flip),b,3545,a)].">
      <j1 rule="hyper" parents="63 3505 3545"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(609(a,1),3529(a,1,1,2))].">
      <j1 rule="para" parents="609 3529"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(998(a,1),3529(a,1,1,2))].">
      <j1 rule="para" parents="998 3529"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,25,a,b,3531,a),flip(a)].">
      <j1 rule="hyper" parents="257 25 3531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      (x * T(y,L(z * K(y,z),y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(2981(a,1),3550(a,2,1))].">
      <j1 rule="para" parents="2981 3550"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(390,a,3532,a),flip(a)].">
      <j1 rule="hyper" parents="390 3532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,3472,a(flip),b,3544,a),flip(a)].">
      <j1 rule="hyper" parents="257 3472 3544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x))
    ]]></literal>
    <justification jstring="[para(102(a,1),3553(a,1,1,2))].">
      <j1 rule="para" parents="102 3553"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,3554,a)].">
      <j1 rule="hyper" parents="125 3554"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      (x * (y * z)) * u != x * (z * y)
    ]]></literal>
    <literal><![CDATA[
      K(z,L(y,z,x)) = u
    ]]></literal>
    <justification jstring="[para(3555(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3555 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(79(a,1),3530(a,1,1,1,2,1))].">
      <j1 rule="para" parents="79 3530"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(z,(x * (y \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(632(a,1),3534(a,1,1,2))].">
      <j1 rule="para" parents="632 3534"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      a(x * K(y * z,x),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2632,a(flip),b,3037,a),flip(a)].">
      <j1 rule="hyper" parents="63 2632 3037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      T(x,y \ R(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(3559(a,1),2792(a,1,2))].">
      <j1 rule="para" parents="3559 2792"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      T(x \ R(x,y,z),z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(113,a,3561,a,b,2480,a)].">
      <j1 rule="hyper" parents="113 3561 2480"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      T(((x * (y / z)) \ (x * y)) \ R((x * (y / z)) \ (x * y),u,w),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(505(a,1),3562(a,2,2))].">
      <j1 rule="para" parents="505 3562"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      (K(x,y) * (((1 / x) * z) * T(((1 / x) * z) \ z,u))) / (K(x,y) * z) = K((1 / x) \ 1,u)
    ]]></literal>
    <justification jstring="[para(3312(a,1),3228(a,2,1,1))].">
      <j1 rule="para" parents="3312 3228"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),3262(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 3262"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3171,a(flip),b,3565,a),flip(a)].">
      <j1 rule="hyper" parents="257 3171 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(3565(a,2),3188(a,1))].">
      <j1 rule="para" parents="3565 3188"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(3566(a,1),400(a,1,1))].">
      <j1 rule="para" parents="3566 400"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      K((((x \ y) * z) / (y * z)) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2427(a,1),3306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2427 3306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3230,a(flip),b,3572,a)].">
      <j1 rule="hyper" parents="63 3230 3572"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(170(a,1),3573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="170 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(97(a,2),3573(a,1,1))].">
      <j1 rule="para" parents="97 3573"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,286,a(flip),b,3577,a),flip(a)].">
      <j1 rule="hyper" parents="257 286 3577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,3577,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="114 3577 20"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3577(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2652(a,1),3577(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2652 3577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(3577(a,1),3500(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3577 3500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[hyper(257,a,3500,a,b,3581,a),flip(a)].">
      <j1 rule="hyper" parents="257 3500 3581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3583(a,2),3504(a,1))].">
      <j1 rule="para" parents="3583 3504"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3200,a(flip),b,3576,a),flip(a)].">
      <j1 rule="hyper" parents="63 3200 3576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3393,a(flip),b,3585,a),flip(a)].">
      <j1 rule="hyper" parents="257 3393 3585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),3586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 3586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),3587(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 3587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(3190(a,1),3307(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3190 3307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(257,a,2811,a(flip),b,3589,a),flip(a)].">
      <j1 rule="hyper" parents="257 2811 3589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(3188,a,3590,a)].">
      <j1 rule="hyper" parents="3188 3590"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(2568(a,1),3591(a,1,2))].">
      <j1 rule="para" parents="2568 3591"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3450,a,b,3592,a)].">
      <j1 rule="hyper" parents="257 3450 3592"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(2914(a,1),3549(a,1,1,2))].">
      <j1 rule="para" parents="2914 3549"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(3331(a,1),3557(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3331 3557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(115,a,3595,a,b,xx)].">
      <j1 rule="hyper" parents="115 3595"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = (y * (K(z,x) * L(z,u,w))) \ (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3341(a,1),3595(a,2,1))].">
      <j1 rule="para" parents="3341 3595"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(3344(a,1),3596(a,1,2,2))].">
      <j1 rule="para" parents="3344 3596"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3496(a,1),3598(a,1,1,1))].">
      <j1 rule="para" parents="3496 3598"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(3036(a,1),540(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3036 540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),T(x,y)) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3119,a,b,3600,a)].">
      <j1 rule="hyper" parents="63 3119 3600"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      R(x,y,z) * (x * (R((u * x) / u,y,z) \ 1)) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(576(a,2),3121(a,1,2,2,1))].">
      <j1 rule="para" parents="576 3121"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(3542(a,1),3522(a,1))].">
      <j1 rule="para" parents="3542 3522"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1449(a,1),3603(a,1,2))].">
      <j1 rule="para" parents="1449 3603"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(652(a,1),3315(a,1,1))].">
      <j1 rule="para" parents="652 3315"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1006(a,1),3607(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1006 3607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = ((x * y) * T(z,u)) / (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3332(a,1),3350(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3332 3350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,20,a,b,3611,a),flip(a)].">
      <j1 rule="hyper" parents="257 20 3611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(3611(a,2),390(a,1))].">
      <j1 rule="para" parents="3611 390"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31,a,b,3612,a)].">
      <j1 rule="hyper" parents="63 31 3612"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(102(a,1),3548(a,1,1,2,2))].">
      <j1 rule="para" parents="102 3548"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2912(a,2),3615(a,1,1))].">
      <j1 rule="para" parents="2912 3615"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(3012(a,1),3551(a,1,1,2))].">
      <j1 rule="para" parents="3012 3551"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(2992(a,1),3617(a,1,2,2))].">
      <j1 rule="para" parents="2992 3617"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(2870(a,1),3608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2870 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3050,a,3619,a(flip))].">
      <j1 rule="hyper" parents="3050 3619"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3620(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(3135(a,1),3621(a,1,2))].">
      <j1 rule="para" parents="3135 3621"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3592(a,2),3622(a,1,1))].">
      <j1 rule="para" parents="3592 3622"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(433,a,3623,a)].">
      <j1 rule="hyper" parents="433 3623"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(3165(a,1),3166(a,2,1))].">
      <j1 rule="para" parents="3165 3166"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,98,a,b,3625,a)].">
      <j1 rule="hyper" parents="35 98 3625"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,2430,a(flip),b,3625,a),flip(a)].">
      <j1 rule="hyper" parents="35 2430 3625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(31(a,1),3627(a,1,2,1))].">
      <j1 rule="para" parents="31 3627"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2599(a,1),3626(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2599 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(3171(a,1),3626(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3171 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(3629(a,1),3258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3629 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      R(x,R(K(y,z),u,w),y) = x
    ]]></literal>
    <justification jstring="[para(3629(a,1),3326(a,1,2))].">
      <j1 rule="para" parents="3629 3326"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * y = x * (R(K(y,z),u,w) * y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3632,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 3632 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(457,a,3631,a)].">
      <j1 rule="hyper" parents="457 3631"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(3211,a,3630,a),flip(a)].">
      <j1 rule="hyper" parents="3211 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),3635(a,2,2,1))].">
      <j1 rule="para" parents="12 3635"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),3635(a,2,2,2))].">
      <j1 rule="para" parents="12 3635"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(76(a,1),3635(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(3100(a,1),3637(a,1,1))].">
      <j1 rule="para" parents="3100 3637"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(x,y,z) / (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(3637(a,1),3584(a,1))].">
      <j1 rule="para" parents="3637 3584"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(97(a,2),3638(a,1,2))].">
      <j1 rule="para" parents="97 3638"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3582,a(flip),b,3641,a)].">
      <j1 rule="hyper" parents="63 3582 3641"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),3641(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(3644(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3644 27"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(2443,a,3639,a),flip(a)].">
      <j1 rule="hyper" parents="2443 3639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,3171,a,b,3639,a),flip(a)].">
      <j1 rule="hyper" parents="257 3171 3639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(3639(a,1),2443(a,1))].">
      <j1 rule="para" parents="3639 2443"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1264(a,1),3647(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1264 3647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(407(a,1),3628(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="407 3628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = T(K(x,(y / (x * z)) \ 1),u)
    ]]></literal>
    <justification jstring="[para(3648(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3648 27"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * y = x * (y * R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2148(a,1),3633(a,2,2))].">
      <j1 rule="para" parents="2148 3633"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(2903(a,1),3651(a,1,2,1))].">
      <j1 rule="para" parents="2903 3651"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3456,a(flip),b,3655,a)].">
      <j1 rule="hyper" parents="63 3456 3655"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(856(a,1),3656(a,1,2)),flip(a)].">
      <j1 rule="para" parents="856 3656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(3272,a,3239,a)].">
      <j1 rule="hyper" parents="3272 3239"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3386,a(flip),b,3658,a),flip(a)].">
      <j1 rule="hyper" parents="257 3386 3658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(3442,a,3659,a)].">
      <j1 rule="hyper" parents="3442 3659"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      x / K(y \ x,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(3660(a,1),2975(a,1,2))].">
      <j1 rule="para" parents="3660 2975"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(3558,a,3594,a),flip(a)].">
      <j1 rule="hyper" parents="3558 3594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(76(a,1),3662(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="76 3662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(332(a,1),3663(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="332 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3509(a,1),3664(a,1,2,1))].">
      <j1 rule="para" parents="3509 3664"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2973(a,1),3665(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2973 3665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((x * z) * u) / ((y * z) * u)) = w
    ]]></literal>
    <justification jstring="[para(3652(a,2),3188(a,1))].">
      <j1 rule="para" parents="3652 3188"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(195(a,1),2831(a,1,1)),flip(a)].">
      <j1 rule="para" parents="195 2831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(2930(a,2),3668(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2930 3668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2930(a,2),3670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2930 3670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,3346,a,b,3671,a),flip(a)].">
      <j1 rule="hyper" parents="35 3346 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3672,a)].">
      <j1 rule="hyper" parents="125 3672"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),3673(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,3674,a)].">
      <j1 rule="hyper" parents="388 3674"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(361,a,3674,a)].">
      <j1 rule="hyper" parents="361 3674"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3675(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3675 27"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(3675(a,1),325(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3675 325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(3604,a,3676,a)].">
      <j1 rule="hyper" parents="3604 3676"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3472,a(flip),b,3676,a)].">
      <j1 rule="hyper" parents="63 3472 3676"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3468,a(flip),b,3676,a)].">
      <j1 rule="hyper" parents="63 3468 3676"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3453,a(flip),b,3676,a),flip(a)].">
      <j1 rule="hyper" parents="63 3453 3676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      K(x,L(y,z,x)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3087,a,b,3684,a),flip(a)].">
      <j1 rule="hyper" parents="257 3087 3684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3685,a(flip),b,2955,a)].">
      <j1 rule="hyper" parents="115 3685 2955"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(2746(a,2),3685(a,1,1))].">
      <j1 rule="para" parents="2746 3685"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2757(a,1),3685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2757 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      x * K(R(x,y,x),z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,3691,a,b,2929,a(flip))].">
      <j1 rule="hyper" parents="115 3691 2929"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3577,a(flip),b,3691,a)].">
      <j1 rule="hyper" parents="63 3577 3691"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,3691,a(flip),b,3088,a),flip(a)].">
      <j1 rule="hyper" parents="172 3691 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(3691(a,1),3069(a,1,1))].">
      <j1 rule="para" parents="3691 3069"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(3691(a,1),3579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3691 3579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3644,a(flip),b,3693,a)].">
      <j1 rule="hyper" parents="63 3644 3693"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,R(y,u,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,3676,a,b,3697,a)].">
      <j1 rule="hyper" parents="257 3676 3697"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(3677(a,1),3614(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3677 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(3092,a,3687,a)].">
      <j1 rule="hyper" parents="3092 3687"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      K(x,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3687(a,2),3090(a,1))].">
      <j1 rule="para" parents="3687 3090"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3475,a,3702,a)].">
      <j1 rule="hyper" parents="3475 3702"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(115,a,3702,a(flip),b,3467,a(flip))].">
      <j1 rule="hyper" parents="115 3702 3467"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),3702(a,1,1))].">
      <j1 rule="para" parents="30 3702"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[para(241(a,1),3702(a,1,1))].">
      <j1 rule="para" parents="241 3702"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(368(a,1),3702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="368 3702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3472,a(flip),b,3704,a)].">
      <j1 rule="hyper" parents="63 3472 3704"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(2477(a,1),3710(a,1,2))].">
      <j1 rule="para" parents="2477 3710"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2757(a,1),3710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2757 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,3714,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 3714 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3641,a(flip),b,3714,a)].">
      <j1 rule="hyper" parents="63 3641 3714"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3714,a(flip),b,3218,a),flip(a)].">
      <j1 rule="hyper" parents="115 3714 3218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(306,a,3716,a),flip(a)].">
      <j1 rule="hyper" parents="306 3716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,104,a(flip),b,3716,a),flip(a)].">
      <j1 rule="hyper" parents="257 104 3716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3716,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 3716 22"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(2579(a,1),3716(a,1,2))].">
      <j1 rule="para" parents="2579 3716"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(114,a,3717,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 3717 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,3692,a(flip),b,3605,a),flip(a)].">
      <j1 rule="hyper" parents="111 3692 3605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3694(a,2),3090(a,1))].">
      <j1 rule="para" parents="3694 3090"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3720,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="115 3720 22"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      L(K(x,(y / x) / z),u,x) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(398(a,1),3698(a,2,2))].">
      <j1 rule="para" parents="398 3698"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),3703(a,1,2))].">
      <j1 rule="para" parents="30 3703"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(241(a,1),3703(a,1,2))].">
      <j1 rule="para" parents="241 3703"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(2746(a,1),3703(a,1,2))].">
      <j1 rule="para" parents="2746 3703"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3470(a,1),3703(a,1))].">
      <j1 rule="para" parents="3470 3703"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(3708(a,1),3381(a,2,2))].">
      <j1 rule="para" parents="3708 3381"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(3708(a,1),3458(a,1,1))].">
      <j1 rule="para" parents="3708 3458"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(3708(a,1),3460(a,1,1))].">
      <j1 rule="para" parents="3708 3460"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),3713(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 3713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(3468(a,1),3732(a,1))].">
      <j1 rule="para" parents="3468 3732"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(113,a,3737,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 3737 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3418,a(flip),b,3737,a),flip(a)].">
      <j1 rule="hyper" parents="63 3418 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(103(a,2),3737(a,1,2))].">
      <j1 rule="para" parents="103 3737"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,3653,a,b,3740,a)].">
      <j1 rule="hyper" parents="257 3653 3740"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3645,a,b,3740,a)].">
      <j1 rule="hyper" parents="257 3645 3740"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(257,a,3457,a,b,3740,a)].">
      <j1 rule="hyper" parents="257 3457 3740"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3380,a,b,3740,a)].">
      <j1 rule="hyper" parents="257 3380 3740"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2159,a(flip),b,3740,a),flip(a)].">
      <j1 rule="hyper" parents="257 2159 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      K(x,T(y,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1025,a(flip),b,3740,a),flip(a)].">
      <j1 rule="hyper" parents="257 1025 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(115,a,3740,a,b,3142,a)].">
      <j1 rule="hyper" parents="115 3740 3142"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,3740,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="115 3740 22"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(115,a,3740,a(flip),b,2929,a(flip))].">
      <j1 rule="hyper" parents="115 3740 2929"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(3740(a,2),232(a,1,2))].">
      <j1 rule="para" parents="3740 232"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3740(a,2),3435(a,1))].">
      <j1 rule="para" parents="3740 3435"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      T(x,R(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(3748(a,1),3238(a,1,2))].">
      <j1 rule="para" parents="3748 3238"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(2757(a,1),3738(a,1,1))].">
      <j1 rule="para" parents="2757 3738"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(306,a,3739,a),flip(a)].">
      <j1 rule="hyper" parents="306 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[para(3419(a,2),3739(a,1,2))].">
      <j1 rule="para" parents="3419 3739"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(2436(a,1),3741(a,1,2))].">
      <j1 rule="para" parents="2436 3741"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[hyper(115,a,3750,a,b,xx)].">
      <j1 rule="hyper" parents="115 3750"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(104(a,1),3750(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="104 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(3503,a,3751,a)].">
      <j1 rule="hyper" parents="3503 3751"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(2173,a,3689,a)].">
      <j1 rule="hyper" parents="2173 3689"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(361,a,3696,a)].">
      <j1 rule="hyper" parents="361 3696"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3068,a(flip),b,3696,a),flip(a)].">
      <j1 rule="hyper" parents="257 3068 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(3768(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="3768 330"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2463,a(flip),b,3700,a),flip(a)].">
      <j1 rule="hyper" parents="257 2463 3700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(T(x,y) * z,T(x,y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(3700(a,1),1289(a,1,1))].">
      <j1 rule="para" parents="3700 1289"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(42,a,965,a,b,3771,a)].">
      <j1 rule="hyper" parents="42 965 3771"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(257,a,2493,a,b,3773,a),flip(a)].">
      <j1 rule="hyper" parents="257 2493 3773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      T(x,(y / T(x,z)) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),3774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3509(a,1),3776(a,1,2))].">
      <j1 rule="para" parents="3509 3776"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      K(x * K(y,z),z) = T(z,x) \ z
    ]]></literal>
    <justification jstring="[para(3777(a,1),2930(a,2,1))].">
      <j1 rule="para" parents="3777 2930"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3496(a,1),3777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3496 3777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3765(a,1),3777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3765 3777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(111,a,3779,a(flip),b,2948,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 3779 2948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,2930,a,b,3778,a),flip(a)].">
      <j1 rule="hyper" parents="257 2930 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(3778(a,2),2989(a,1))].">
      <j1 rule="para" parents="3778 2989"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(821(a,1),3782(a,1,1))].">
      <j1 rule="para" parents="821 3782"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3299(a,1),3782(a,1,1,2))].">
      <j1 rule="para" parents="3299 3782"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3496(a,1),3782(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3496 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(3765(a,1),3782(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3765 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = R(x * K(u,x),y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3787(a,1),3219(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3787 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(3788(a,1),3359(a,1,1))].">
      <j1 rule="para" parents="3788 3359"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2929,a,b,3781,a),flip(a)].">
      <j1 rule="hyper" parents="257 2929 3781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[para(3794(a,2),2099(a,1,2))].">
      <j1 rule="para" parents="3794 2099"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3496(a,1),3794(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3496 3794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3750(a,1),3794(a,1,2))].">
      <j1 rule="para" parents="3750 3794"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3751(a,1),3794(a,1,2))].">
      <j1 rule="para" parents="3751 3794"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,3693,a,b,3796,a)].">
      <j1 rule="hyper" parents="257 3693 3796"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3797(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(2950(a,1),3798(a,1,2))].">
      <j1 rule="para" parents="2950 3798"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(3255(a,1),3801(a,1,2,1))].">
      <j1 rule="para" parents="3255 3801"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),3785(a,1,1,2))].">
      <j1 rule="para" parents="22 3785"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(821(a,1),3783(a,1,1))].">
      <j1 rule="para" parents="821 3783"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3540(a,1),3786(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3540 3786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      R(K(x,y / z),u,x) = K(x,T(y,x) / z)
    ]]></literal>
    <justification jstring="[para(819(a,1),3799(a,2,2))].">
      <j1 rule="para" parents="819 3799"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3799(a,1),2443(a,1))].">
      <j1 rule="para" parents="3799 2443"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(3644(a,1),3803(a,1,2,1))].">
      <j1 rule="para" parents="3644 3803"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2928(a,1),3810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2928 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(3132(a,1),3810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3132 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3404(a,1),3810(a,1,2))].">
      <j1 rule="para" parents="3404 3810"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3124(a,1),3813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3124 3813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(3427(a,1),3814(a,1,2))].">
      <j1 rule="para" parents="3427 3814"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,3705,a)].">
      <j1 rule="hyper" parents="388 3705"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1325(a,1),3817(a,1,3))].">
      <j1 rule="para" parents="1325 3817"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      R(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3817(a,1),3641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3817 3641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(3818(a,1),379(a,1,1))].">
      <j1 rule="para" parents="3818 379"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,3820,a(flip),b,2475,a),flip(a)].">
      <j1 rule="hyper" parents="115 3820 2475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3480,a,b,3707,a)].">
      <j1 rule="hyper" parents="63 3480 3707"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3055,a,b,3707,a)].">
      <j1 rule="hyper" parents="63 3055 3707"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(3707(a,1),3397(a,1,2))].">
      <j1 rule="para" parents="3707 3397"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3719,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 3719 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(3250,a,3722,a),flip(a)].">
      <j1 rule="hyper" parents="3250 3722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(361,a,3723,a)].">
      <j1 rule="hyper" parents="361 3723"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      L(L(x,y,z),u,K(w,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3829(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3829 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      (K(x,y) * z) * R(y,u,w) = K(x,y) * (z * R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3829(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="3829 330"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3829(a,1),3466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3829 3466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3472,a(flip),b,3832,a)].">
      <j1 rule="hyper" parents="63 3472 3832"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),3833(a,1,2))].">
      <j1 rule="para" parents="30 3833"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(3147(a,1),3833(a,1,2))].">
      <j1 rule="para" parents="3147 3833"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(z,K(x * y,x))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(3733(a,2),3040(a,1,1))].">
      <j1 rule="para" parents="3733 3040"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      K(x,T(y,x \ y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3749,a(flip),b,3759,a),flip(a)].">
      <j1 rule="hyper" parents="63 3749 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(3407(a,1),3759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3407 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      T(x,T(y,x \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,3837,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 3837 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      T(x,T(y,y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2400(a,2),3839(a,1,2))].">
      <j1 rule="para" parents="2400 3839"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(3137(a,1),3840(a,1,2,2))].">
      <j1 rule="para" parents="3137 3840"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      x * K(y,x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z / x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(3764(a,1),3204(a,1))].">
      <j1 rule="para" parents="3764 3204"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(203,a,3769,a,b,2962,a)].">
      <j1 rule="hyper" parents="203 3769 2962"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(2965(a,2),3769(a,1,1))].">
      <j1 rule="para" parents="2965 3769"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(3751(a,1),3807(a,1,1,2))].">
      <j1 rule="para" parents="3751 3807"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(3132(a,1),3822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3132 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = R(y,w,v5) \ R(y * K(x * u,y),w,v5)
    ]]></literal>
    <justification jstring="[para(3846(a,1),3218(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3846 3218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(3503,a,3847,a)].">
      <j1 rule="hyper" parents="3503 3847"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(517,a,3848,a),flip(a)].">
      <j1 rule="hyper" parents="517 3848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,3848,a(flip),b,1124,a),flip(a)].">
      <j1 rule="hyper" parents="114 3848 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3848(a,1),3317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3848 3317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(3848(a,1),3529(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3848 3529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,10,a(flip),b,3850,a),flip(a)].">
      <j1 rule="hyper" parents="112 10 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,2959,a,b,3850,a)].">
      <j1 rule="hyper" parents="35 2959 3850"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1501,a,b,3850,a),flip(a)].">
      <j1 rule="hyper" parents="35 1501 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(203,a,3850,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="203 3850 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3740,a,b,3858,a)].">
      <j1 rule="hyper" parents="63 3740 3858"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,2948,a(flip),b,3857,a),flip(a)].">
      <j1 rule="hyper" parents="34 2948 3857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3857(a,1),3028(a,1,1))].">
      <j1 rule="para" parents="3857 3028"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(3153,a,3862,a)].">
      <j1 rule="hyper" parents="3153 3862"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3095,a,b,3862,a)].">
      <j1 rule="hyper" parents="63 3095 3862"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3094,a,b,3862,a)].">
      <j1 rule="hyper" parents="63 3094 3862"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(115,a,3862,a(flip),b,2929,a(flip))].">
      <j1 rule="hyper" parents="115 3862 2929"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[hyper(114,a,3862,a(flip),b,2932,a)].">
      <j1 rule="hyper" parents="114 3862 2932"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(3864(a,1),3091(a,1))].">
      <j1 rule="para" parents="3864 3091"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(3851(a,2),3802(a,1,2))].">
      <j1 rule="para" parents="3851 3802"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3430,a(flip),b,3865,a)].">
      <j1 rule="hyper" parents="63 3430 3865"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3448,a,b,3866,a)].">
      <j1 rule="hyper" parents="63 3448 3866"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(34,a,2972,a(flip),b,3866,a)].">
      <j1 rule="hyper" parents="34 2972 3866"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3740(a,2),3866(a,1,2))].">
      <j1 rule="para" parents="3740 3866"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3740,a,b,3874,a),flip(a)].">
      <j1 rule="hyper" parents="257 3740 3874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(39,a,3088,a,b,3877,a)].">
      <j1 rule="hyper" parents="39 3088 3877"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3740,a,b,3879,a),flip(a)].">
      <j1 rule="hyper" parents="257 3740 3879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,1499,a(flip),b,3879,a),flip(a)].">
      <j1 rule="hyper" parents="257 1499 3879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(115,a,3879,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="115 3879 22"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(3879(a,2),3752(a,1,2))].">
      <j1 rule="para" parents="3879 3752"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3392,a(flip),b,3880,a),flip(a)].">
      <j1 rule="hyper" parents="63 3392 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(172,a,3880,a(flip),b,2930,a(flip))].">
      <j1 rule="hyper" parents="172 3880 2930"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(111,a,3880,a(flip),b,2972,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 3880 2972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      K(L(T(x,y),z,u),w) = K(L(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(25(a,2),3880(a,1,1))].">
      <j1 rule="para" parents="25 3880"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      K(R(T(x,y),z,u),w) = K(R(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(27(a,2),3880(a,1,1))].">
      <j1 rule="para" parents="27 3880"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      K(T(x,R(y,z,u)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(152(a,1),3880(a,2,2))].">
      <j1 rule="para" parents="152 3880"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),3880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),3880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="194 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(183(a,1),3880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="183 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      K(x,T(y,K(z,L(x,u,w)))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2100(a,1),3880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2100 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(3880(a,1),3146(a,1,1))].">
      <j1 rule="para" parents="3880 3146"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(3880(a,1),3115(a,1,1))].">
      <j1 rule="para" parents="3880 3115"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(3880(a,1),3504(a,1,1,2))].">
      <j1 rule="para" parents="3880 3504"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[para(3880(a,1),3765(a,1,2))].">
      <j1 rule="para" parents="3880 3765"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(3780(a,1),3880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3780 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = u
    ]]></literal>
    <justification jstring="[para(3881(a,1),2958(a,1,1))].">
      <j1 rule="para" parents="3881 2958"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(z,T(y,u)),u,x) = w
    ]]></literal>
    <justification jstring="[para(3883(a,1),3543(a,1,1,2))].">
      <j1 rule="para" parents="3883 3543"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3740,a,b,3885,a),flip(a)].">
      <j1 rule="hyper" parents="257 3740 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(3661,a,3886,a)].">
      <j1 rule="hyper" parents="3661 3886"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3233,a(flip),b,3891,a),flip(a)].">
      <j1 rule="hyper" parents="63 3233 3891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,3892,a(flip),b,3159,a)].">
      <j1 rule="hyper" parents="114 3892 3159"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      R(x,(y * z) / y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[para(3892(a,1),3345(a,1,3))].">
      <j1 rule="para" parents="3892 3345"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(3892(a,1),3366(a,1,3))].">
      <j1 rule="para" parents="3892 3366"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,3907,a)].">
      <j1 rule="hyper" parents="52 3907"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ (x * K(z,u)) = ((y * z) / y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(3906(a,1),380(a,1,1))].">
      <j1 rule="para" parents="3906 380"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3207,a,b,3909,a)].">
      <j1 rule="hyper" parents="63 3207 3909"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(3902(a,1),3580(a,1,1))].">
      <j1 rule="para" parents="3902 3580"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3740,a,b,3867,a),flip(a)].">
      <j1 rule="hyper" parents="257 3740 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3867(a,1),3148(a,1,2))].">
      <j1 rule="para" parents="3867 3148"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3862,a(flip),b,3872,a),flip(a)].">
      <j1 rule="hyper" parents="63 3862 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      R(x,y,z) * (x \ K(u,T(x,w))) = T(x,T(u,w)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3887(a,1),1351(a,1,2))].">
      <j1 rule="para" parents="3887 1351"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,3880,a(flip),b,3899,a),flip(a)].">
      <j1 rule="hyper" parents="257 3880 3899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      K(T(x,x \ y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3395,a,b,3904,a)].">
      <j1 rule="hyper" parents="63 3395 3904"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      ((x * y) * z) / ((x * T(y,T(u,x))) * z) = R(K(u,y),x * y,z)
    ]]></literal>
    <justification jstring="[para(3905(a,1),3634(a,1,2,1))].">
      <j1 rule="para" parents="3905 3634"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      K(x,T(y,T(z,x) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(3110(a,1),3919(a,1,2,2))].">
      <j1 rule="para" parents="3110 3919"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,x) * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(152(a,1),3753(a,1,2,2))].">
      <j1 rule="para" parents="152 3753"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),3806(a,1,1,2))].">
      <j1 rule="para" parents="22 3806"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      R(x * K(R(y \ 1,z,u) \ 1,x),w,x) = R(x,w,x) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3256(a,1),3718(a,2,2))].">
      <j1 rule="para" parents="3256 3718"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(3825(a,1),2889(a,2,1))].">
      <j1 rule="para" parents="3825 2889"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(203,a,3844,a,b,715,a)].">
      <j1 rule="hyper" parents="203 3844 715"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      K(R(T(x,y),z,u),L(y,w,v5)) = K(R(x,z,u),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(155(a,1),3889(a,2,2))].">
      <j1 rule="para" parents="155 3889"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(T(x,y),w)
    ]]></literal>
    <justification jstring="[para(1223(a,1),3889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1223 3889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(3482(a,2),3730(a,1))].">
      <j1 rule="para" parents="3482 3730"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3468,a(flip),b,3793,a)].">
      <j1 rule="hyper" parents="63 3468 3793"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3788,a(flip),b,3932,a),flip(a)].">
      <j1 rule="hyper" parents="257 3788 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(241(a,1),3933(a,1,1))].">
      <j1 rule="para" parents="241 3933"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3842,a,3514,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3842 3514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(165,a,3936,a)].">
      <j1 rule="hyper" parents="165 3936"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(3937(a,1),3737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3937 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(3135(a,1),3895(a,1))].">
      <j1 rule="para" parents="3135 3895"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(2994(a,1),3897(a,1))].">
      <j1 rule="para" parents="2994 3897"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3879(a,1),3942(a,1))].">
      <j1 rule="para" parents="3879 3942"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3422(a,2),3943(a,1))].">
      <j1 rule="para" parents="3422 3943"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(485(a,2),3944(a,1))].">
      <j1 rule="para" parents="485 3944"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3425(a,1),3915(a,1,2))].">
      <j1 rule="para" parents="3425 3915"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(3824(a,2),3924(a,1))].">
      <j1 rule="para" parents="3824 3924"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      L(K(x,x \ (y \ z)),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(3454(a,2),3931(a,1))].">
      <j1 rule="para" parents="3454 3931"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(3879(a,1),3941(a,1,1))].">
      <j1 rule="para" parents="3879 3941"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(2687,a,3695,a(flip))].">
      <j1 rule="hyper" parents="2687 3695"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,3951,a(flip),b,2965,a)].">
      <j1 rule="hyper" parents="111 3951 2965"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2636,a,b,3952,a),flip(a)].">
      <j1 rule="hyper" parents="63 2636 3952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      R(x,y,x) / a(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(172,a,2636,a,b,3952,a(flip))].">
      <j1 rule="hyper" parents="172 2636 3952"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,2636,a,b,3952,a(flip))].">
      <j1 rule="hyper" parents="115 2636 3952"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3212,a,b,3953,a)].">
      <j1 rule="hyper" parents="63 3212 3953"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1937,a,b,3953,a)].">
      <j1 rule="hyper" parents="63 1937 3953"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,3953,a(flip),b,3952,a)].">
      <j1 rule="hyper" parents="115 3953 3952"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(115,a,3953,a(flip),b,2632,a)].">
      <j1 rule="hyper" parents="115 3953 2632"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(3953(a,1),2631(a,2,2))].">
      <j1 rule="para" parents="3953 2631"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(3953(a,1),3535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3953 3535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,3954,a(flip),b,2771,a)].">
      <j1 rule="hyper" parents="111 3954 2771"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(114,a,3955,a(flip),b,2665,a),flip(a)].">
      <j1 rule="hyper" parents="114 3955 2665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(111,a,3967,a(flip),b,1280,a)].">
      <j1 rule="hyper" parents="111 3967 1280"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(3503,a,3956,a)].">
      <j1 rule="hyper" parents="3503 3956"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(3956(a,1),3139(a,1,2))].">
      <j1 rule="para" parents="3956 3139"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = R(y,z,u) * a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1236,a,b,3966,a)].">
      <j1 rule="hyper" parents="63 1236 3966"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),3966(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (T(u * L(z,y,x),u) / u)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(3966(a,2),358(a,1,2,2))].">
      <j1 rule="para" parents="3966 358"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(a(u,z,u),z,y),y * z,x) = w
    ]]></literal>
    <justification jstring="[para(3966(a,2),567(a,1,2,2,2))].">
      <j1 rule="para" parents="3966 567"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(3971(a,1),1480(a,1,3))].">
      <j1 rule="para" parents="3971 1480"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      a(K(x * y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3971(a,1),1595(a,1,1))].">
      <j1 rule="para" parents="3971 1595"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2489,a(flip),b,3960,a),flip(a)].">
      <j1 rule="hyper" parents="257 2489 3960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,12,a(flip),b,3960,a),flip(a)].">
      <j1 rule="hyper" parents="112 12 3960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3726,a,b,3963,a)].">
      <j1 rule="hyper" parents="63 3726 3963"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = R(x,y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1281,a,b,3968,a),flip(a)].">
      <j1 rule="hyper" parents="34 1281 3968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(3970(a,1),2910(a,2,2))].">
      <j1 rule="para" parents="3970 2910"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(2433,a,3978,a),flip(a)].">
      <j1 rule="hyper" parents="2433 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(3024(a,1),3988(a,1,3))].">
      <j1 rule="para" parents="3024 3988"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(3988(a,1),3014(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3988 3014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3979(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,192,a(flip),b,3990,a)].">
      <j1 rule="hyper" parents="63 192 3990"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3721,a(flip),b,3985,a),flip(a)].">
      <j1 rule="hyper" parents="257 3721 3985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(111,a,12,a(flip),b,3993,a),flip(a)].">
      <j1 rule="hyper" parents="111 12 3993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(114,a,3994,a(flip),b,3981,a(flip))].">
      <j1 rule="hyper" parents="114 3994 3981"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,1933,a(flip),b,3995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="42 1933 3995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3959,a(flip),b,3996,a),flip(a)].">
      <j1 rule="hyper" parents="257 3959 3996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(203,a,3996,a,b,xx)].">
      <j1 rule="hyper" parents="203 3996"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) = R(T(u,x * a(y,z,y)),x,a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(111,a,3996,a,b,462,a)].">
      <j1 rule="hyper" parents="111 3996 462"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(3996(a,1),218(a,1))].">
      <j1 rule="para" parents="3996 218"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(3996(a,1),331(a,1,1))].">
      <j1 rule="para" parents="3996 331"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(u,x),x,a(y,z,y)) = w
    ]]></literal>
    <justification jstring="[para(3996(a,1),523(a,1,1))].">
      <j1 rule="para" parents="3996 523"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3996(a,1),1480(a,1,3))].">
      <j1 rule="para" parents="3996 1480"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(3996(a,2),2661(a,1,1))].">
      <j1 rule="para" parents="3996 2661"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      L(T(T(a(x,y,x),z),u),z,u) = R(a(x,y,x),u,z)
    ]]></literal>
    <justification jstring="[para(3998(a,1),2885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3998 2885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2659,a(flip),b,4003,a),flip(a)].">
      <j1 rule="hyper" parents="63 2659 4003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(422,a,4006,a),flip(a)].">
      <j1 rule="hyper" parents="422 4006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      x * (a(y,z,y) * (x \ u)) = a(y,z,y) * u
    ]]></literal>
    <justification jstring="[hyper(268,a,4008,a),flip(a)].">
      <j1 rule="hyper" parents="268 4008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      T(a(x,y,x) \ z,a(x,y,x) * u) = (a(x,y,x) * u) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(318,a,500,a(flip),b,4008,a(flip))].">
      <j1 rule="hyper" parents="318 500 4008"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = (x * u) \ (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(4008(a,1),420(a,1,1))].">
      <j1 rule="para" parents="4008 420"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(4009(a,1),4002(a,1,1))].">
      <j1 rule="para" parents="4009 4002"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),3743(a,2,2))].">
      <j1 rule="para" parents="27 3743"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(3740(a,2),3821(a,1,2,2))].">
      <j1 rule="para" parents="3740 3821"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(3826(a,1),3504(a,1,1))].">
      <j1 rule="para" parents="3826 3504"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3510,a(flip),b,3855,a),flip(a)].">
      <j1 rule="hyper" parents="257 3510 3855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3496(a,1),4018(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3496 4018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3751(a,1),4018(a,1,2,1))].">
      <j1 rule="para" parents="3751 4018"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(257,a,3510,a,b,4019,a),flip(a)].">
      <j1 rule="hyper" parents="257 3510 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(3892(a,1),4019(a,1,2,1,2))].">
      <j1 rule="para" parents="3892 4019"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(3868(a,2),3950(a,1))].">
      <j1 rule="para" parents="3868 3950"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(3752(a,1),3873(a,1,2,2))].">
      <j1 rule="para" parents="3752 3873"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(3438(a,2),4026(a,1,2))].">
      <j1 rule="para" parents="3438 4026"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2990,a,4027,a)].">
      <j1 rule="hyper" parents="2990 4027"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      K(x,y) * K(x * y,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4028(a,2),3914(a,1,2))].">
      <j1 rule="para" parents="4028 3914"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3927(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3791,a(flip),b,3935,a),flip(a)].">
      <j1 rule="hyper" parents="257 3791 3935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(3555(a,1),4032(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3555 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(3898(a,1),4032(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3898 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      K(x \ K(y,z),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3445,a,4035,a)].">
      <j1 rule="hyper" parents="3445 4035"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      K(L(x \ y,x,K(z,u)),u) = K(x \ (K(z,u) * y),u)
    ]]></literal>
    <justification jstring="[para(92(a,2),4035(a,1,1))].">
      <j1 rule="para" parents="92 4035"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(115,a,4036,a(flip),b,3343,a)].">
      <j1 rule="hyper" parents="115 4036 3343"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      L(T(a(x,y,x),z),u,z) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3998(a,1),4007(a,1,1,1))].">
      <j1 rule="para" parents="3998 4007"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = L(a(x,y,x),u,z)
    ]]></literal>
    <justification jstring="[para(3998(a,1),4040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3998 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(564,a,4043,a),flip(a)].">
      <j1 rule="hyper" parents="564 4043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(115,a,4045,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 4045 18"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,4048,a)].">
      <j1 rule="hyper" parents="388 4048"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      (((x * y) * z) * a(u,w,u)) / ((y * z) * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,386,a,b,4049,a)].">
      <j1 rule="hyper" parents="63 386 4049"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(3740(a,2),4014(a,1,1))].">
      <j1 rule="para" parents="3740 4014"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      (x \ R(x,y,z)) * T(K(u,x),w) = R(x,y,z) * (x \ K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(1287,a,4016,a),flip(a)].">
      <j1 rule="hyper" parents="1287 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(4021(a,2),3521(a,1))].">
      <j1 rule="para" parents="4021 3521"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(3431(a,1),4053(a,1,2,1))].">
      <j1 rule="para" parents="3431 4053"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(3883(a,1),4053(a,1,2,1))].">
      <j1 rule="para" parents="3883 4053"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(4055,a,3835,a),flip(a)].">
      <j1 rule="hyper" parents="4055 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2952(a,2),4056(a,1,2,2))].">
      <j1 rule="para" parents="2952 4056"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(2928(a,1),4056(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2928 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(113,a,4058,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4058 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      T(x,T(y \ x,z)) = T(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3903,a(flip),b,4060,a)].">
      <j1 rule="hyper" parents="63 3903 4060"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(257,a,3686,a,b,4059,a)].">
      <j1 rule="hyper" parents="257 3686 4059"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      K(x,R(x,y,z) \ (u * x)) = K(x,x * (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(1279(a,1),4059(a,2,2))].">
      <j1 rule="para" parents="1279 4059"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4062(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(4062(a,1),3454(a,1,1))].">
      <j1 rule="para" parents="4062 3454"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (x \ y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(4062(a,1),3604(a,1,1))].">
      <j1 rule="para" parents="4062 3604"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      T(T(x,y) * R(x \ z,u,w),x) = T(x,y) * R(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(1227(a,1),4031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1227 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      T(T(x,y) * L(x \ z,u,w),x) = T(x,y) * L(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(1272(a,1),4031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1272 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ u,w)) = R(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),4051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,286,a(flip),b,4070,a),flip(a)].">
      <j1 rule="hyper" parents="257 286 4070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(257,a,3740,a(flip),b,4071,a),flip(a)].">
      <j1 rule="hyper" parents="257 3740 4071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = K(y,x) * R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(3923,a,3718,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3923 3718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4073(a,2),3546(a,1,2))].">
      <j1 rule="para" parents="4073 3546"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(3947,a,3876,a)].">
      <j1 rule="hyper" parents="3947 3876"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3917,a,b,4075,a)].">
      <j1 rule="hyper" parents="63 3917 4075"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4028,a(flip),b,4076,a)].">
      <j1 rule="hyper" parents="63 4028 4076"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4076(a,1),4029(a,1,2))].">
      <j1 rule="para" parents="4076 4029"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3869,a,4077,a)].">
      <j1 rule="hyper" parents="3869 4077"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,4028,a(flip),b,4077,a),flip(a)].">
      <j1 rule="hyper" parents="257 4028 4077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(114,a,4077,a,b,2938,a(flip))].">
      <j1 rule="hyper" parents="114 4077 2938"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4077(a,1),3864(a,1,1))].">
      <j1 rule="para" parents="4077 3864"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4077(a,1),3859(a,1,1))].">
      <j1 rule="para" parents="4077 3859"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4077(a,1),3867(a,1,2))].">
      <j1 rule="para" parents="4077 3867"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(115,a,4079,a(flip),b,3337,a)].">
      <j1 rule="hyper" parents="115 4079 3337"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(4079(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="4079 2957"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3174(a,1),4080(a,1,2))].">
      <j1 rule="para" parents="3174 4080"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4081(a,1),3919(a,1,2,2))].">
      <j1 rule="para" parents="4081 3919"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(3091,a,4082,a)].">
      <j1 rule="hyper" parents="3091 4082"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3864,a(flip),b,4082,a)].">
      <j1 rule="hyper" parents="63 3864 4082"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4079,a(flip),b,4091,a),flip(a)].">
      <j1 rule="hyper" parents="63 4079 4091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(3798(a,1),4092(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3798 4092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,4092,a,b,4093,a)].">
      <j1 rule="hyper" parents="257 4092 4093"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,4091,a,b,4093,a)].">
      <j1 rule="hyper" parents="257 4091 4093"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3866,a,b,4093,a)].">
      <j1 rule="hyper" parents="257 3866 4093"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(113,a,4098,a,b,3175,a)].">
      <j1 rule="hyper" parents="113 4098 3175"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4098(a,1),3914(a,1,2))].">
      <j1 rule="para" parents="4098 3914"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(115,a,4099,a,b,2929,a(flip))].">
      <j1 rule="hyper" parents="115 4099 2929"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3136,a,b,4107,a)].">
      <j1 rule="hyper" parents="257 3136 4107"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3822,a(flip),b,4107,a),flip(a)].">
      <j1 rule="hyper" parents="257 3822 4107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3438,a(flip),b,4107,a),flip(a)].">
      <j1 rule="hyper" parents="257 3438 4107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(113,a,4089,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4089 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),4089(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 4089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(4110(a,1),3552(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4110 3552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,4107,a,b,4115,a),flip(a)].">
      <j1 rule="hyper" parents="257 4107 4115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3047(a,1),4116(a,1,2))].">
      <j1 rule="para" parents="3047 4116"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(3439(a,1),4116(a,1,2))].">
      <j1 rule="para" parents="3439 4116"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3174(a,2),4119(a,1,2))].">
      <j1 rule="para" parents="3174 4119"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3860(a,1),4084(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3860 4084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(3797(a,1),4085(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3797 4085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4085(a,2),3943(a,1))].">
      <j1 rule="para" parents="4085 3943"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3740,a(flip),b,4090,a)].">
      <j1 rule="hyper" parents="63 3740 4090"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,4092,a,b,4096,a),flip(a)].">
      <j1 rule="hyper" parents="257 4092 4096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4100(a,1),3915(a,1))].">
      <j1 rule="para" parents="4100 3915"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4077(a,1),4128(a,1))].">
      <j1 rule="para" parents="4077 4128"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(114,a,4109,a(flip),b,2945,a)].">
      <j1 rule="hyper" parents="114 4109 2945"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4109(a,1),2981(a,1,1))].">
      <j1 rule="para" parents="4109 2981"/>
    </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(4109(a,1),3028(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4109 3028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4109(a,1),3010(a,1,1,1))].">
      <j1 rule="para" parents="4109 3010"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3943,a,4133,a)].">
      <j1 rule="hyper" parents="3943 4133"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3879,a,b,4133,a)].">
      <j1 rule="hyper" parents="63 3879 4133"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,4136,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4136 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3888,a,b,4136,a)].">
      <j1 rule="hyper" parents="63 3888 4136"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3892,a(flip),b,4136,a),flip(a)].">
      <j1 rule="hyper" parents="63 3892 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(554(a,2),4136(a,1,2))].">
      <j1 rule="para" parents="554 4136"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      K(T(x,y),z) * (y * K(z,x)) = y
    ]]></literal>
    <justification jstring="[para(4136(a,1),3763(a,1,2,2))].">
      <j1 rule="para" parents="4136 3763"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      K(T(x,y),z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(3754,a,4137,a)].">
      <j1 rule="hyper" parents="3754 4137"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),4137(a,1,2))].">
      <j1 rule="para" parents="25 4137"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y),u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),4137(a,1,2))].">
      <j1 rule="para" parents="27 4137"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(104(a,1),4137(a,1,2))].">
      <j1 rule="para" parents="104 4137"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(194(a,1),4137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="194 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      K(x * T(x \ y,y),z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(968(a,1),4137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="968 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(2981(a,1),4137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2981 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4137(a,1),3644(a,1,1))].">
      <j1 rule="para" parents="4137 3644"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(4137(a,1),3763(a,1,2,2))].">
      <j1 rule="para" parents="4137 3763"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(194(a,1),4138(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="194 4138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(4138(a,1),3905(a,2,2))].">
      <j1 rule="para" parents="4138 3905"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(115,a,4132,a(flip),b,3080,a),flip(a)].">
      <j1 rule="hyper" parents="115 4132 3080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(T(y,z),u),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(4132(a,1),3143(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="4132 3143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(82(a,1),4141(a,1,1,1))].">
      <j1 rule="para" parents="82 4141"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      R(K(x,y / z),u,x) = K(T(x,y),z \ y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3693,a,b,4146,a)].">
      <j1 rule="hyper" parents="257 3693 4146"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(3777(a,1),4150(a,1,1))].">
      <j1 rule="para" parents="3777 4150"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3038,a,b,4151,a)].">
      <j1 rule="hyper" parents="63 3038 4151"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      K(x,T(y,z * K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4156(a,1),3919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4156 3919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(576(a,2),4157(a,1,2))].">
      <j1 rule="para" parents="576 4157"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(104(a,1),4134(a,1,1,2))].">
      <j1 rule="para" parents="104 4134"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3383(a,1),4134(a,1))].">
      <j1 rule="para" parents="3383 4134"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3740(a,2),4134(a,1))].">
      <j1 rule="para" parents="3740 4134"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(3879(a,2),4134(a,1))].">
      <j1 rule="para" parents="3879 4134"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(104(a,1),4169(a,1,2,1))].">
      <j1 rule="para" parents="104 4169"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3893(a,1),4169(a,1))].">
      <j1 rule="para" parents="3893 4169"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(3889(a,2),4169(a,1))].">
      <j1 rule="para" parents="3889 4169"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(3940(a,1),4169(a,1))].">
      <j1 rule="para" parents="3940 4169"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      K(T(x,y),T(T(z,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(23(a,1),4170(a,1,2))].">
      <j1 rule="para" parents="23 4170"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27(a,2),4170(a,1,2))].">
      <j1 rule="para" parents="27 4170"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(104(a,1),4170(a,1,2))].">
      <j1 rule="para" parents="104 4170"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      (x * y) \ T(z * (x * y),K(x,y)) = T(z,T(x * y,y))
    ]]></literal>
    <justification jstring="[hyper(111,a,4122,a(flip),b,4114,a(flip))].">
      <j1 rule="hyper" parents="111 4122 4114"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(4129,a,4121,a),flip(a)].">
      <j1 rule="hyper" parents="4129 4121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(4128,a,4127,a)].">
      <j1 rule="hyper" parents="4128 4127"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(112,a,4158,a(flip),b,3068,a(flip))].">
      <j1 rule="hyper" parents="112 4158 3068"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3885(a,1),4158(a,1,1))].">
      <j1 rule="para" parents="3885 4158"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w))
    ]]></literal>
    <justification jstring="[para(4159(a,2),3644(a,1,2))].">
      <j1 rule="para" parents="4159 3644"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,4116,a(flip),b,4179,a),flip(a)].">
      <j1 rule="hyper" parents="257 4116 4179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),4186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="76 4186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(4129,a,4187,a)].">
      <j1 rule="hyper" parents="4129 4187"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4120,a,b,4188,a)].">
      <j1 rule="hyper" parents="63 4120 4188"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,4098,a,b,4189,a),flip(a)].">
      <j1 rule="hyper" parents="257 4098 4189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(4191(a,1),4085(a,1,2))].">
      <j1 rule="para" parents="4191 4085"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,4093,a(flip),b,4180,a),flip(a)].">
      <j1 rule="hyper" parents="257 4093 4180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / T(x,y) = T(y,T(y \ z,x))
    ]]></literal>
    <justification jstring="[para(103(a,1),4183(a,1,1,2))].">
      <j1 rule="para" parents="103 4183"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(4199(a,1),3345(a,1,3))].">
      <j1 rule="para" parents="4199 3345"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(3613,a,4202,a)].">
      <j1 rule="hyper" parents="3613 4202"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      K(T(x,y),z \ y) = K(x,T(y,x) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3808,a(flip),b,4162,a),flip(a)].">
      <j1 rule="hyper" parents="63 3808 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      K(T(x,y / x),z \ (y / x)) = K(x,(x \ y) / z)
    ]]></literal>
    <justification jstring="[para(104(a,1),4207(a,2,2,1))].">
      <j1 rule="para" parents="104 4207"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      K(x / y,x / z) = K(y \ x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(4168,a,3713,a)].">
      <j1 rule="hyper" parents="4168 3713"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      K((x / y) / ((y \ x) / y),(x / y) / z) = K(T(y,y \ x),z \ (x / y))
    ]]></literal>
    <justification jstring="[para(962(a,1),4210(a,2,1))].">
      <j1 rule="para" parents="962 4210"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      L(K(T(x,y),T(z,y)),u,w) = K(L(x,u / T(x,y),w),z)
    ]]></literal>
    <justification jstring="[hyper(3475,a,4140,a)].">
      <j1 rule="hyper" parents="3475 4140"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      K(T(x,L(x,y,z) * u),T(w,u)) = K(L(x,u,L(x,y,z)),w)
    ]]></literal>
    <justification jstring="[para(1143(a,1),4140(a,1,1))].">
      <j1 rule="para" parents="1143 4140"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      K(x,R(y * K(z,y),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2981(a,1),4143(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2981 4143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      L(K(T(x,y),T(z,y)),u,w) = K(x,L(z,u / T(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(3471,a,4148,a)].">
      <j1 rule="hyper" parents="3471 4148"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      K(T(x * K(y \ x,x),x),z) = K(x,T(z,T(y,x) \ x))
    ]]></literal>
    <justification jstring="[para(3389(a,1),4152(a,1,1))].">
      <j1 rule="para" parents="3389 4152"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4078,a(flip),b,4196,a),flip(a)].">
      <j1 rule="hyper" parents="63 4078 4196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3943,a,4223,a)].">
      <j1 rule="hyper" parents="3943 4223"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(113,a,4224,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4224 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(3407(a,1),4224(a,1,2))].">
      <j1 rule="para" parents="3407 4224"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3902,a(flip),b,4226,a),flip(a)].">
      <j1 rule="hyper" parents="257 3902 4226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4226(a,1),3944(a,1))].">
      <j1 rule="para" parents="4226 3944"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),4227(a,1,2,2))].">
      <j1 rule="para" parents="9 4227"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(153(a,1),4229(a,1,2)),flip(a)].">
      <j1 rule="para" parents="153 4229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(3838(a,1),4228(a,1))].">
      <j1 rule="para" parents="3838 4228"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      R(x,K(y,z),T(K(z,y) * u,K(y,w))) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4204(a,2),3150(a,1,1))].">
      <j1 rule="para" parents="4204 3150"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4076(a,1),4125(a,1,2))].">
      <j1 rule="para" parents="4076 4125"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(4227(a,2),4231(a,1))].">
      <j1 rule="para" parents="4227 4231"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(3496(a,1),4087(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3496 4087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(257,a,4204,a(flip),b,4118,a),flip(a)].">
      <j1 rule="hyper" parents="257 4204 4118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(257,a,4084,a(flip),b,4123,a),flip(a)].">
      <j1 rule="hyper" parents="257 4084 4123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(3856(a,1),4241(a,1,2))].">
      <j1 rule="para" parents="3856 4241"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(4124(a,2),4088(a,1))].">
      <j1 rule="para" parents="4124 4088"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,v5)) = (z * K(y,v5)) * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(3779(a,1),4135(a,1,1,1,2))].">
      <j1 rule="para" parents="3779 4135"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(257,a,3884,a,b,4166,a),flip(a)].">
      <j1 rule="hyper" parents="257 3884 4166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      (T(x,T(x \ y,z)) * z) \ (z * ((x \ y) \ y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(4201(a,1),3348(a,1,1,1))].">
      <j1 rule="para" parents="4201 3348"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      K(T(x,x \ y),z \ (y / x)) = K(x,(x \ y) / z)
    ]]></literal>
    <justification jstring="[para(2470(a,1),4208(a,1,1))].">
      <j1 rule="para" parents="2470 4208"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4230(a,1),3601(a,1,2))].">
      <j1 rule="para" parents="4230 3601"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(K(y,x),z) = K(y * x,x) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(3215(a,1),4238(a,1,1))].">
      <j1 rule="para" parents="3215 4238"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4243,a,4242,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4243 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3499(a,1),4250(a,1,2))].">
      <j1 rule="para" parents="3499 4250"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u * K(z,w)) = R(x,K(y,z),u * K(z,w))
    ]]></literal>
    <justification jstring="[para(4251(a,1),4239(a,1,2))].">
      <j1 rule="para" parents="4251 4239"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = L(K(z * L(y,u,w),y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4248(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4248 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,x) = v5
    ]]></literal>
    <justification jstring="[para(3678(a,1),3504(a,1,1))].">
      <j1 rule="para" parents="3678 3504"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(388,a,3770,a)].">
      <j1 rule="hyper" parents="388 3770"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3637,a(flip),b,4255,a)].">
      <j1 rule="hyper" parents="63 3637 4255"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3580,a(flip),b,4255,a)].">
      <j1 rule="hyper" parents="63 3580 4255"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w * R(x,v5,v6)) = K(x,R(x,v5,v6) * w)
    ]]></literal>
    <justification jstring="[hyper(257,a,3811,a,b,4257,a),flip(a)].">
      <j1 rule="hyper" parents="257 3811 4257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      R(K(x,y),z,R(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(388,a,3831,a)].">
      <j1 rule="hyper" parents="388 3831"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3644,a(flip),b,4259,a)].">
      <j1 rule="hyper" parents="63 3644 4259"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) / T(x,y) = K(y * R(x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3241,a(flip),b,4260,a)].">
      <j1 rule="hyper" parents="63 3241 4260"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = R(y,x,R(y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4261(a,1),3330(a,1,1))].">
      <j1 rule="para" parents="4261 3330"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3580,a(flip),b,3913,a),flip(a)].">
      <j1 rule="hyper" parents="63 3580 3913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,4264,a,b,3141,a),flip(a)].">
      <j1 rule="hyper" parents="110 4264 3141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(3996(a,1),4012(a,1,1,2))].">
      <j1 rule="para" parents="3996 4012"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(4155(a,2),4176(a,1))].">
      <j1 rule="para" parents="4155 4176"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4022,a(flip),b,4163,a)].">
      <j1 rule="hyper" parents="63 4022 4163"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(4177,a,4273,a),flip(a)].">
      <j1 rule="hyper" parents="4177 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(85(a,1),4274(a,1,2,2))].">
      <j1 rule="para" parents="85 4274"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3496(a,1),4274(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3496 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(99(a,2),4276(a,2,2)),flip(a)].">
      <j1 rule="para" parents="99 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(3596(a,1),4277(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3596 4277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3027,a(flip),b,4279,a)].">
      <j1 rule="hyper" parents="63 3027 4279"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(246(a,1),4280(a,1,2,2,1))].">
      <j1 rule="para" parents="246 4280"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(3765(a,1),4280(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3765 4280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(2945(a,1),4164(a,1,1,1,2))].">
      <j1 rule="para" parents="2945 4164"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      K(L(x,y / T(x,z),u),w) = L(K(x,w),y,u)
    ]]></literal>
    <justification jstring="[para(4137(a,1),4217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4137 4217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(164(a,1),4289(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="164 4289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3453,a(flip),b,4290,a),flip(a)].">
      <j1 rule="hyper" parents="63 3453 4290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = L(K(x,u),K(y,x),z)
    ]]></literal>
    <justification jstring="[para(2972(a,2),4290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2972 4290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z))
    ]]></literal>
    <justification jstring="[para(4137(a,1),4290(a,1,1))].">
      <j1 rule="para" parents="4137 4290"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(4137(a,1),4220(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4137 4220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(164(a,1),4295(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="164 4295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(115,a,4296,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 4296 18"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      K(T(x * K(y \ (z * x),x),x),u) = K(x,T(u,T(z \ y,x) \ x))
    ]]></literal>
    <justification jstring="[para(3462(a,1),4221(a,1,1,1,2))].">
      <j1 rule="para" parents="3462 4221"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2503(a,1),4245(a,1,2,1))].">
      <j1 rule="para" parents="2503 4245"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(257,a,3816,a(flip),b,4256,a),flip(a)].">
      <j1 rule="hyper" parents="257 3816 4256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(3089,a,4265,a),flip(a)].">
      <j1 rule="hyper" parents="3089 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(4048(a,1),4266(a,1,1,2))].">
      <j1 rule="para" parents="4048 4266"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(124,a,4284,a)].">
      <j1 rule="hyper" parents="124 4284"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,4140,a(flip),b,4294,a),flip(a)].">
      <j1 rule="hyper" parents="257 4140 4294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),4313(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(4315(a,2),282(a,1)),flip(b)].">
      <j1 rule="para" parents="4315 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4316,a,4293,a),flip(a)].">
      <j1 rule="hyper" parents="4316 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,4317,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="115 4317 18"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,u),w,v5) = x * (K(y,z) * R(K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4317(a,1),330(a,1,2,1))].">
      <j1 rule="para" parents="4317 330"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,4319,a)].">
      <j1 rule="hyper" parents="388 4319"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(1501(a,2),4319(a,2,2))].">
      <j1 rule="para" parents="1501 4319"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4322(a,1),3349(a,1,1))].">
      <j1 rule="para" parents="4322 3349"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      (x * (y * R(x,z,u))) \ ((x * y) * R(x,z,u)) = K(y * R(x,z,u),x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1224(a,1),4326(a,1,2))].">
      <j1 rule="para" parents="1224 4326"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(4326(a,2),1506(a,1))].">
      <j1 rule="para" parents="4326 1506"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3599,a,b,4323,a)].">
      <j1 rule="hyper" parents="63 3599 4323"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(361,a,4335,a)].">
      <j1 rule="hyper" parents="361 4335"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4137(a,1),4339(a,1,2))].">
      <j1 rule="para" parents="4137 4339"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(172,a,4312,a(flip),b,3135,a)].">
      <j1 rule="hyper" parents="172 4312 3135"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(3233(a,1),4345(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3233 4345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(3740(a,2),3744(a,1,1))].">
      <j1 rule="para" parents="3740 3744"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,T(x,K(y,z))) = T(K(z,y),T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(3850(a,1),3772(a,1,2,1))].">
      <j1 rule="para" parents="3850 3772"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3880,a(flip),b,3929,a),flip(a)].">
      <j1 rule="hyper" parents="257 3880 3929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(4017,a,3616,a),flip(a)].">
      <j1 rule="hyper" parents="4017 3616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),4350(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(4350(a,1),3500(a,1,1,2))].">
      <j1 rule="para" parents="4350 3500"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(4077(a,1),4025(a,1,1))].">
      <j1 rule="para" parents="4077 4025"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(4218(a,1),4175(a,1))].">
      <j1 rule="para" parents="4218 4175"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      K(L(x,y * z,u),(u \ (u * (x * y))) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[para(359(a,1),4292(a,2,2))].">
      <j1 rule="para" parents="359 4292"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      (x * (y * z)) * u != x * ((y * z) * K(w,y))
    ]]></literal>
    <literal><![CDATA[
      K(w,L(y,z,x)) = u
    ]]></literal>
    <justification jstring="[para(4298(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4298 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(3364,a,4347,a)].">
      <j1 rule="hyper" parents="3364 4347"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      T(x,T((y \ z) \ x,u)) = T(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(113,a,4362,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4362 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4257,a(flip),b,4349,a)].">
      <j1 rule="hyper" parents="63 4257 4349"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),4364(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,336,a(flip),b,3853,a),flip(a)].">
      <j1 rule="hyper" parents="257 336 3853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ (x * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * T(z,u) = w
    ]]></literal>
    <justification jstring="[para(3911(a,2),3433(a,1))].">
      <j1 rule="para" parents="3911 3433"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3982,a(flip),b,3918,a),flip(a)].">
      <j1 rule="hyper" parents="63 3982 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(3926(a,1),3266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3926 3266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      R(x,y,z) * a(u,R(x,y,z),u) = R(x * a(u,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3966(a,1),3974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3966 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      a(x,R(y,z,u),x) * R(y,z,u) = R(y * a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3996,a,b,4371,a)].">
      <j1 rule="hyper" parents="63 3996 4371"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      (R(x * a(y,x,y),z,u) * (z * u)) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4372(a,1),1291(a,1,1,1))].">
      <j1 rule="para" parents="4372 1291"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,1445,a(flip),b,3987,a),flip(a)].">
      <j1 rule="hyper" parents="257 1445 3987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3107(a,1),4374(a,1,2))].">
      <j1 rule="para" parents="3107 4374"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(3767(a,1),4375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3767 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3724,a,b,4376,a)].">
      <j1 rule="hyper" parents="63 3724 4376"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      T(x / ((y \ L(T(y,z),u,y)) \ y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(4377(a,1),3757(a,1,1,2,1))].">
      <j1 rule="para" parents="4377 3757"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(4272,a,4185,a),flip(a)].">
      <j1 rule="hyper" parents="4272 4185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3751(a,1),4379(a,1,2,2))].">
      <j1 rule="para" parents="3751 4379"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(4380(a,1),3500(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4380 3500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(257,a,3500,a(flip),b,4381,a),flip(a)].">
      <j1 rule="hyper" parents="257 3500 4381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(3132(a,1),4382(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3132 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      R(x,K(y,T(z,u)),u * K(z,w)) = R(x,K(y,z),u * K(z,w))
    ]]></literal>
    <justification jstring="[para(3740(a,2),4252(a,1,2))].">
      <j1 rule="para" parents="3740 4252"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4303(a,1),4301(a,2,2))].">
      <j1 rule="para" parents="4303 4301"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(257,a,4245,a,b,4385,a)].">
      <j1 rule="hyper" parents="257 4245 4385"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(4352(a,1),3504(a,1))].">
      <j1 rule="para" parents="4352 3504"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(4034(a,1),4392(a,1))].">
      <j1 rule="para" parents="4034 4392"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ u,x)) = z * T(z \ (K(x,y) * u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4367(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 4367"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ 1)) = u
    ]]></literal>
    <justification jstring="[para(4370(a,2),3145(a,1))].">
      <j1 rule="para" parents="4370 3145"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(4395,a,3292,a),flip(a)].">
      <j1 rule="hyper" parents="4395 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,4276,a,b,4396,a)].">
      <j1 rule="hyper" parents="63 4276 4396"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),4397(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 4397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(2533(a,1),4397(a,1,2,2,1))].">
      <j1 rule="para" parents="2533 4397"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      R(K(x,T((y / z) \ x,u)),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[para(3740(a,2),3742(a,1,1))].">
      <j1 rule="para" parents="3740 3742"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3219,a(flip),b,3790,a),flip(a)].">
      <j1 rule="hyper" parents="257 3219 3790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3496(a,1),4401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3496 4401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u * a(x,y,x)) = (a(x,y,x) * u) \ (z * u)
    ]]></literal>
    <justification jstring="[para(3996(a,1),4011(a,1,2))].">
      <j1 rule="para" parents="3996 4011"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / ((y * z) * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),4050(a,1,1))].">
      <j1 rule="para" parents="4048 4050"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(4054,a,4066,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4054 4066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3541(a,1),4254(a,1))].">
      <j1 rule="para" parents="3541 4254"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      L(K(x,y),z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(128(a,1),4406(a,1,3))].">
      <j1 rule="para" parents="128 4406"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      K((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(3460(a,1),4407(a,1))].">
      <j1 rule="para" parents="3460 4407"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(3480(a,2),4410(a,1))].">
      <j1 rule="para" parents="3480 4410"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      K(x,T((y / (x * z)) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((y / z) \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(4400(a,1),2443(a,1))].">
      <j1 rule="para" parents="4400 2443"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u * a(x,y,x)) = a(x,y,x) \ (u \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(257,a,4006,a(flip),b,4403,a),flip(a)].">
      <j1 rule="hyper" parents="257 4006 4403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / (y * (z * a(u,w,u))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),4404(a,1,2))].">
      <j1 rule="para" parents="4048 4404"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u * a(x,y,x)) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),4418(a,2,2))].">
      <j1 rule="para" parents="22 4418"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      T(a(x,y,x) \ z,a(x,y,x) * u) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(3996(a,2),4420(a,1,2))].">
      <j1 rule="para" parents="3996 4420"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      a(x,y,x) \ T(a(x,y,x) * z,u) = T(z,a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),4421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      a(x,y,x) \ T(a(x,y,x) * z,u) = z * K(z,a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(257,a,2948,a(flip),b,4422,a),flip(a)].">
      <j1 rule="hyper" parents="257 2948 4422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(390,a,4419,a)].">
      <j1 rule="hyper" parents="390 4419"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      R(x,y,K(z * u,z)) = R(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(3972(a,1),4424(a,1,3))].">
      <j1 rule="para" parents="3972 4424"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      R(x,y,K(z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,3345,a(flip),b,4425,a),flip(a)].">
      <j1 rule="hyper" parents="257 3345 4425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,3345,a(flip),b,4425,a),flip(a)].">
      <j1 rule="hyper" parents="63 3345 4425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3613,a,4427,a)].">
      <j1 rule="hyper" parents="3613 4427"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      ((x * y) * R(T(z,y),u,w)) / (R(z,u,w) * y) = R(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,600,a,b,4428,a)].">
      <j1 rule="hyper" parents="63 600 4428"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3485,a(flip),b,4428,a)].">
      <j1 rule="hyper" parents="63 3485 4428"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3636,a(flip),b,4430,a),flip(a)].">
      <j1 rule="hyper" parents="63 3636 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(3319,a,4423,a)].">
      <j1 rule="hyper" parents="3319 4423"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[para(3996(a,1),4435(a,1,1))].">
      <j1 rule="para" parents="3996 4435"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(3402(a,1),3828(a,1,1))].">
      <j1 rule="para" parents="3402 3828"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      (x \ R(x,y,z)) * T(K(u,x),w) = T(x,T(u,w)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,3918,a(flip),b,4052,a),flip(a)].">
      <j1 rule="hyper" parents="257 3918 4052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4249,a(flip),b,4438,a)].">
      <j1 rule="hyper" parents="63 4249 4438"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(4439(a,1),4236(a,1))].">
      <j1 rule="para" parents="4439 4236"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4440,a,4369,a),flip(a)].">
      <j1 rule="hyper" parents="4440 4369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4441(a,1),2763(a,1,1))].">
      <j1 rule="para" parents="4441 2763"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2105(a,1),4442(a,1,2))].">
      <j1 rule="para" parents="2105 4442"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3896,a,4443,a)].">
      <j1 rule="hyper" parents="3896 4443"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      T(T(x,x * y) * R(x \ (x * y),z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2483,a(flip),b,4068,a),flip(a)].">
      <j1 rule="hyper" parents="257 2483 4068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2482,a(flip),b,4069,a),flip(a)].">
      <j1 rule="hyper" parents="257 2482 4069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      T(x * L(x \ (x * y),z,u),x * y) = T(T(x,x * y) * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4446(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      K(T(x * K(y \ (x \ (z * x)),x),x),u) = K(x,T(u,T(z \ (x * y),x) \ x))
    ]]></literal>
    <justification jstring="[para(3707(a,1),4299(a,1,1,1,2))].">
      <j1 rule="para" parents="3707 4299"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(4359,a,3690,a),flip(a)].">
      <j1 rule="hyper" parents="4359 3690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),4454(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 4454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(257,a,4398,a(flip),b,4399,a),flip(a)].">
      <j1 rule="hyper" parents="257 4398 4399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4281,a,b,4456,a)].">
      <j1 rule="hyper" parents="63 4281 4456"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(79(a,1),4457(a,2,2,2,1))].">
      <j1 rule="para" parents="79 4457"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      K(R(x \ R(x,y,z),x,y * z),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(1943(a,2),4161(a,1,1))].">
      <j1 rule="para" parents="1943 4161"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      R(x * R(K(y,x),z,u),w,x) = R(x,w,x) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3256(a,1),3925(a,1,1,2))].">
      <j1 rule="para" parents="3256 3925"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      R(x * R(K(y,x),z,u),w,x) \ R(x,w,x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4470(a,2),3642(a,1,1))].">
      <j1 rule="para" parents="4470 3642"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(4405(a,1),4067(a,1))].">
      <j1 rule="para" parents="4405 4067"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(4472,a,4351,a)].">
      <j1 rule="hyper" parents="4472 4351"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      K((x * ((x \ y) / x)) \ y,(y / x) / z) = K(T(x,x \ y),z \ (y / x))
    ]]></literal>
    <justification jstring="[para(2562(a,1),4211(a,1,1))].">
      <j1 rule="para" parents="2562 4211"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,4345,a(flip),b,4346,a),flip(a)].">
      <j1 rule="hyper" parents="257 4345 4346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),4475(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(104(a,1),4477(a,2,2))].">
      <j1 rule="para" parents="104 4477"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(4417,a,4478,a)].">
      <j1 rule="hyper" parents="4417 4478"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(257,a,4059,a,b,4479,a),flip(a)].">
      <j1 rule="hyper" parents="257 4059 4479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(76(a,1),4480(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 4480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[para(4480(a,1),4133(a,1,1))].">
      <j1 rule="para" parents="4480 4133"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((u \ R(T(x,w),y,z)) * x)) = K(x,T(u \ x,R(T(x,w),y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3815,a(flip),b,4481,a)].">
      <j1 rule="hyper" parents="63 3815 4481"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4167,a,4482,a)].">
      <j1 rule="hyper" parents="4167 4482"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      (((x * a(y,x,y)) * z) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(98(a,1),4373(a,1,1))].">
      <j1 rule="para" parents="98 4373"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2659(a,1),4485(a,1,1,1))].">
      <j1 rule="para" parents="2659 4485"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      ((x * (a(y,x,y) * (x \ z))) * u) / (z * u) = a(y,R(x,x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4486(a,1,2,1))].">
      <j1 rule="para" parents="10 4486"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(4010(a,1),4487(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4010 4487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,20,a,b,4488,a),flip(a)].">
      <j1 rule="hyper" parents="257 20 4488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4489(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(564,a,4492,a),flip(a)].">
      <j1 rule="hyper" parents="564 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4493(a,1),3997(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4493 3997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3997,a(flip),b,4495,a),flip(a)].">
      <j1 rule="hyper" parents="257 3997 4495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      T(T(x,x * y) * R(y,z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4445(a,1,1,2,1))].">
      <j1 rule="para" parents="9 4445"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4447(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      L(K(x,(y / x) / z),x \ y,x) = K(T(x,x \ y),z \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3465,a(flip),b,4474,a)].">
      <j1 rule="hyper" parents="63 3465 4474"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      L(K(x,(y / x) / z),x \ y,x) = K(x,(x \ y) / z)
    ]]></literal>
    <justification jstring="[hyper(257,a,4247,a(flip),b,4499,a),flip(a)].">
      <j1 rule="hyper" parents="257 4247 4499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3728,a(flip),b,4500,a),flip(a)].">
      <j1 rule="hyper" parents="63 3728 4500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(257,a,3218,a(flip),b,3849,a),flip(a)].">
      <j1 rule="hyper" parents="257 3218 3849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      K(K(x,y) * z,R(y,u,w)) = K(z,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3132(a,1),4504(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3132 4504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      K(K(x,y) * z,R(x,u,w)) = K(z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(3132(a,1),4505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3132 4505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      (K(x,y) * z) * K(z,R(x,u,w)) = T(K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(115,a,4506,a(flip),b,2929,a(flip))].">
      <j1 rule="hyper" parents="115 4506 2929"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      T(K(x,y) * z,R(x,u,w)) = K(x,y) * T(z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(3355,a,4507,a),flip(a)].">
      <j1 rule="hyper" parents="3355 4507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4113(a,1),4232(a,1,1,3))].">
      <j1 rule="para" parents="4113 4232"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(3135(a,1),4509(a,2,2))].">
      <j1 rule="para" parents="3135 4509"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,v5) = L(x,w,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(569,a,2890,a)].">
      <j1 rule="hyper" parents="569 2890"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(257,a,4005,a(flip),b,4520,a),flip(a)].">
      <j1 rule="hyper" parents="257 4005 4520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      L(x,L(y,z,u),w * a(u,z,y)) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(2741(a,1),4520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2741 4520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(2741(a,1),4522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2741 4522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      L(x,y * a(z,u,z),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(3996(a,1),4522(a,1,2))].">
      <j1 rule="para" parents="3996 4522"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = a(u,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,2743,a(flip),b,4524,a),flip(a)].">
      <j1 rule="hyper" parents="257 2743 4524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      L(x,T(y,z) / z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(3975(a,1),4525(a,1,2))].">
      <j1 rule="para" parents="3975 4525"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2744,a,4526,a)].">
      <j1 rule="hyper" parents="2744 4526"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      a(x,T(y / z,y),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2477(a,1),4530(a,1,2))].">
      <j1 rule="para" parents="2477 4530"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      L(x,y / T(z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2465(a,1),4529(a,1,2))].">
      <j1 rule="para" parents="2465 4529"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      L(x,((y * z) / y) \ y,u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[para(194(a,1),4532(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="194 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (K(x,y) / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(3122(a,1),3011(a,2,1))].">
      <j1 rule="para" parents="3122 3011"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2981(a,1),4537(a,1,1,1))].">
      <j1 rule="para" parents="2981 4537"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(165,a,4538,a)].">
      <j1 rule="hyper" parents="165 4538"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ L(R(x,y,x),y,x) = R(x,y,x) * K(z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(2473(a,1),4539(a,1,1,2))].">
      <j1 rule="para" parents="2473 4539"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(3667,a,3630,a),flip(a)].">
      <j1 rule="hyper" parents="3667 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(3100(a,1),4544(a,1,1))].">
      <j1 rule="para" parents="3100 4544"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3580,a(flip),b,4545,a),flip(a)].">
      <j1 rule="hyper" parents="63 3580 4545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),4546(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      K(x,((y * z) * R(x,y,z)) / ((u * (K(y * z,x) * y)) * z)) = K(R(x,K(y * z,x) * y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(3193(a,1),4546(a,1,2,1))].">
      <j1 rule="para" parents="3193 4546"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3577,a(flip),b,4547,a),flip(a)].">
      <j1 rule="hyper" parents="63 3577 4547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = K(z * L(y,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3909,a(flip),b,4253,a),flip(a)].">
      <j1 rule="hyper" parents="257 3909 4253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(T(x * K(u \ z,x),x),y)
    ]]></literal>
    <justification jstring="[para(3804(a,1),4450(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3804 4450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x * K(u \ z,x),y)
    ]]></literal>
    <justification jstring="[para(973(a,1),4552(a,2,1))].">
      <j1 rule="para" parents="973 4552"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(257,a,4153,a(flip),b,4553,a),flip(a)].">
      <j1 rule="hyper" parents="257 4153 4553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      K(x,T(y,(z \ (x * u)) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3922,a(flip),b,4554,a)].">
      <j1 rule="hyper" parents="63 3922 4554"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(4237,a,4555,a)].">
      <j1 rule="hyper" parents="4237 4555"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ ((x * z) * u))) = K(x,T(y,a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(14(a,2),4556(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14 4556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z * u),z,u))) = K(x,T(y,a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(463(a,1),4557(a,1,2,2))].">
      <j1 rule="para" parents="463 4557"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4172,a,4558,a),flip(a)].">
      <j1 rule="hyper" parents="4172 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      T(x,T(y,a(x,z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,4559,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4559 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      (T(x,x \ y) * a(x,z,u)) \ (a(x,z,u) * ((x \ y) \ y)) = K(a(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(4561(a,1),4246(a,1,1,1))].">
      <j1 rule="para" parents="4561 4246"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      K(a(x,y,z),T(x,u)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(3945,a,4562,a)].">
      <j1 rule="hyper" parents="3945 4562"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      T(x,T((1 / y) \ x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4061(a,2),3243(a,1,1))].">
      <j1 rule="para" parents="4061 3243"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      K(x,y \ R(T(z,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3284(a,1),3809(a,1,2))].">
      <j1 rule="para" parents="3284 3809"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) * (T(x,u) \ w) = R(x,u,R(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(4258(a,1),3295(a,1,1))].">
      <j1 rule="para" parents="4258 3295"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3636,a(flip),b,3568,a),flip(a)].">
      <j1 rule="hyper" parents="63 3636 3568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      R(T(x,y * a(z,u,z)),y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = w
    ]]></literal>
    <justification jstring="[para(3999(a,1),4004(a,1))].">
      <j1 rule="para" parents="3999 4004"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(4572,a,4049,a)].">
      <j1 rule="hyper" parents="4572 4049"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(212,a,4573,a),flip(a)].">
      <j1 rule="hyper" parents="212 4573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,4574,a(flip),b,2976,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="172 4574 2976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(3980(a,1),4574(a,1,2))].">
      <j1 rule="para" parents="3980 4574"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3758,a,b,4579,a)].">
      <j1 rule="hyper" parents="63 3758 4579"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,2971,a,b,4577,a),flip(a)].">
      <j1 rule="hyper" parents="257 2971 4577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(4577(a,2),3006(a,1))].">
      <j1 rule="para" parents="4577 3006"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4436,a(flip),b,4581,a)].">
      <j1 rule="hyper" parents="63 4436 4581"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2045(a,1),4581(a,1,1,2))].">
      <j1 rule="para" parents="2045 4581"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2045(a,1),4583(a,1,2,1))].">
      <j1 rule="para" parents="2045 4583"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3993(a,1),4583(a,1,2))].">
      <j1 rule="para" parents="3993 4583"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(1788(a,1),4584(a,1,1))].">
      <j1 rule="para" parents="1788 4584"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1751(a,1),4586(a,1,2))].">
      <j1 rule="para" parents="1751 4586"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3174,a(flip),b,4587,a),flip(a)].">
      <j1 rule="hyper" parents="257 3174 4587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(113,a,4592,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4592 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4225,a(flip),b,4580,a)].">
      <j1 rule="hyper" parents="63 4225 4580"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = (y * z) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(115,a,4595,a(flip),b,4178,a),flip(a)].">
      <j1 rule="hyper" parents="115 4595 4178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      K(T(x * y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(3980(a,1),4582(a,1,1))].">
      <j1 rule="para" parents="3980 4582"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(3477,a,4589,a)].">
      <j1 rule="hyper" parents="3477 4589"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1081(a,1),4590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1081 4590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(4597,a,4137,a)].">
      <j1 rule="hyper" parents="4597 4137"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(4597,a,3890,a),flip(a)].">
      <j1 rule="hyper" parents="4597 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = K(y,z) * (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3992,a,b,4596,a),flip(a)].">
      <j1 rule="hyper" parents="257 3992 4596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4112,a,b,4603,a(flip))].">
      <j1 rule="hyper" parents="34 4112 4603"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3556,a,4604,a)].">
      <j1 rule="hyper" parents="3556 4604"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(4604(a,1),4165(a,1,2,2))].">
      <j1 rule="para" parents="4604 4165"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,4605,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4605 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3455,a,b,4605,a)].">
      <j1 rule="hyper" parents="63 3455 4605"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(4607(a,1),3618(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4607 3618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(3949,a,4608,a)].">
      <j1 rule="hyper" parents="3949 4608"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3681,a,b,4613,a)].">
      <j1 rule="hyper" parents="63 3681 4613"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      K(x,x \ ((y * (x \ z)) \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4473,a(flip),b,4613,a),flip(a)].">
      <j1 rule="hyper" parents="63 4473 4613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4065,a(flip),b,4614,a),flip(a)].">
      <j1 rule="hyper" parents="63 4065 4614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,18,a,b,4612,a)].">
      <j1 rule="hyper" parents="257 18 4612"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),4617(a,1,2)),flip(a)].">
      <j1 rule="para" parents="104 4617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(4619(a,1),3475(a,1,1))].">
      <j1 rule="para" parents="4619 3475"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4616,a(flip),b,4615,a)].">
      <j1 rule="hyper" parents="63 4616 4615"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(4054,a,4621,a)].">
      <j1 rule="hyper" parents="4054 4621"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(4622(a,1),3126(a,1,2,2))].">
      <j1 rule="para" parents="4622 3126"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(3154,a,4623,a),flip(a)].">
      <j1 rule="hyper" parents="3154 4623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(4621(a,2),4623(a,1,2,2))].">
      <j1 rule="para" parents="4621 4623"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(4625(a,1),3154(a,1))].">
      <j1 rule="para" parents="4625 3154"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(4626,a,4624,a)].">
      <j1 rule="hyper" parents="4626 4624"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),4627(a,2,1,1))].">
      <j1 rule="para" parents="8 4627"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3735,a,b,4628,a)].">
      <j1 rule="hyper" parents="63 3735 4628"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3734,a,b,4628,a)].">
      <j1 rule="hyper" parents="63 3734 4628"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(4630(a,1),3539(a,1,2))].">
      <j1 rule="para" parents="4630 3539"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(4631(a,1),3141(a,1,2))].">
      <j1 rule="para" parents="4631 3141"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(2780,a,4632,a)].">
      <j1 rule="hyper" parents="2780 4632"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),4633(a,2,2,2,1))].">
      <j1 rule="para" parents="10 4633"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,T(u,z)),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(3880(a,1),4160(a,2,1,2))].">
      <j1 rule="para" parents="3880 4160"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(498,a,4330,a),flip(a)].">
      <j1 rule="hyper" parents="498 4330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) / x = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4263,a(flip),b,4636,a)].">
      <j1 rule="hyper" parents="63 4263 4636"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) * K(x,u) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4601(a,2),4636(a,1,1))].">
      <j1 rule="para" parents="4601 4636"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(115,a,4637,a(flip),b,1937,a(flip))].">
      <j1 rule="hyper" parents="115 4637 1937"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      K(x,y) * a(y,x,R(y,z,u)) = K(R(y,z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(4638(a,1),3139(a,1,2))].">
      <j1 rule="para" parents="4638 3139"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((u \ R(T(x,w),y,z)) * x)) = K(x,u \ x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3893,a(flip),b,4483,a),flip(a)].">
      <j1 rule="hyper" parents="257 3893 4483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ (u \ R(T(x,w),y,z)))) = K(x,u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4063,a(flip),b,4641,a)].">
      <j1 rule="hyper" parents="63 4063 4641"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      T(x,T((y \ 1) \ x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2860(a,1),4564(a,1,1))].">
      <j1 rule="para" parents="2860 4564"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,u),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(4384(a,1),4635(a,2,1))].">
      <j1 rule="para" parents="4384 4635"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = (x * K(y,u)) * (K(u,y) * z)
    ]]></literal>
    <justification jstring="[hyper(257,a,4510,a(flip),b,4657,a),flip(a)].">
      <j1 rule="hyper" parents="257 4510 4657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (K(z,T(y,u)) * u) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(3880(a,1),4658(a,1,1,2))].">
      <j1 rule="para" parents="3880 4658"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4132(a,1),4659(a,1,2))].">
      <j1 rule="para" parents="4132 4659"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      T(x,T(1 \ (y * x),z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),4644(a,1,1))].">
      <j1 rule="para" parents="4363 4644"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(65(a,1),4662(a,1,1,2,1))].">
      <j1 rule="para" parents="65 4662"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2835(a,1),2843(a,2,1))].">
      <j1 rule="para" parents="2835 2843"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[para(2983(a,1),3117(a,2,2))].">
      <j1 rule="para" parents="2983 3117"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,18,a,b,4665,a),flip(a)].">
      <j1 rule="hyper" parents="257 18 4665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3989,a(flip),b,4666,a)].">
      <j1 rule="hyper" parents="63 3989 4666"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3830,a(flip),b,4666,a)].">
      <j1 rule="hyper" parents="63 3830 4666"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      L(x,y,(y * z) / y) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),4668(a,1,3)),flip(a)].">
      <j1 rule="para" parents="194 4668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(4669(a,1),25(a,2,1))].">
      <j1 rule="para" parents="4669 25"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,25,a,b,4672,a),flip(a)].">
      <j1 rule="hyper" parents="257 25 4672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      L(T(x,y),z,(x \ u) \ u) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(103(a,1),4674(a,1,3))].">
      <j1 rule="para" parents="103 4674"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      L(T(x,x \ y),y / x,(x \ z) \ z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2532,a(flip),b,4675,a),flip(a)].">
      <j1 rule="hyper" parents="257 2532 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      L((x \ y) \ y,y / x,(x \ z) \ z) = T(x,y)
    ]]></literal>
    <justification jstring="[para(103(a,1),4677(a,1,1))].">
      <j1 rule="para" parents="103 4677"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4678(a,1),4524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4678 4524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),4664(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (K(x \ 1,x) * (z * u)) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[para(1803(a,1),2871(a,1,2))].">
      <j1 rule="para" parents="1803 2871"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(2730(a,1),2872(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2730 2872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,18,a,b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="257 18 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(1778(a,2),4690(a,1,2))].">
      <j1 rule="para" parents="1778 4690"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      L(x,T((y \ 1) \ 1,z) \ u,w) = L(x,T(y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(2178(a,1),4692(a,1,2))].">
      <j1 rule="para" parents="2178 4692"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      L(x,T(1 / y,z) \ u,w) = L(x,T(y \ 1,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),4693(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 4693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      ((x * y) * z) / ((x * T(x \ (x * y),u)) * z) = K(u,R(y * K(x,y),x,z))
    ]]></literal>
    <justification jstring="[para(1000(a,1),3283(a,1,2))].">
      <j1 rule="para" parents="1000 3283"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      ((x * y) * z) / ((x * T(y,u)) * z) = K(u,R(y * K(x,y),x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),4695(a,1,2,1,2,1))].">
      <j1 rule="para" parents="9 4695"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      ((x * y) * z) / ((x * T(y,u)) * z) = K(u,R(T(y,x),x,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,4219,a(flip),b,4696,a),flip(a)].">
      <j1 rule="hyper" parents="257 4219 4696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(T(x,z),R(T(y,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3921,a(flip),b,4697,a)].">
      <j1 rule="hyper" parents="63 3921 4697"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(257,a,4149,a(flip),b,4698,a),flip(a)].">
      <j1 rule="hyper" parents="257 4149 4698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      R(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(4698(a,2),4176(a,1))].">
      <j1 rule="para" parents="4698 4176"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      K(R(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,x,z)) = u
    ]]></literal>
    <justification jstring="[para(3580(a,1),4700(a,1))].">
      <j1 rule="para" parents="3580 4700"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      K(a(x,y,z),T(x,x * (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = u
    ]]></literal>
    <justification jstring="[para(4468(a,1),4703(a,1))].">
      <j1 rule="para" parents="4468 4703"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = T(K(z,y),T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(3841(a,1),4348(a,1,2))].">
      <j1 rule="para" parents="3841 4348"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,4126,a(flip),b,4705,a),flip(a)].">
      <j1 rule="hyper" parents="257 4126 4705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      K(L(x,y * z,u),(x * y) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),4360(a,1,2,1))].">
      <j1 rule="para" parents="9 4360"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      K(L(x,y * z,u),L(z,y,x)) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),4708(a,1,2))].">
      <j1 rule="para" parents="18 4708"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(3731,a,4710,a)].">
      <j1 rule="hyper" parents="3731 4710"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(3729,a,4711,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3729 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),4712(a,2,2,2))].">
      <j1 rule="para" parents="10 4712"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      K(x,L(y,x * (z / y),u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4712(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      K(L(x,T(y * (x \ z),y),u),R(y,x \ z,y)) = K(x,L(R(y,x \ z,y),z,u))
    ]]></literal>
    <justification jstring="[para(2489(a,1),4713(a,1,1,2))].">
      <j1 rule="para" parents="2489 4713"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(3829(a,1),4714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3829 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4037,a(flip),b,4716,a)].">
      <j1 rule="hyper" parents="63 4037 4716"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(3002(a,1),4717(a,1,1,2))].">
      <j1 rule="para" parents="3002 4717"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4145(a,1),4717(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4145 4717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(3555(a,1),4720(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3555 4720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      R((x \ y) * K(z \ (x \ y),x \ y),u,w) \ R(x \ y,u,w) = K(R(x \ y,u,w),z \ (y / x))
    ]]></literal>
    <justification jstring="[para(4719(a,1),3219(a,1,1,1,2))].">
      <j1 rule="para" parents="4719 3219"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(L(u,z,y),y * z,x),y)
    ]]></literal>
    <justification jstring="[para(359(a,1),4721(a,2,1))].">
      <j1 rule="para" parents="359 4721"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3706,a(flip),b,4723,a),flip(a)].">
      <j1 rule="hyper" parents="257 3706 4723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(4393,a,4724,a)].">
      <j1 rule="hyper" parents="4393 4724"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      K(L(x,T(y * (x \ z),y),u),y) = K(x,L(R(y,x \ z,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(3725,a,4715,a)].">
      <j1 rule="hyper" parents="3725 4715"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * ((y * z) * u)) / (z * u)) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2740,a(flip),b,4688,a)].">
      <j1 rule="hyper" parents="63 2740 4688"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[para(1295(a,1),4730(a,1,2))].">
      <j1 rule="para" parents="1295 4730"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1816,a(flip),b,4732,a),flip(a)].">
      <j1 rule="hyper" parents="63 1816 4732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(780(a,1),4733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="780 4733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      a(x,x \ 1,y) * x = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2857,a,b,4735,a)].">
      <j1 rule="hyper" parents="63 2857 4735"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      a(x,x \ 1,y) * (x * z) = R(x,x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(4738(a,1),331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4738 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      ((R(x,x \ 1,y) * z) * u) / ((x * z) * u) = R(a(x,x \ 1,y),x * z,u)
    ]]></literal>
    <justification jstring="[para(4745(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4745 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),x \ 1,u) = R(a(x,x \ 1,u),x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3274,a(flip),b,4747,a)].">
      <j1 rule="hyper" parents="63 3274 4747"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      R(x,y,z) * a(x,x \ 1,u) = R(R(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(115,a,560,a(flip),b,4761,a)].">
      <j1 rule="hyper" parents="115 560 4761"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(113,a,676,a(flip),b,3564,a)].">
      <j1 rule="hyper" parents="113 676 3564"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(203,a,4765,a(flip),b,3063,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="203 4765 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ (K(z,u) * y),z) = K(z,u) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(4765(a,1),4394(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4765 4394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K((1 / x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4765(a,1),3564(a,1,1,2))].">
      <j1 rule="para" parents="4765 3564"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(2180,a,4766,a)].">
      <j1 rule="hyper" parents="2180 4766"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(76(a,1),4766(a,1,1,1,1))].">
      <j1 rule="para" parents="76 4766"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(3443,a,4769,a)].">
      <j1 rule="hyper" parents="3443 4769"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,3740,a,b,4770,a),flip(a)].">
      <j1 rule="hyper" parents="257 3740 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3920,a(flip),b,4772,a),flip(a)].">
      <j1 rule="hyper" parents="63 3920 4772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      T(K(T(x,y) \ 1,z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4772(a,2),4133(a,1,1))].">
      <j1 rule="para" parents="4772 4133"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K((y \ 1) \ 1,T(x,z)) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4772(a,1),4663(a,1,2))].">
      <j1 rule="para" parents="4772 4663"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      K(T(T(x,y),y) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4770,a,b,4776,a)].">
      <j1 rule="hyper" parents="63 4770 4776"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      K(T(T(x,x * y),y) \ 1,z) = K(L(x,y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(469(a,1),4778(a,1,1,1,1))].">
      <j1 rule="para" parents="469 4778"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      K(x \ 1,T(y,x * z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),4775(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      K(T(T(x,y),x * y) \ 1,z) = K(L(x,y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(23(a,1),4779(a,1,1,1))].">
      <j1 rule="para" parents="23 4779"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,x * y)) = K(L(x,y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4772,a(flip),b,4781,a)].">
      <j1 rule="hyper" parents="63 4772 4781"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      K(x \ 1,T(T(y,x * z),z)) = K(L(x,z,x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4772,a(flip),b,4782,a)].">
      <j1 rule="hyper" parents="63 4772 4782"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      K(x \ 1,T(T(y,z),x * z)) = K(L(x,z,x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(23(a,1),4783(a,1,2))].">
      <j1 rule="para" parents="23 4783"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4780,a(flip),b,4784,a),flip(a)].">
      <j1 rule="hyper" parents="63 4780 4784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,4136,a(flip),b,4785,a),flip(a)].">
      <j1 rule="hyper" parents="257 4136 4785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[para(4786(a,1),3298(a,1,2))].">
      <j1 rule="para" parents="4786 3298"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(388,a,4788,a)].">
      <j1 rule="hyper" parents="388 4788"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      R(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2144(a,1),4789(a,1,3))].">
      <j1 rule="para" parents="2144 4789"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,4790,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="114 4790 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4361,a,4791,a)].">
      <j1 rule="hyper" parents="4361 4791"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,u,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3578,a,b,4792,a)].">
      <j1 rule="hyper" parents="63 3578 4792"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,676,a(flip),b,4768,a),flip(a)].">
      <j1 rule="hyper" parents="257 676 4768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(114,a,676,a(flip),b,4768,a)].">
      <j1 rule="hyper" parents="114 676 4768"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[hyper(36,a,3137,a,b,4794,a)].">
      <j1 rule="hyper" parents="36 3137 4794"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(4358,a,4795,a),flip(a)].">
      <j1 rule="hyper" parents="4358 4795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(3132(a,1),4797(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3132 4797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,3176,a,b,4798,a),flip(a)].">
      <j1 rule="hyper" parents="34 3176 4798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3177,a,4800,a)].">
      <j1 rule="hyper" parents="3177 4800"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(4077(a,1),4800(a,1,1))].">
      <j1 rule="para" parents="4077 4800"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3900,a,4801,a)].">
      <j1 rule="hyper" parents="3900 4801"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(315,a,4803,a)].">
      <j1 rule="hyper" parents="315 4803"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      K(x,T(y,T(z,L(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4804(a,1),3894(a,1,2))].">
      <j1 rule="para" parents="4804 3894"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4802(a,1),3813(a,1,2))].">
      <j1 rule="para" parents="4802 3813"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,L(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(104(a,1),4805(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="104 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(104(a,1),4806(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="104 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,4455,a(flip),b,4807,a),flip(a)].">
      <j1 rule="hyper" parents="257 4455 4807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(163(a,1),4809(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="163 4809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4606,a(flip),b,4811,a)].">
      <j1 rule="hyper" parents="63 4606 4811"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),4812(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 4812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (y * (x \ z))) = w
    ]]></literal>
    <justification jstring="[para(4813(a,1),4171(a,1))].">
      <j1 rule="para" parents="4813 4171"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4366,a(flip),b,4808,a),flip(a)].">
      <j1 rule="hyper" parents="63 4366 4808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),4815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(R(x,z,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(4817(a,1),4174(a,1))].">
      <j1 rule="para" parents="4817 4174"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2144(a,1),4777(a,1,2))].">
      <j1 rule="para" parents="2144 4777"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,T(y \ 1,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,4694,a(flip),b,4819,a),flip(a)].">
      <j1 rule="hyper" parents="257 4694 4819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      L(x,T(y \ 1,z) \ 1,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4444,a(flip),b,4820,a),flip(a)].">
      <j1 rule="hyper" parents="63 4444 4820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4693,a(flip),b,4821,a)].">
      <j1 rule="hyper" parents="63 4693 4821"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(104(a,1),4823(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="104 4823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,941,a(flip),b,4767,a)].">
      <j1 rule="hyper" parents="63 941 4767"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(4038(a,2),4825(a,1,1))].">
      <j1 rule="para" parents="4038 4825"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),4826(a,1,1,2,1))].">
      <j1 rule="para" parents="79 4826"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(361,a,4827,a)].">
      <j1 rule="hyper" parents="361 4827"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(257,a,4799,a(flip),b,4827,a),flip(a)].">
      <j1 rule="hyper" parents="257 4799 4827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      L(T(x / (x / y),y \ x),K(z,u),K(u,w)) = y
    ]]></literal>
    <justification jstring="[hyper(257,a,2518,a(flip),b,4828,a),flip(a)].">
      <j1 rule="hyper" parents="257 2518 4828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(1501(a,1),4829(a,1,1))].">
      <j1 rule="para" parents="1501 4829"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(112,a,4797,a(flip),b,4833,a)].">
      <j1 rule="hyper" parents="112 4797 4833"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(2922(a,1),4835(a,1,1))].">
      <j1 rule="para" parents="2922 4835"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      x / (K(((y \ 1) * x) \ x,z) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(186(a,2),4838(a,1,2,2,2))].">
      <j1 rule="para" parents="186 4838"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x,y,x) * K(z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(2473(a,1),4540(a,1,2))].">
      <j1 rule="para" parents="2473 4540"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3216,a(flip),b,4844,a),flip(a)].">
      <j1 rule="hyper" parents="257 3216 4844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(3691(a,1),4845(a,1,1,1,1))].">
      <j1 rule="para" parents="3691 4845"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[para(3293(a,1),4846(a,1,1))].">
      <j1 rule="para" parents="3293 4846"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(4376(a,1),4847(a,1,1))].">
      <j1 rule="para" parents="4376 4847"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      (x * (y * (K(z,z \ 1) * u))) \ ((x * y) * (K(z,z \ 1) * u)) = a(x,y * K(z,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2718(a,1),2714(a,1,2))].">
      <j1 rule="para" parents="2718 2714"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z
    ]]></literal>
    <justification jstring="[para(333(a,1),3183(a,1,2))].">
      <j1 rule="para" parents="333 3183"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (T(u,x) * (u \ z))) = y * z
    ]]></literal>
    <justification jstring="[para(200(a,1),4851(a,1,2,2))].">
      <j1 rule="para" parents="200 4851"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(2965(a,1),4852(a,1,2,2))].">
      <j1 rule="para" parents="2965 4852"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(4853(a,1),4020(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4853 4020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(4853(a,1),4056(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4853 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(4853(a,1),4283(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4853 4283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),K(u,x) * z,w)) = K(x,(w * (K(u,x) * z)) \ (w * (z * y)))
    ]]></literal>
    <justification jstring="[para(359(a,1),4855(a,1,2))].">
      <j1 rule="para" parents="359 4855"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ (y * (u * w))) = K(x,L(w,K(z,x) * u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3834,a(flip),b,4857,a),flip(a)].">
      <j1 rule="hyper" parents="63 3834 4857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4854,a(flip),b,4858,a),flip(a)].">
      <j1 rule="hyper" parents="63 4854 4858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),4860(a,2,2))].">
      <j1 rule="para" parents="18 4860"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(3132(a,1),4862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3132 4862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(4863(a,1),3126(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4863 3126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3126,a(flip),b,4864,a),flip(a)].">
      <j1 rule="hyper" parents="257 3126 4864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(2967(a,1),4865(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2967 4865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4727,a(flip),b,4866,a)].">
      <j1 rule="hyper" parents="63 4727 4866"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(4093(a,1),3836(a,1,2,2))].">
      <j1 rule="para" parents="4093 3836"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(4704,a,4563,a)].">
      <j1 rule="hyper" parents="4704 4563"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      K(a(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(3290,a,4869,a),flip(a)].">
      <j1 rule="hyper" parents="3290 4869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      K(x,a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,4870,a,b,3083,a),flip(a)].">
      <j1 rule="hyper" parents="110 4870 3083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      T(x,a(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,4872,a)].">
      <j1 rule="hyper" parents="56 4872"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      (x * a(x,y,z)) / x = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(172,a,4873,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="172 4873 22"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      a(x,y,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4873(a,1),232(a,1,2))].">
      <j1 rule="para" parents="4873 232"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      ((x * a(x,y,z)) * (x \ u)) / u = R(a(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[para(4874(a,1),399(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4874 399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      (x * a(x,y,z)) * (x \ u) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(114,a,560,a(flip),b,4876,a),flip(a)].">
      <j1 rule="hyper" parents="114 560 4876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      R(1 / x,x,y) * ((1 / x) \ z) = a(1 / x,x,y) * z
    ]]></literal>
    <justification jstring="[para(2793(a,1),4878(a,1,1))].">
      <j1 rule="para" parents="2793 4878"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      R(1 / x,x,y) * ((1 / x) \ z) = a(x \ 1,x,y) * z
    ]]></literal>
    <justification jstring="[para(2755(a,1),4880(a,2,1))].">
      <j1 rule="para" parents="2755 4880"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      a(x \ 1,x,y) * (R(1 / x,x,y) \ z) = (1 / x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,1283,a(flip),b,4881,a),flip(a)].">
      <j1 rule="hyper" parents="63 1283 4881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      a(x \ 1,x,y) * (x * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(297(a,1),4882(a,1,2))].">
      <j1 rule="para" parents="297 4882"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      a((x \ 1) \ 1,x \ 1,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[para(76(a,1),4883(a,2,1))].">
      <j1 rule="para" parents="76 4883"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      a(x,x \ 1,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[para(2758(a,1),4884(a,1,1))].">
      <j1 rule="para" parents="2758 4884"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      (x * (y \ z)) / ((y \ 1) * z) = x * a(y,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4885(a,1),2665(a,1,1,2))].">
      <j1 rule="para" parents="4885 2665"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) / ((x \ 1) * u) = R(R(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,4763,a(flip),b,4886,a),flip(a)].">
      <j1 rule="hyper" parents="257 4763 4886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(37,a,758,a,b,4887,a)].">
      <j1 rule="hyper" parents="37 758 4887"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      (R(x,y,z) * u) / (x * u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(112,a,132,a(flip),b,4888,a)].">
      <j1 rule="hyper" parents="112 132 4888"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4889(a,1),243(a,1,1))].">
      <j1 rule="para" parents="4889 243"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ w = y * (R(y,z,u) \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2654,a,b,4890,a)].">
      <j1 rule="hyper" parents="63 2654 4890"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      x * (R(x,y,z) \ ((u * x) \ w)) = (u * R(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(2630(a,1),4891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2630 4891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * w) = y * (R(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),4892(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      L(x,y,R((y * z) / y,y,x)) = z * (R(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,838,a,b,4893,a)].">
      <j1 rule="hyper" parents="63 838 4893"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(498,a,4850,a),flip(a)].">
      <j1 rule="hyper" parents="498 4850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x,T(x * y,z)),K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(3877(a,1),4868(a,2,1))].">
      <j1 rule="para" parents="3877 4868"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(257,a,4343,a(flip),b,4897,a),flip(a)].">
      <j1 rule="hyper" parents="257 4343 4897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ (K(x,z) * K(y,K(u,y * K(x,z)))) = K(y,T(y * K(x,z),u))
    ]]></literal>
    <justification jstring="[para(3592(a,2),4898(a,1,1))].">
      <j1 rule="para" parents="3592 4898"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ (K(x,z) * 1) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[para(3795(a,1),4901(a,1,2,2))].">
      <j1 rule="para" parents="3795 4901"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(240,a,4902,a)].">
      <j1 rule="hyper" parents="240 4902"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(3146,a,4903,a)].">
      <j1 rule="hyper" parents="3146 4903"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(3593(a,1),4904(a,1,1))].">
      <j1 rule="para" parents="3593 4904"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(257,a,3871,a(flip),b,4905,a),flip(a)].">
      <j1 rule="hyper" parents="257 3871 4905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3624,a(flip),b,4906,a)].">
      <j1 rule="hyper" parents="63 3624 4906"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      T(T(x * K(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x)
    ]]></literal>
    <justification jstring="[para(4907(a,1),3242(a,1,1,1,2))].">
      <j1 rule="para" parents="4907 3242"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      T(T(T(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x)
    ]]></literal>
    <justification jstring="[para(2948(a,2),4908(a,1,1,1))].">
      <j1 rule="para" parents="2948 4908"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3863,a,4909,a)].">
      <j1 rule="hyper" parents="3863 4909"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(4910(a,1),4706(a,1,1))].">
      <j1 rule="para" parents="4910 4706"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * (w \ z)) \ u) * x,x) = K(w,T((y * (w \ z)) \ u,x))
    ]]></literal>
    <justification jstring="[para(4627(a,1),4911(a,1,1,2,2))].">
      <j1 rule="para" parents="4627 4911"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,T(z,L(z,u,w))),L(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(3901,a,3597,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3901 3597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(153(a,1),4913(a,2,1,2))].">
      <j1 rule="para" parents="153 4913"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1267(a,1),4914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1267 4914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4598,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="63 4598 4915"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3459,a(flip),b,4915,a),flip(a)].">
      <j1 rule="hyper" parents="63 3459 4915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),4687(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="79 4687"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),4919(a,1,2))].">
      <j1 rule="para" parents="79 4919"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(4920(a,1),4570(a,1,1))].">
      <j1 rule="para" parents="4920 4570"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(3567,a,4921,a)].">
      <j1 rule="hyper" parents="3567 4921"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      R(a(x,y,R(z,u,w)),L(R(z,u,w),y,x),u * w) = ((z * u) * w) / ((L(z,y,x) * u) * w)
    ]]></literal>
    <justification jstring="[para(325(a,1),2749(a,2,2))].">
      <j1 rule="para" parents="325 2749"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      ((x * y) * z) / ((L(x,u,w) * y) * z) = a(w,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(564,a,4936,a),flip(a)].">
      <j1 rule="hyper" parents="564 4936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      R(a(x,y,z),L(z,y,x) * u,w) = a(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2761,a,b,4937,a)].">
      <j1 rule="hyper" parents="63 2761 4937"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(564,a,4939,a),flip(a)].">
      <j1 rule="hyper" parents="564 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      a(x,y,z / (u * z)) = a(x,y,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2805,a(flip),b,4940,a)].">
      <j1 rule="hyper" parents="63 2805 4940"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(397(a,1),4940(a,1,3))].">
      <j1 rule="para" parents="397 4940"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(899(a,1),4940(a,1,3)),flip(a)].">
      <j1 rule="para" parents="899 4940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4940(a,1),4639(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4940 4639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u,x) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(4940(a,1),4640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4940 4640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3955,a(flip),b,4945,a),flip(a)].">
      <j1 rule="hyper" parents="257 3955 4945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      a(x,y,(z \ u) / u) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),4942(a,1,3,2))].">
      <j1 rule="para" parents="10 4942"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(x * u,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3972,a(flip),b,4946,a),flip(a)].">
      <j1 rule="hyper" parents="257 3972 4946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      K(x * R(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4601,a(flip),b,4951,a)].">
      <j1 rule="hyper" parents="63 4601 4951"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(L(z,u,w),y,x),w * u) = (w * (u * L(z,y,x))) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(329(a,1),2783(a,2,1))].">
      <j1 rule="para" parents="329 2783"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) \ (x * (y * z)) = a(w,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2854,a(flip),b,4955,a),flip(a)].">
      <j1 rule="hyper" parents="63 2854 4955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      L(a(x,y,z),u * L(z,y,x),w) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2788,a,b,4956,a)].">
      <j1 rule="hyper" parents="63 2788 4956"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4045,a(flip),b,4958,a),flip(a)].">
      <j1 rule="hyper" parents="63 4045 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      a(x,y,L(z,u / L(z,y,x),w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),4958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = R(x,y,x) / x
    ]]></literal>
    <justification jstring="[hyper(257,a,3958,a,b,4959,a),flip(a)].">
      <j1 rule="hyper" parents="257 3958 4959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4944,a(flip),b,4960,a),flip(a)].">
      <j1 rule="hyper" parents="63 4944 4960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(115,a,4962,a(flip),b,4689,a(flip))].">
      <j1 rule="hyper" parents="115 4962 4689"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      T((x * y) / L(x,z,u),x) = y * a(u,z,x)
    ]]></literal>
    <justification jstring="[hyper(203,a,2765,a,b,4963,a(flip))].">
      <j1 rule="hyper" parents="203 2765 4963"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = (y \ x) * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4964(a,1,1,1))].">
      <j1 rule="para" parents="10 4964"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      T(L(x,y,z) \ u,a(z,y,x)) = T(u / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(257,a,2789,a,b,4965,a)].">
      <j1 rule="hyper" parents="257 2789 4965"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      T((L(x,y,z) * u) / L(x,y,z),x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),4966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(4967(a,1),226(a,1,1))].">
      <j1 rule="para" parents="4967 226"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      T(x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,4607,a,b,4968,a),flip(a)].">
      <j1 rule="hyper" parents="40 4607 4968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(113,a,4969,a,b,2480,a)].">
      <j1 rule="hyper" parents="113 4969 2480"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      (T(x,y) \ z) / (R(x,y,R(x,u,w)) \ z) = K(R(x,u,w) * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4429(a,1),3189(a,1,2,1))].">
      <j1 rule="para" parents="4429 3189"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      (T(x,y) \ z) / (R(x,y,R(x,u,w)) \ z) = K(y * R(x,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(257,a,4600,a(flip),b,4971,a),flip(a)].">
      <j1 rule="hyper" parents="257 4600 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      K(x * R(y,z,u),y) = (T(y,x) \ w) / (R(y,x,y) \ w)
    ]]></literal>
    <justification jstring="[para(4947(a,1),4972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4947 4972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      (T(x,y) \ z) / (R(x,y,x) \ z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4953,a(flip),b,4973,a),flip(a)].">
      <j1 rule="hyper" parents="63 4953 4973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      K(x,x * y) * (T(x,y) \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(36,a,3137,a,b,4974,a)].">
      <j1 rule="hyper" parents="36 3137 4974"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ w = K(x,x * y) * (T(x,y) \ w)
    ]]></literal>
    <justification jstring="[para(4947(a,2),4976(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4947 4976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(35,a,4568,a,b,4977,a(flip))].">
      <j1 rule="hyper" parents="35 4568 4977"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,u) * w) = K(x,x * w)
    ]]></literal>
    <justification jstring="[hyper(3756,a,4978,a)].">
      <j1 rule="hyper" parents="3756 4978"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(113,a,4978,a,b,3175,a),flip(a)].">
      <j1 rule="hyper" parents="113 4978 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),4978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),z,u) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(4980(a,1),2561(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4980 2561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4643,a(flip),b,4982,a),flip(a)].">
      <j1 rule="hyper" parents="63 4643 4982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4566,a,4985,a)].">
      <j1 rule="hyper" parents="4566 4985"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      R(T(x,x * (x \ (R(x,y,z) \ u))),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2569,a(flip),b,4984,a),flip(a)].">
      <j1 rule="hyper" parents="63 2569 4984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),4988(a,1,1,2))].">
      <j1 rule="para" parents="10 4988"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(446,a,4991,a),flip(a)].">
      <j1 rule="hyper" parents="446 4991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(467(a,1),4992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="467 4992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(4994(a,1),3666(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4994 3666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(T(u * z,u) / u,y,x)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(1275(a,2),3976(a,1,2,2))].">
      <j1 rule="para" parents="1275 3976"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(3520,a,4722,a),flip(a)].">
      <j1 rule="hyper" parents="3520 4722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(x \ (x * y),z,u),w * K(x,y))
    ]]></literal>
    <justification jstring="[para(3031(a,1),4997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3031 4997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      L(a(x,L(y,z,u),x),L(y,z,u),u * z) = (u * (z * y)) \ (u * (z * (T(x * y,x) / x)))
    ]]></literal>
    <justification jstring="[para(90(a,1),4996(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,((y * z) * R(x,y,z)) / ((u * y) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4856,a(flip),b,4548,a),flip(a)].">
      <j1 rule="hyper" parents="63 4856 4548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      T(x / R(y * K(z,y),u,y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(4849(a,1),4378(a,1,1,2))].">
      <j1 rule="para" parents="4849 4378"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),T(R((u * y) / u,z,y),y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(4074(a,1),5043(a,1,1))].">
      <j1 rule="para" parents="4074 5043"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R(T((u * y) / u,y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(27(a,2),5044(a,1,2))].">
      <j1 rule="para" parents="27 5044"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R((u * y) / u,z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(228(a,1),5045(a,1,2,1))].">
      <j1 rule="para" parents="228 5045"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R(u / (u / y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4386,a(flip),b,5046,a)].">
      <j1 rule="hyper" parents="63 4386 5046"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w * K(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),4998(a,2,1,1))].">
      <j1 rule="para" parents="9 4998"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(257,a,4402,a(flip),b,5048,a),flip(a)].">
      <j1 rule="hyper" parents="257 4402 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,K(w,x)) \ (w \ (w * x))) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),5049(a,1,1,1))].">
      <j1 rule="para" parents="9 5049"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,K(w,x)) \ x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),5051(a,1,2,2))].">
      <j1 rule="para" parents="9 5051"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,L(K(w,x),v5,v6)) \ x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3299(a,1),5052(a,1,2,1,3))].">
      <j1 rule="para" parents="3299 5052"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * z) \ (u * w)) * x,x) = K(w,T((y * (w \ z)) \ u,x))
    ]]></literal>
    <justification jstring="[para(4621(a,1),4912(a,1,2,1,1))].">
      <j1 rule="para" parents="4621 4912"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4911,a(flip),b,5054,a),flip(a)].">
      <j1 rule="hyper" parents="63 4911 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(4814,a,5055,a),flip(a)].">
      <j1 rule="hyper" parents="4814 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(4171,a,5056,a)].">
      <j1 rule="hyper" parents="4171 5056"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4484,a(flip),b,5057,a),flip(a)].">
      <j1 rule="hyper" parents="63 4484 5057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5058(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(5058(a,1),4432(a,1,1))].">
      <j1 rule="para" parents="5058 4432"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5059(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(5061(a,1),4432(a,1,1))].">
      <j1 rule="para" parents="5061 4432"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5062,a(flip),b,5060,a)].">
      <j1 rule="hyper" parents="63 5062 5060"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ (((x * K(y,y \ 1)) * z) * u) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1739(a,1),2686(a,1,1,2))].">
      <j1 rule="para" parents="1739 2686"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * R(x \ (x * K(y,z)),u,w)) * y) = (y * K(z,y)) * R((y * K(z,y)) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(3339(a,1),3379(a,2,2,1,1))].">
      <j1 rule="para" parents="3339 3379"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * R(x \ (x * K(y,z)),u,w)) * y) = (y * K(z,y)) * R(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3043(a,1),5065(a,2,2,1))].">
      <j1 rule="para" parents="3043 5065"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ ((K(y,y \ 1) * (x * z)) * u) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1791(a,1),5064(a,1,2,1))].">
      <j1 rule="para" parents="1791 5064"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ (K(y,y \ 1) * ((x * z) * u)) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1739(a,1),5069(a,1,2))].">
      <j1 rule="para" parents="1739 5069"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2692,a(flip),b,5070,a)].">
      <j1 rule="hyper" parents="63 2692 5070"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(R(x,K(u,u \ 1),y),K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2737(a,1),5071(a,1,1))].">
      <j1 rule="para" parents="2737 5071"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u) = (a(x,z,u) * K(y \ 1,y)) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(14(a,2),5072(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14 5072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      a(R(x,K(y,y \ 1),z),K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3496,a(flip),b,5073,a),flip(a)].">
      <j1 rule="hyper" parents="257 3496 5073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2676(a,1),5074(a,1,1))].">
      <j1 rule="para" parents="2676 5074"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(1773(a,1),5076(a,1,2))].">
      <j1 rule="para" parents="1773 5076"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4896,a(flip),b,5077,a)].">
      <j1 rule="hyper" parents="63 4896 5077"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2008(a,1),5078(a,1,3))].">
      <j1 rule="para" parents="2008 5078"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      a(x,y,z / (u \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4943,a(flip),b,5080,a)].">
      <j1 rule="hyper" parents="63 4943 5080"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      T(a(x,y,z * u),z) = a(x,y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(5081(a,1),2804(a,1,1))].">
      <j1 rule="para" parents="5081 2804"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      a(x,y,z * u) \ z = u \ L(u * z,y,x)
    ]]></literal>
    <justification jstring="[para(5081(a,1),2795(a,1,1))].">
      <j1 rule="para" parents="5081 2795"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      (x * y) / (a(z,u,y * x) \ y) = a(z,u,x * y) * x
    ]]></literal>
    <justification jstring="[hyper(172,a,5083,a,b,2750,a)].">
      <j1 rule="hyper" parents="172 5083 2750"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      a(x,y,z * u) * z = z * a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2664,a(flip),b,5084,a),flip(a)].">
      <j1 rule="hyper" parents="63 2664 5084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      T(a(x,y,z * u),z) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(203,a,5084,a(flip),b,2664,a(flip))].">
      <j1 rule="hyper" parents="203 5084 2664"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5082,a(flip),b,5086,a)].">
      <j1 rule="hyper" parents="63 5082 5086"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      (x \ L(y,z,u)) \ (x \ y) = a(u,z,x * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2806,a(flip),b,5087,a)].">
      <j1 rule="hyper" parents="63 2806 5087"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      a(x,y,z * (u / z)) * z = z * a(x,y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),5085(a,2,2,3))].">
      <j1 rule="para" parents="12 5085"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      L(x,y,z * a(u,w,v5)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5090(a,1),1480(a,1,3))].">
      <j1 rule="para" parents="5090 1480"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      L(x,L(y,z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4523,a(flip),b,5091,a),flip(a)].">
      <j1 rule="hyper" parents="63 4523 5091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3013(a,2),5091(a,1,3))].">
      <j1 rule="para" parents="3013 5091"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      L(x,L(y / x,z,u),w) = (w * (y / x)) \ (w * y)
    ]]></literal>
    <justification jstring="[hyper(257,a,94,a(flip),b,5093,a),flip(a)].">
      <j1 rule="hyper" parents="257 94 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      L(x,(y * z) \ y,u) = L(x,z \ 1,u)
    ]]></literal>
    <justification jstring="[para(187(a,1),5093(a,1,2))].">
      <j1 rule="para" parents="187 5093"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      L(x,(y \ z) \ 1,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(293(a,1),5093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="293 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      L(x,y,(y * z) / y) = z * (R(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4894,a(flip),b,5094,a),flip(a)].">
      <j1 rule="hyper" parents="63 4894 5094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4824,a,b,5099,a)].">
      <j1 rule="hyper" parents="63 4824 5099"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      L(x,y,z) = z * (R(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4670,a(flip),b,5102,a)].">
      <j1 rule="hyper" parents="63 4670 5102"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      R(x,y,z) \ z = x \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(111,a,4670,a(flip),b,5102,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="111 4670 5102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      R(x,y,z) = (x * z) / L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,5105,a,b,1279,a),flip(a)].">
      <j1 rule="hyper" parents="172 5105 1279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(39,a,2750,a,b,5106,a),flip(a)].">
      <j1 rule="hyper" parents="39 2750 5106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      L(x,y,z) = (x * z) / R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(172,a,5108,a,b,2778,a),flip(a)].">
      <j1 rule="hyper" parents="172 5108 2778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      a(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(112,a,5108,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="112 5108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4875,a,5108,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4875 5108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1939,a,b,5108,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 1939 5108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = R(K(x,T(y,z)),u,w) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(5108(a,2),4660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5108 4660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,4961,a(flip),b,5111,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 4961 5111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(115,a,5114,a,b,3135,a)].">
      <j1 rule="hyper" parents="115 5114 3135"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(257,a,3275,a,b,5115,a),flip(a)].">
      <j1 rule="hyper" parents="257 3275 5115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      a(x,y,z) = T(x \ R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(5115(a,1),4970(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5115 4970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      K(R(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5120(a,2),3691(a,1,1))].">
      <j1 rule="para" parents="5120 3691"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(5120(a,1),4550(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5120 4550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(113,a,4426,a(flip),b,5107,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="113 4426 5107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      R(K(x,y),y * x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(113,a,3988,a(flip),b,5110,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="113 3988 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3644,a(flip),b,5137,a)].">
      <j1 rule="hyper" parents="63 3644 5137"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4458,a(flip),b,5138,a)].">
      <j1 rule="hyper" parents="63 4458 5138"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      T(((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x),u) = a((x * (y / z)) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(505(a,1),5132(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="505 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(R(x,u,L(T(x,y),w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(4173,a,5133,a),flip(a)].">
      <j1 rule="hyper" parents="4173 5133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3302,a,b,5136,a)].">
      <j1 rule="hyper" parents="63 3302 5136"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4629,a(flip),b,5136,a)].">
      <j1 rule="hyper" parents="63 4629 5136"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4922,a(flip),b,5139,a)].">
      <j1 rule="hyper" parents="63 4922 5139"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4503,a(flip),b,5139,a),flip(a)].">
      <j1 rule="hyper" parents="63 4503 5139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(3464,a,5143,a)].">
      <j1 rule="hyper" parents="3464 5143"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,x) = u
    ]]></literal>
    <justification jstring="[para(5143(a,1),3948(a,1))].">
      <j1 rule="para" parents="5143 3948"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z / (u * u)))) * (u * u)) = a(x,y,z / (u * u))
    ]]></literal>
    <justification jstring="[hyper(257,a,506,a(flip),b,5127,a)].">
      <j1 rule="hyper" parents="257 506 5127"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3087,a,b,5142,a),flip(a)].">
      <j1 rule="hyper" parents="36 3087 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4634,a(flip),b,5151,a)].">
      <j1 rule="hyper" parents="63 4634 5151"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(257,a,5151,a,b,5152,a)].">
      <j1 rule="hyper" parents="257 5151 5152"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,y),u,w) = x * a(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5121(a,1),4320(a,2,2))].">
      <j1 rule="para" parents="5121 4320"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(4699(a,1),5121(a,1,2))].">
      <j1 rule="para" parents="4699 5121"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      (x \ L(y,z,u)) \ (x \ y) = a(u,z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5088(a,2,3))].">
      <j1 rule="para" parents="10 5088"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      (x \ L(y,z,u)) * a(u,z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,5158,a)].">
      <j1 rule="hyper" parents="125 5158"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      L(x,y \ L(z,u,z),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),4525(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 4525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      L(x,((y * (z * y)) / y) \ y,u) = L(x,(y * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(2794(a,1),5160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2794 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      K(R(x,y,L(T(x,z),u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(4170,a,5141,a),flip(a)].">
      <j1 rule="hyper" parents="4170 5141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5162(a,1),2977(a,2,1,1))].">
      <j1 rule="para" parents="5162 2977"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4282,a(flip),b,5145,a),flip(a)].">
      <j1 rule="hyper" parents="63 4282 5145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      T(x,R(y,z,u)) * K(y,x) = x * a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5157(a,1),3086(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5157 3086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,2977,a,b,5164,a),flip(a)].">
      <j1 rule="hyper" parents="257 2977 5164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,z)) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(4831(a,1),5168(a,1,2,3))].">
      <j1 rule="para" parents="4831 5168"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),u / (u / y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,5047,a(flip),b,5169,a),flip(a)].">
      <j1 rule="hyper" parents="63 5047 5169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5146,a(flip),b,5165,a),flip(a)].">
      <j1 rule="hyper" parents="63 5146 5165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(5171(a,1),3649(a,1))].">
      <j1 rule="para" parents="5171 3649"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(5153(a,1),212(a,1))].">
      <j1 rule="para" parents="5153 212"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = w
    ]]></literal>
    <justification jstring="[para(856(a,1),5173(a,1,2))].">
      <j1 rule="para" parents="856 5173"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3912,a(flip),b,5134,a),flip(a)].">
      <j1 rule="hyper" parents="257 3912 5134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4916,a(flip),b,5175,a)].">
      <j1 rule="hyper" parents="63 4916 5175"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3588,a(flip),b,5177,a),flip(a)].">
      <j1 rule="hyper" parents="257 3588 5177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4917,a(flip),b,5179,a)].">
      <j1 rule="hyper" parents="63 4917 5179"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(257,a,5147,a(flip),b,5180,a),flip(a)].">
      <j1 rule="hyper" parents="257 5147 5180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,3390,a(flip),b,5180,a),flip(a)].">
      <j1 rule="hyper" parents="257 3390 5180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),5183(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 5183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),5182(a,1,1,2))].">
      <j1 rule="para" parents="90 5182"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(4411,a,5185,a)].">
      <j1 rule="hyper" parents="4411 5185"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * R(x \ (x * K(y,z)),u,w)) * y) = y * a(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5066,a,b,5156,a)].">
      <j1 rule="hyper" parents="63 5066 5156"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4244,a,b,5156,a)].">
      <j1 rule="hyper" parents="63 4244 5156"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      L(x,((y * (z * y)) / y) \ y,u) = L(x,z \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,5098,a(flip),b,5161,a),flip(a)].">
      <j1 rule="hyper" parents="257 5098 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      L(x,y / (z * y),u) = L(x,z \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4533,a(flip),b,5189,a)].">
      <j1 rule="hyper" parents="63 4533 5189"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      L(x,(y / z) \ 1,u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),5191(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5103,a(flip),b,5192,a),flip(a)].">
      <j1 rule="hyper" parents="63 5103 5192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      L(x,(y \ z) \ z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(76(a,1),5193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="76 5193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4679,a(flip),b,5194,a)].">
      <j1 rule="hyper" parents="63 4679 5194"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(257,a,2743,a(flip),b,5195,a),flip(a)].">
      <j1 rule="hyper" parents="257 2743 5195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2744,a,5196,a)].">
      <j1 rule="hyper" parents="2744 5196"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4531,a(flip),b,5197,a),flip(a)].">
      <j1 rule="hyper" parents="63 4531 5197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(2981(a,1),5197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2981 5197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y * K(w,y),x)
    ]]></literal>
    <justification jstring="[hyper(257,a,4045,a,b,5199,a)].">
      <j1 rule="hyper" parents="257 4045 5199"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      L(a(x,L(y,z,u),x),w,v5) = a(x,L(y * K(v6,y),z,u),x)
    ]]></literal>
    <justification jstring="[para(3220(a,1),5201(a,2,2))].">
      <j1 rule="para" parents="3220 5201"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      T(x * K(y,x),R(y,z,u)) = x * a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(3755,a,5167,a)].">
      <j1 rule="hyper" parents="3755 5167"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      T(x * K(y,x),R(y,z,u)) != x * w
    ]]></literal>
    <literal><![CDATA[
      a(K(x,y),z * y,u) = w
    ]]></literal>
    <justification jstring="[para(5203(a,2),43(a,1))].">
      <j1 rule="para" parents="5203 43"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(5172,a,5063,a),flip(a)].">
      <j1 rule="hyper" parents="5172 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      a(x,L(y * K(z,y),u,w),x) = (w * (u * y)) \ (w * (u * (T(x * y,x) / x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4999,a(flip),b,5202,a),flip(a)].">
      <j1 rule="hyper" parents="63 4999 5202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (z * u),y) = w
    ]]></literal>
    <justification jstring="[para(5186(a,2),5149(a,1))].">
      <j1 rule="para" parents="5186 5149"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(5207,a,4725,a),flip(a)].">
      <j1 rule="hyper" parents="5207 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),5208(a,2,1))].">
      <j1 rule="para" parents="18 5208"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4549,a(flip),b,5205,a),flip(a)].">
      <j1 rule="hyper" parents="63 4549 5205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),5210(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 5210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3101(a,1),5211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3101 5211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      R(K(x,R(y \ x,z,u) \ x),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(4995(a,1),5211(a,1,1))].">
      <j1 rule="para" parents="4995 5211"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      K(x,R(R(x / y,z,u),w,v5) \ x) = R(R(K(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5212(a,1),5213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5212 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((y * (z / (u * u))) * (u * u))) = a(x,y,z / (u * u))
    ]]></literal>
    <justification jstring="[para(32(a,1),5150(a,1,2))].">
      <j1 rule="para" parents="32 5150"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * ((z / (u * u)) * (u * u)))) = a(x,y,z / (u * u))
    ]]></literal>
    <justification jstring="[para(32(a,1),5217(a,1,2,2))].">
      <j1 rule="para" parents="32 5217"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      a(x,y,z / (u * u)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),5218(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 5218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      a(x,y,z / (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,5127,a,b,5219,a),flip(a)].">
      <j1 rule="hyper" parents="257 5127 5219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4950,a(flip),b,5220,a),flip(a)].">
      <j1 rule="hyper" parents="63 4950 5220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4942,a(flip),b,5220,a)].">
      <j1 rule="hyper" parents="63 4942 5220"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5220(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11 5220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      a(x,y,z * K(u,z)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(3111(a,1),5220(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3111 5220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      a(x,y,z * (u * (w * w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(32(a,1),5223(a,1,3))].">
      <j1 rule="para" parents="32 5223"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      a(x,y,T(z \ (u * u),z)) = a(x,y,((z \ (u * u)) \ (u * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(2491(a,2),5221(a,1,3))].">
      <j1 rule="para" parents="2491 5221"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      a(x,y,T(T(z,u),u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2944(a,1),5224(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2944 5224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      a(x,y,T(z \ u,z)) = a(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(2961(a,1),5224(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2961 5224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      a(x,y,T(R(z \ u,z,z),z)) = a(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(541(a,1),5227(a,1,3,1))].">
      <j1 rule="para" parents="541 5227"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(184(a,1),5225(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="184 5225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      a(x,y,R(T(z \ u,z),z,z)) = a(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(27(a,2),5229(a,1,3))].">
      <j1 rule="para" parents="27 5229"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      a(x,y,R(T(z \ u,z),z,z)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(257,a,5230,a(flip),b,5231,a),flip(a)].">
      <j1 rule="hyper" parents="257 5230 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      a(x,y,T(z \ u,z)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4940,a(flip),b,5232,a)].">
      <j1 rule="hyper" parents="63 4940 5232"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      a(x,y,T(z \ (u * u),z)) = a(x,y,(z \ (u * u)) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(257,a,5222,a(flip),b,5226,a),flip(a)].">
      <j1 rule="hyper" parents="257 5222 5226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      a(x,y,T(z \ (u * u),z)) = a(x,y,(z \ (u * u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,5221,a(flip),b,5235,a),flip(a)].">
      <j1 rule="hyper" parents="257 5221 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      a(x,y,T(z \ (u * u),z)) = a(x,y,z \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(257,a,5222,a(flip),b,5236,a),flip(a)].">
      <j1 rule="hyper" parents="257 5222 5236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      a(x,y,T(z \ (u * u),z)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(257,a,5221,a(flip),b,5238,a),flip(a)].">
      <j1 rule="hyper" parents="257 5221 5238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      a(x,y,T(z \ (u * u),z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,5222,a(flip),b,5239,a),flip(a)].">
      <j1 rule="hyper" parents="257 5222 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5233,a(flip),b,5241,a)].">
      <j1 rule="hyper" parents="63 5233 5241"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      a(x,y,(z * z) / u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5228,a(flip),b,5241,a)].">
      <j1 rule="hyper" parents="63 5228 5241"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      a(x,y,R(z * K(u,z),u,u * z)) = a(x,y,u * (u * z))
    ]]></literal>
    <justification jstring="[para(3030(a,2),5243(a,1,3))].">
      <j1 rule="para" parents="3030 5243"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      a(x,y,z * K(u,z)) = a(x,y,u * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4940,a(flip),b,5244,a)].">
      <j1 rule="hyper" parents="63 4940 5244"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      a(x,y,z * (z * u)) = a(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5224,a(flip),b,5245,a),flip(a)].">
      <j1 rule="hyper" parents="63 5224 5245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * R(K(y,z),u,w)) * y) = y * a(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),5187(a,1,2,1,2,1))].">
      <j1 rule="para" parents="9 5187"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (y * R(K(y,z),u,w))) = y * a(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3654(a,1),5248(a,1,2))].">
      <j1 rule="para" parents="3654 5248"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ ((x / z) * (z * R(K(z,y),u,w))) = z * a(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(3401(a,2),5250(a,1,1))].">
      <j1 rule="para" parents="3401 5250"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(3034(a,1),5206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3034 5206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ (x * R(K(z,y),u,w)) = z * a(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(3362(a,1),5251(a,1,2))].">
      <j1 rule="para" parents="3362 5251"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      L(L(a(x,y,x),y,z),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(3977,a,5253,a)].">
      <j1 rule="hyper" parents="3977 5253"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(4045(a,1),5255(a,1,1))].">
      <j1 rule="para" parents="4045 5255"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(257,a,5198,a(flip),b,5256,a),flip(a)].">
      <j1 rule="hyper" parents="257 5198 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),5257(a,2,2))].">
      <j1 rule="para" parents="18 5257"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4045,a(flip),b,5259,a),flip(a)].">
      <j1 rule="hyper" parents="63 4045 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(115,a,5260,a(flip),b,3953,a),flip(a)].">
      <j1 rule="hyper" parents="115 5260 3953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(257,a,5114,a,b,5262,a),flip(a)].">
      <j1 rule="hyper" parents="257 5114 5262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ ((u / R(y,z,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4437,a(flip),b,5170,a),flip(a)].">
      <j1 rule="hyper" parents="63 4437 5170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(3827(a,1),5265(a,2,2))].">
      <j1 rule="para" parents="3827 5265"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(257,a,2530,a(flip),b,5266,a),flip(a)].">
      <j1 rule="hyper" parents="257 2530 5266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u))
    ]]></literal>
    <justification jstring="[para(4377(a,1),5267(a,1,1,1))].">
      <j1 rule="para" parents="4377 5267"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u
    ]]></literal>
    <justification jstring="[para(4849(a,1),5268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4849 5268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      R(x * K(y,x),z,x) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(5269(a,1),3071(a,1))].">
      <j1 rule="para" parents="5269 3071"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(257,a,5188,a(flip),b,5118,a),flip(a)].">
      <j1 rule="hyper" parents="257 5188 5118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * (K(x,y) * (K(y,x) * z)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(559,a,5271,a)].">
      <j1 rule="hyper" parents="559 5271"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(3132(a,1),5272(a,1,2))].">
      <j1 rule="para" parents="3132 5272"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(4136(a,1),5273(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4136 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(204,a,5274,a),flip(a)].">
      <j1 rule="hyper" parents="204 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K((x \ u) \ u,w \ (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),3478(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,T(w \ (R(x,y,z) * u),u))
    ]]></literal>
    <justification jstring="[hyper(257,a,3745,a(flip),b,5332,a),flip(a)].">
      <j1 rule="hyper" parents="257 3745 5332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,(R(x,y,z) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(4818,a,5333,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4818 5333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * (x \ w))) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(3942,a,5335,a)].">
      <j1 rule="hyper" parents="3942 5335"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4813,a(flip),b,5336,a)].">
      <j1 rule="hyper" parents="63 4813 5336"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4817,a(flip),b,5337,a)].">
      <j1 rule="hyper" parents="63 4817 5337"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(4174,a,5338,a),flip(a)].">
      <j1 rule="hyper" parents="4174 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(3640,a,5339,a)].">
      <j1 rule="hyper" parents="3640 5339"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(3437,a,5341,a),flip(a)].">
      <j1 rule="hyper" parents="3437 5341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4302,a,b,5342,a)].">
      <j1 rule="hyper" parents="63 4302 5342"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,(((u * y) * z) / (y * z)) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5001,a,b,5343,a)].">
      <j1 rule="hyper" parents="63 5001 5343"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,R(u,y,z) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),5344(a,2,2,1))].">
      <j1 rule="para" parents="20 5344"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4383,a(flip),b,5345,a),flip(a)].">
      <j1 rule="hyper" parents="63 4383 5345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4986,a(flip),b,5346,a),flip(a)].">
      <j1 rule="hyper" parents="63 4986 5346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      K(x,R(R(x / y,y,L(K(z,x),u,w)),v5,v6) \ x) = K(R(x,v5,v6),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5053,a(flip),b,5348,a),flip(a)].">
      <j1 rule="hyper" parents="63 5053 5348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      R(R(K(x,y),y,L(K(z,x),u,w)),v5,v6) = K(R(x,v5,v6),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5216,a(flip),b,5350,a)].">
      <j1 rule="hyper" parents="63 5216 5350"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2709(a,1),5351(a,1,1))].">
      <j1 rule="para" parents="2709 5351"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      R(x * K(R(y,z,u),x),w,x) \ R(x,w,x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5352(a,1),4471(a,1,1,1,2))].">
      <j1 rule="para" parents="5352 4471"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (R(x,w,x) \ R(x,w,x)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5270,a,5354,a)].">
      <j1 rule="hyper" parents="5270 5354"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(179,a,5355,a),flip(a)].">
      <j1 rule="hyper" parents="179 5355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ (x * K(z,R(y,u,w))) = z * a(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5356(a,1),5254(a,1,2,2))].">
      <j1 rule="para" parents="5356 5254"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      K(x,y) * T(y,R(x,z,u)) = y * a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(4368,a,5358,a)].">
      <j1 rule="hyper" parents="4368 5358"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      T(K(x,y) * y,R(x,z,u)) = y * a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4508,a,b,5359,a)].">
      <j1 rule="hyper" parents="63 4508 5359"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      T(x * K(y,x),R(y,z,u)) = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2096(a,1),5360(a,1,1))].">
      <j1 rule="para" parents="2096 5360"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5204,a,5361,a)].">
      <j1 rule="hyper" parents="5204 5361"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      T((x * y) \ ((x * (y / z)) * R((x * (y / z)) \ (x * y),u,w)),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(2634(a,1),3563(a,1,1))].">
      <j1 rule="para" parents="2634 3563"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      T((x * y) \ (x * ((y / z) * R((y / z) \ y,u,w))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(688(a,1),5363(a,1,1,2))].">
      <j1 rule="para" parents="688 5363"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      T((x * y) \ (x * ((y / z) * R(z,u,w))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),5365(a,1,1,2,2,2,1))].">
      <j1 rule="para" parents="79 5365"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      T((x * y) \ (x * (y * (z \ R(z,u,w)))),w) = ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x)
    ]]></literal>
    <justification jstring="[para(2631(a,1),5366(a,1,1,2,2))].">
      <j1 rule="para" parents="2631 5366"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      T(L(x \ R(x,y,z),u,w),z) = ((w * (u / x)) \ (w * u)) \ L(R(x,y,z),u / x,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),5367(a,1,1))].">
      <j1 rule="para" parents="18 5367"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),z),u,w) = ((w * (u / x)) \ (w * u)) \ L(R(x,y,z),u / x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,5368,a)].">
      <j1 rule="hyper" parents="63 25 5368"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      ((x * (y / z)) \ (x * y)) \ L(R(z,u,w),y / z,x) = L(z \ R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(3562(a,1),5369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3562 5369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      T(L(x \ R(x,y,z),u,w),y) = a((w * (u / x)) \ (w * u),y,z)
    ]]></literal>
    <justification jstring="[para(5370(a,1),5140(a,1,1))].">
      <j1 rule="para" parents="5370 5140"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),y),u,w) = a((w * (u / x)) \ (w * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,5371,a)].">
      <j1 rule="hyper" parents="63 25 5371"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      a((x * (y / z)) \ (x * y),u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(5132(a,2),5372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5132 5372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      a(L(x,y / x,z),u,w) = L(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(94(a,2),5373(a,1,1))].">
      <j1 rule="para" parents="94 5373"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      L(a(x,y,z),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2747,a(flip),b,5374,a),flip(a)].">
      <j1 rule="hyper" parents="63 2747 5374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      (x * y) / a(z,u,w) = x * (y / a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(172,a,5375,a(flip),b,5097,a(flip))].">
      <j1 rule="hyper" parents="172 5375 5097"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      (x * y) * a(z,u,w) = x * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(115,a,5375,a(flip),b,4689,a(flip))].">
      <j1 rule="hyper" parents="115 5375 4689"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(113,a,5375,a(flip),b,5110,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="113 5375 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      (x / a(y,z,u)) / w = x / (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(444,a,5384,a),flip(a)].">
      <j1 rule="hyper" parents="444 5384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      x \ (y * a(z,u,w)) = (x \ y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5384(a,1),379(a,1,1))].">
      <j1 rule="para" parents="5384 379"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      (x * ((y * x) \ z)) * a(y,x,(y * x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[para(5384(a,1),1135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5384 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,v5))) / ((y * z) * a(u,w,v5)) = R(R(x,y,z),y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),386(a,1,1))].">
      <j1 rule="para" parents="5383 386"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      (x * (y / a(z,u,w))) / v5 = (x * y) / (v5 * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(5382(a,1),5387(a,1,1))].">
      <j1 rule="para" parents="5382 5387"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,v5))) = (x \ (y * z)) * a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(5383(a,1),5389(a,1,2))].">
      <j1 rule="para" parents="5383 5389"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      (K(x \ 1,x) * (R(x,y,z) \ u)) * a(R((x \ 1) \ 1,y,z),K(x \ 1,x),(R((x \ 1) \ 1,y,z) * K(x \ 1,x)) \ u) = R((x \ 1) \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(1956(a,1),5390(a,1,1,2,1))].">
      <j1 rule="para" parents="1956 5390"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z / a(u,w,v5)))) * a(u,w,v5)) = a(x,y,z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5127,a,b,5392,a),flip(a)].">
      <j1 rule="hyper" parents="63 5127 5392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      ((x * (y * (z * a(u,w,v5)))) \ ((x * y) * z)) * a(u,w,v5) = a(x,y,z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(498,a,5393,a),flip(a)].">
      <j1 rule="hyper" parents="498 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((y * (z / a(u,w,v5))) * a(u,w,v5))) = a(x,y,z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),5395(a,1,2))].">
      <j1 rule="para" parents="5383 5395"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      ((x * (y * z)) \ (a(u,w,u) \ ((x * y) * z))) * a(u,w,u) = a(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[para(4304(a,1),5396(a,1,1))].">
      <j1 rule="para" parents="4304 5396"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * ((z / a(u,w,v5)) * a(u,w,v5)))) = a(x,y,z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),5397(a,1,2,2))].">
      <j1 rule="para" parents="5383 5397"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(4013,a,5398,a),flip(a)].">
      <j1 rule="hyper" parents="4013 5398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,14,a,b,5400,a),flip(a)].">
      <j1 rule="hyper" parents="257 14 5400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(3972(a,1),5401(a,1,3))].">
      <j1 rule="para" parents="3972 5401"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),5402(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 5402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      a(x,y,z / a(u,w,v5)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),5399(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 5399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      a(x,y,z / a(u,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,5127,a,b,5404,a),flip(a)].">
      <j1 rule="hyper" parents="257 5127 5404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(161(a,1),5405(a,1,3)),flip(a)].">
      <j1 rule="para" parents="161 5405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      a(x,y,z * (z * u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5242,a(flip),b,5407,a),flip(a)].">
      <j1 rule="hyper" parents="63 5242 5407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      a(x,y,T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5247,a(flip),b,5408,a)].">
      <j1 rule="hyper" parents="63 5247 5408"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      R(x,y,T(z,u)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(115,a,5409,a(flip),b,5115,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="115 5409 5115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,5114,a,b,5414,a),flip(a)].">
      <j1 rule="hyper" parents="257 5114 5414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      R(x,y * z,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,3614,a(flip),b,5416,a),flip(a)].">
      <j1 rule="hyper" parents="42 3614 5416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      R(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),5429(a,1,2))].">
      <j1 rule="para" parents="12 5429"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(110,a,5435,a(flip),b,5114,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="110 5435 5114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,v5))) / (y * (z * a(u,w,v5))) = R(R(x,y,z),y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5383(a,1),5391(a,1,2))].">
      <j1 rule="para" parents="5383 5391"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5464(a,1),390(a,1))].">
      <j1 rule="para" parents="5464 390"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      R(x,y,z * a(u,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5466,a,5384,a)].">
      <j1 rule="hyper" parents="5466 5384"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      R(x,y,L(z,u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2774(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2774 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      R(L(x,y,z),u,L(w,v5,v6)) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(257,a,29,a(flip),b,5468,a),flip(a)].">
      <j1 rule="hyper" parents="257 29 5468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      K(x,L(R(y,z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(5470(a,1),3725(a,1,2))].">
      <j1 rule="para" parents="5470 3725"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      K(L(x,y * (x \ z),u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(4867(a,1),5472(a,1))].">
      <j1 rule="para" parents="4867 5472"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(5473,a,5209,a),flip(a)].">
      <j1 rule="hyper" parents="5473 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4620,a,5474,a)].">
      <j1 rule="hyper" parents="4620 5474"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(115,a,5475,a(flip),b,2743,a(flip))].">
      <j1 rule="hyper" parents="115 5475 2743"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(3503,a,5476,a)].">
      <j1 rule="hyper" parents="3503 5476"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      x / (T(K(y,z),x) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(4771(a,1),4841(a,1,2,1))].">
      <j1 rule="para" parents="4771 4841"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / (T(K(y,x),z) * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[para(2363(a,1),5482(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2363 5482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / ((y \ z) * T(y,x))
    ]]></literal>
    <justification jstring="[para(4184(a,1),5483(a,2,2))].">
      <j1 rule="para" parents="4184 5483"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ (y * z)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),5484(a,2,2,1))].">
      <j1 rule="para" parents="9 5484"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = K(u,u * x) * T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4979(a,1),3313(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4979 3313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(K(u,u * x) * (u * L(x,y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3843,a,b,5486,a),flip(a)].">
      <j1 rule="hyper" parents="257 3843 5486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2950(a,1),5487(a,2,1))].">
      <j1 rule="para" parents="2950 5487"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5263(a,1),5489(a,1,2,1))].">
      <j1 rule="para" parents="5263 5489"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),R(u,x,u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5263(a,1),5490(a,1,2,2,1))].">
      <j1 rule="para" parents="5263 5490"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),x * R(u,x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2493(a,2),5491(a,1,2))].">
      <j1 rule="para" parents="2493 5491"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2489(a,1),5493(a,1,2,2))].">
      <j1 rule="para" parents="2489 5493"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),x * u) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4579(a,1),5495(a,1,2))].">
      <j1 rule="para" parents="4579 5495"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(548(a,1),5496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="548 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4498,a(flip),b,5497,a)].">
      <j1 rule="hyper" parents="63 4498 5497"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (L(y,z,u) * T(x,y)) = K(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(111,a,5498,a(flip),b,2948,a(flip))].">
      <j1 rule="hyper" parents="111 5498 2948"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(4331,a,5499,a),flip(a)].">
      <j1 rule="hyper" parents="4331 5499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,5477,a(flip),b,5500,a),flip(a)].">
      <j1 rule="hyper" parents="257 5477 5500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[para(12(a,1),5501(a,1,1))].">
      <j1 rule="para" parents="12 5501"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3657,a(flip),b,5502,a)].">
      <j1 rule="hyper" parents="63 3657 5502"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(5184(a,1),5503(a,2,3))].">
      <j1 rule="para" parents="5184 5503"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,5403,a(flip),b,5504,a),flip(a)].">
      <j1 rule="hyper" parents="257 5403 5504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5174,a,5505,a)].">
      <j1 rule="hyper" parents="5174 5505"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(2777(a,2),5507(a,1,2,2))].">
      <j1 rule="para" parents="2777 5507"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = K(u,u * x) * T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4979(a,1),3314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4979 3314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(K(u,u * x) * (u * R(x,y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3843,a,b,5509,a),flip(a)].">
      <j1 rule="hyper" parents="257 3843 5509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(T(u,u * x) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2950(a,1),5510(a,2,1))].">
      <j1 rule="para" parents="2950 5510"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(257,a,4497,a(flip),b,5512,a),flip(a)].">
      <j1 rule="hyper" parents="257 4497 5512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * R(u,R(x,y,z),u)),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(2496(a,2),5513(a,1,2))].">
      <j1 rule="para" parents="2496 5513"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,u * x),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(4593(a,1),5514(a,1,2,1))].">
      <j1 rule="para" parents="4593 5514"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * u),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(2493(a,2),5515(a,1,2,1))].">
      <j1 rule="para" parents="2493 5515"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * u),x,u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(4496(a,1),5516(a,1,2))].">
      <j1 rule="para" parents="4496 5516"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(549(a,1),5518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="549 5518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(172,a,5519,a(flip),b,2976,a(flip))].">
      <j1 rule="hyper" parents="172 5519 2976"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      (K(x \ 1,x) * (R(x,y,z) \ u)) * 1 = R((x \ 1) \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(2196(a,1),5394(a,1,2))].">
      <j1 rule="para" parents="2196 5394"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x,y,z) \ u) = R((x \ 1) \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(120,a,5522,a)].">
      <j1 rule="hyper" parents="120 5522"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      (R(x,y,z) \ u) * K(x \ 1,x) = R((x \ 1) \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(1780,a,5523,a)].">
      <j1 rule="hyper" parents="1780 5523"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      x / (R((y \ 1) \ 1,z,u) \ x) = (R(y,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5525(a,1),1974(a,1,2))].">
      <j1 rule="para" parents="5525 1974"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      1 / R((x \ 1) \ 1,y,z) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(436,a,5526,a(flip))].">
      <j1 rule="hyper" parents="436 5526"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(171(a,1),5527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="171 5527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1664(a,1),5528(a,1,1,1))].">
      <j1 rule="para" parents="1664 5528"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(515(a,1),5529(a,1,1)),flip(a)].">
      <j1 rule="para" parents="515 5529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4735(a,1),5530(a,1,2))].">
      <j1 rule="para" parents="4735 5530"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2694(a,1),5531(a,1,2,1))].">
      <j1 rule="para" parents="2694 5531"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(2863(a,1),5532(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2863 5532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(2613(a,1),5533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2613 5533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(165,a,5534,a)].">
      <j1 rule="hyper" parents="165 5534"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1915,a(flip),b,5535,a)].">
      <j1 rule="hyper" parents="63 1915 5535"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,z * y)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(5536(a,1),5485(a,1,1,2))].">
      <j1 rule="para" parents="5536 5485"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      T(K(x,y),z) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(4072(a,1),5537(a,1,1))].">
      <j1 rule="para" parents="4072 5537"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(5536(a,1),5538(a,1,2,1))].">
      <j1 rule="para" parents="5536 5538"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(4599(a,1),5540(a,1,2))].">
      <j1 rule="para" parents="4599 5540"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(y,y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(3928(a,1),5541(a,1,2))].">
      <j1 rule="para" parents="3928 5541"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4793(a,1),5542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4793 5542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(257,a,3854,a,b,5543,a),flip(a)].">
      <j1 rule="hyper" parents="257 3854 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      T(K(x,y) * K(y,R(x,z,u)),R(x,z,u)) = K(y * x,y * R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5521,a(flip),b,5544,a),flip(a)].">
      <j1 rule="hyper" parents="63 5521 5544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      T(a(K(x,y),z * y,u),R(y,z,u)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5157(a,1),5546(a,1,1))].">
      <j1 rule="para" parents="5157 5546"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,T(y,R(y,z,u))),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5275,a,b,5547,a),flip(a)].">
      <j1 rule="hyper" parents="63 5275 5547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(152(a,1),5548(a,2,1,2))].">
      <j1 rule="para" parents="152 5548"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      K(x,(x / y) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),5549(a,1,1))].">
      <j1 rule="para" parents="12 5549"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(2631(a,1),5550(a,1,2))].">
      <j1 rule="para" parents="2631 5550"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(3016(a,1),5551(a,2,1))].">
      <j1 rule="para" parents="3016 5551"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,3991,a(flip),b,5552,a),flip(a)].">
      <j1 rule="hyper" parents="257 3991 5552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5115(a,2),5553(a,1,2,2))].">
      <j1 rule="para" parents="5115 5553"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(257,a,5362,a(flip),b,5554,a),flip(a)].">
      <j1 rule="hyper" parents="257 5362 5554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5508,a(flip),b,5555,a),flip(a)].">
      <j1 rule="hyper" parents="63 5508 5555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(257,a,5450,a(flip),b,5556,a),flip(a)].">
      <j1 rule="hyper" parents="257 5450 5556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aK1")
    ]]></attribute>
    <justification jstring="[resolve(5557,a,64,a)].">
      <j1 rule="resolve" parents="5557 64"/>
    </justification>
  </clause>

</proof>

</proofs>
