<?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>nslm_to_aK1.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 729545 was started by veroff on b146-03,
Thu Apr  9 09:28:19 2026
The command was "prover9 -f nslm_to_aK1.in".
]]></heading>

<proof number="1" length="17605" max_count="65">

<comments><![CDATA[
% Proof 1 at 4124.79 (+ 0.21) seconds: "aK1".
% Length of proof: 17605 (0 new hints)
% Level of proof: 834
% Maximum clause weight: 1008.000 (65 w/o degradation)
% Given clauses in run: 18236
% Given clauses in proof: 17587 (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 * x) * (y * z) = ((x * x) * y) * z
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_l")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      ((x * x) * y) * z = (x * x) * (y * z)
    ]]></literal>
    <justification jstring="[copy(32),flip(a)].">
      <j1 rule="copy" parents="32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      (x * (y * y)) * z = x * ((y * y) * z)
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_m")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="35" 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="36" 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="37" 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="38" 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="39" 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="40" 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="41" 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="42" 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="43" 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="44" 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="45" 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="46" 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="47" 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="48" 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="49" 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="50" 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="51" 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="52" 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="53" 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="54" 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="55" 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="56" 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="57" 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="58" 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="59" 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="60" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x / z = y / z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="61" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / x = z / y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="62" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x \ z = y \ z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 5")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="63" 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="64" 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="65" 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="66">
    <literal><![CDATA[
      1 \ x = x
    ]]></literal>
    <justification jstring="[para(7(a,1),9(a,1,2))].">
      <j1 rule="para" parents="7 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      x \ x = 1
    ]]></literal>
    <justification jstring="[para(8(a,1),9(a,1,2))].">
      <j1 rule="para" parents="8 9"/>
    </justification>
  </clause>

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

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

  <clause id="71">
    <literal><![CDATA[
      (x * (x \ 1)) * y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),7(a,1,1))].">
      <j1 rule="para" parents="10 7"/>
    </justification>
  </clause>

  <clause id="72">
    <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="73">
    <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="74">
    <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="75">
    <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="76">
    <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="77">
    <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="78">
    <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="79">
    <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="80">
    <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="81">
    <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="82">
    <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="83">
    <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="84">
    <literal><![CDATA[
      (((x / y) / z) * z) * y = x
    ]]></literal>
    <justification jstring="[para(12(a,2),12(a,1,1))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="85">
    <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="86">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

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

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

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

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

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

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

  <clause id="93">
    <literal><![CDATA[
      (x * y) \ (x * y) = L(1,y,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="94">
    <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="95">
    <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="96">
    <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="97">
    <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="98">
    <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="99">
    <literal><![CDATA[
      L(x,y,z / (y * x)) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,2))].">
      <j1 rule="para" parents="12 18"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      (x * y) / (x * y) = R(1,x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      (x * y) / (y * 1) = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(8(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="102">
    <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="103">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,1))].">
      <j1 rule="para" parents="10 20"/>
    </justification>
  </clause>

  <clause id="104">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / z = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="105">
    <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="106">
    <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="107">
    <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="108">
    <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="109">
    <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="110">
    <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="111">
    <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="112">
    <literal><![CDATA[
      T(x,x * x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),18(a,2)),flip(a)].">
      <j1 rule="para" parents="22 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="113">
    <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="114">
    <literal><![CDATA[
      T(T(T(x,y),z),u) = T(T(T(x,u),y),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="115">
    <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="116">
    <literal><![CDATA[
      (x * x) * (((x * x) \ y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(10(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="33 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      ((x * x) * (y * (z * u))) \ ((((x * x) * y) * z) * u) = a((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      ((x * x) * (y * z)) \ (((x * x) * y) * (z * u)) = L(u,z,(x * x) * y)
    ]]></literal>
    <justification jstring="[para(33(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) = L(u,(y * y) * z,x)
    ]]></literal>
    <justification jstring="[para(33(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="33 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      (((x * x) * (y * z)) * u) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="33 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      (x * ((y * y) * z)) / z = x * (y * y)
    ]]></literal>
    <justification jstring="[para(34(a,1),11(a,1,1))].">
      <j1 rule="para" parents="34 11"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ (((x * (y * y)) * z) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(34(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="34 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(34(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="34 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),35(b,1))].">
      <j1 rule="para" parents="7 35"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),35(a,1))].">
      <j1 rule="para" parents="8 35"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,1),35(a,1))].">
      <j1 rule="para" parents="10 35"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),36(a,1))].">
      <j1 rule="para" parents="12 36"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (x * z) / u != y
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(11(a,1),37(a,1))].">
      <j1 rule="para" parents="11 37"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / u != y
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(11(a,1),38(a,1))].">
      <j1 rule="para" parents="11 38"/>
    </justification>
  </clause>

  <clause id="131">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(9(a,1),39(a,1))].">
      <j1 rule="para" parents="9 39"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(7(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),44(a,2))].">
      <j1 rule="para" parents="7 44"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="10 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      (x / y) * z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></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="137">
    <literal><![CDATA[
      x * y != y
    ]]></literal>
    <literal><![CDATA[
      1 = x
    ]]></literal>
    <justification jstring="[para(7(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="7 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(8(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="8 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(8(a,1),45(a,2))].">
      <j1 rule="para" parents="8 45"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(10(a,1),45(a,2))].">
      <j1 rule="para" parents="10 45"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="12 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="11 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></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="146">
    <literal><![CDATA[
      x \ (x * (y \ z)) != y \ u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9(a,2),48(a,1))].">
      <j1 rule="para" parents="9 48"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(9(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="9 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),50(a,1))].">
      <j1 rule="para" parents="23 50"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      R(L(x,y,z),u,w) != L(v5,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(29(a,2),51(a,1))].">
      <j1 rule="para" parents="29 51"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,12,a)].">
      <j1 rule="hyper" parents="58 12"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10,a)].">
      <j1 rule="hyper" parents="58 10"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,10,a)].">
      <j1 rule="hyper" parents="59 10"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,9,a)].">
      <j1 rule="hyper" parents="59 9"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      ((x / y) * y) / z = x / z
    ]]></literal>
    <justification jstring="[hyper(60,a,12,a)].">
      <j1 rule="hyper" parents="60 12"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      (x * (x \ y)) / z = y / z
    ]]></literal>
    <justification jstring="[hyper(60,a,10,a)].">
      <j1 rule="hyper" parents="60 10"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      T(T(x,y),z) \ u = T(T(x,z),y) \ u
    ]]></literal>
    <justification jstring="[hyper(62,a,23,a)].">
      <j1 rule="hyper" parents="62 23"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (x * (x \ y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,10,a)].">
      <j1 rule="hyper" parents="62 10"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      x \ T(T(y,z),u) = x \ T(T(y,u),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23,a)].">
      <j1 rule="hyper" parents="63 23"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="64 12 10"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      (x / y) * y = x * 1
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="64 12 8"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="64 12 7"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      (x * y) / y = x * 1
    ]]></literal>
    <justification jstring="[hyper(64,a,11,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="64 11 8"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10,a,b,9,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 10 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(64,a,10,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="64 10 8"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,66,a,b,8,a)].">
      <j1 rule="hyper" parents="64 66 8"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),66(a,1,1))].">
      <j1 rule="para" parents="10 66"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),66(a,1,1))].">
      <j1 rule="para" parents="12 66"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(66(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="66 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(66(a,1),48(a,2))].">
      <j1 rule="para" parents="66 48"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,16,a,b,68,a)].">
      <j1 rule="hyper" parents="64 16 68"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      x \ x = 1 * 1
    ]]></literal>
    <justification jstring="[hyper(64,a,68,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="64 68 8"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(68(a,2),7(a,1,1))].">
      <j1 rule="para" parents="68 7"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),8(a,1,2))].">
      <j1 rule="para" parents="68 8"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      (x / x) * y = y
    ]]></literal>
    <justification jstring="[para(75(a,2),7(a,1,1))].">
      <j1 rule="para" parents="75 7"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),76(a,1,2))].">
      <j1 rule="para" parents="10 76"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),76(a,1,2))].">
      <j1 rule="para" parents="12 76"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(76(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="76 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,27,a,b,108,a(flip))].">
      <j1 rule="hyper" parents="43 27 108"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,108,a(flip))].">
      <j1 rule="hyper" parents="42 25 108"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,108,a(flip))].">
      <j1 rule="hyper" parents="41 23 108"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(108(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(108(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="108 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(175(a,2),8(a,1,2))].">
      <j1 rule="para" parents="175 8"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      x / (y \ x) = (y / z) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,78,a,b,12,a(flip))].">
      <j1 rule="hyper" parents="64 78 12"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,78,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="64 78 10"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x * (y / (z \ y)) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,78,a)].">
      <j1 rule="hyper" parents="59 78"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(58,a,78,a)].">
      <j1 rule="hyper" parents="58 78"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(37,a,20,a(flip),b,78,a),flip(a)].">
      <j1 rule="hyper" parents="37 20 78"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),78(a,1,2))].">
      <j1 rule="para" parents="14 78"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),78(a,1,2))].">
      <j1 rule="para" parents="16 78"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),78(a,1,2))].">
      <j1 rule="para" parents="18 78"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),78(a,1,2))].">
      <j1 rule="para" parents="22 78"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(78(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="78 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(78(a,2),78(a,1,2))].">
      <j1 rule="para" parents="78 78"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,81,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="64 81 10"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(58,a,81,a)].">
      <j1 rule="hyper" parents="58 81"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      x * ((y / (x \ z)) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(39,a,9,a,b,81,a(flip))].">
      <j1 rule="hyper" parents="39 9 81"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      ((x / (y / z)) \ x) * z = y
    ]]></literal>
    <justification jstring="[hyper(38,a,11,a,b,81,a(flip))].">
      <j1 rule="hyper" parents="38 11 81"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(37,a,78,a,b,81,a(flip))].">
      <j1 rule="hyper" parents="37 78 81"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(81(a,1),40(a,1))].">
      <j1 rule="para" parents="81 40"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(81(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="81 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,22,a,b,170,a)].">
      <j1 rule="hyper" parents="64 22 170"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,208,a)].">
      <j1 rule="hyper" parents="56 208"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,208,a)].">
      <j1 rule="hyper" parents="55 208"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      T(x,y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),208(a,1,2))].">
      <j1 rule="para" parents="10 208"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(208(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="208 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      T(x,y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),208(a,1,2))].">
      <j1 rule="para" parents="68 208"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,210,a)].">
      <j1 rule="hyper" parents="56 210"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(178(a,1),45(a,2))].">
      <j1 rule="para" parents="178 45"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(176(a,2),132(a,1)),flip(b)].">
      <j1 rule="para" parents="176 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      ((1 / x) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,2),133(a,1,1))].">
      <j1 rule="para" parents="12 133"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(209(a,2),133(a,1,1))].">
      <j1 rule="para" parents="209 133"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(10(a,2),139(a,1,2))].">
      <j1 rule="para" parents="10 139"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(12(a,2),173(a,1,1))].">
      <j1 rule="para" parents="12 173"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,2),182(a,1,2))].">
      <j1 rule="para" parents="10 182"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,183,a(flip))].">
      <j1 rule="hyper" parents="41 23 183"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(71(a,1),20(a,2,1))].">
      <j1 rule="para" parents="71 20"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),18(a,2,2))].">
      <j1 rule="para" parents="72 18"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),20(a,2,1))].">
      <j1 rule="para" parents="79 20"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      (x * x) * (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a,b,80,a(flip))].">
      <j1 rule="hyper" parents="36 33 80"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),18(a,2,2))].">
      <j1 rule="para" parents="80 18"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,109,a,b,10,a)].">
      <j1 rule="hyper" parents="64 109 10"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(59,a,109,a)].">
      <j1 rule="hyper" parents="59 109"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,109,a)].">
      <j1 rule="hyper" parents="58 109"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="35 12 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(36,a,12,a,b,109,a(flip))].">
      <j1 rule="hyper" parents="36 12 109"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,109,a(flip))].">
      <j1 rule="hyper" parents="35 10 109"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(109(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(109(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="109 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(109(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="109 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(109(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(109(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="109 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(109(a,1),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="109 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),109(a,1,2))].">
      <j1 rule="para" parents="23 109"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),109(a,1,2))].">
      <j1 rule="para" parents="25 109"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),109(a,1,2))].">
      <j1 rule="para" parents="27 109"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),35(a,1))].">
      <j1 rule="para" parents="109 35"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(109(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="109 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(109(a,2),45(a,1))].">
      <j1 rule="para" parents="109 45"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(109(a,2),45(a,2)),flip(a)].">
      <j1 rule="para" parents="109 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(185(a,1),109(a,1,2))].">
      <j1 rule="para" parents="185 109"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,111,a,b,81,a)].">
      <j1 rule="hyper" parents="64 111 81"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(111(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="111 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(164(a,2),138(a,1))].">
      <j1 rule="para" parents="164 138"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(164(a,2),139(a,1))].">
      <j1 rule="para" parents="164 139"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(166(a,2),138(a,1))].">
      <j1 rule="para" parents="166 138"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(166(a,2),139(a,1))].">
      <j1 rule="para" parents="166 139"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,168,a(flip))].">
      <j1 rule="hyper" parents="35 10 168"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(168(a,1),44(a,1))].">
      <j1 rule="para" parents="168 44"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(168(a,2),138(a,1))].">
      <j1 rule="para" parents="168 138"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(168(a,2),139(a,1))].">
      <j1 rule="para" parents="168 139"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a,b,171,a),flip(a)].">
      <j1 rule="hyper" parents="64 18 171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,16,a,b,171,a)].">
      <j1 rule="hyper" parents="64 16 171"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a,b,172,a),flip(a)].">
      <j1 rule="hyper" parents="64 18 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16,a,b,172,a)].">
      <j1 rule="hyper" parents="64 16 172"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,20,a,b,180,a),flip(a)].">
      <j1 rule="hyper" parents="64 20 180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20,a,b,181,a),flip(a)].">
      <j1 rule="hyper" parents="64 20 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,186,a)].">
      <j1 rule="hyper" parents="56 186"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      K(x \ y,y / x) = 1
    ]]></literal>
    <justification jstring="[para(111(a,1),268(a,1,1))].">
      <j1 rule="para" parents="111 268"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),198(a,1,1))].">
      <j1 rule="para" parents="10 198"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      (T(x,y) * z) / T(T(x,z),y) = z
    ]]></literal>
    <justification jstring="[para(23(a,1),198(a,1,2))].">
      <j1 rule="para" parents="23 198"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(198(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="198 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      (x * T(x,y)) / x = T(x,y)
    ]]></literal>
    <justification jstring="[para(185(a,1),198(a,1,2))].">
      <j1 rule="para" parents="185 198"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      (x * x) \ x = 1 / x
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,226,a)].">
      <j1 rule="hyper" parents="35 10 226"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      (x * x) * ((1 / x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(226(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="226 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,231,a),flip(a)].">
      <j1 rule="hyper" parents="41 23 231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(231(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="231 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(231(a,1),185(a,1,2))].">
      <j1 rule="para" parents="231 185"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      (x * y) * T(R(z,x,y),x * y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(38,a,20,a(flip),b,232,a),flip(a)].">
      <j1 rule="hyper" parents="38 20 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(T(x,u),y,z)) = u
    ]]></literal>
    <justification jstring="[para(25(a,2),233(a,1,2,2))].">
      <j1 rule="para" parents="25 233"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(57,a,269,a)].">
      <j1 rule="hyper" parents="57 269"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(109(a,1),134(a,1)),flip(b)].">
      <j1 rule="para" parents="109 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(11(a,1),135(a,1,1))].">
      <j1 rule="para" parents="11 135"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,1),148(a,1,2))].">
      <j1 rule="para" parents="10 148"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(198(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="198 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(232(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="232 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),256(a,1,1))].">
      <j1 rule="para" parents="10 256"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (x * y) / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(109(a,1),256(a,1,1))].">
      <j1 rule="para" parents="109 256"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(109(a,2),256(a,1,1))].">
      <j1 rule="para" parents="109 256"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(165(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="165 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,1),257(a,1,1))].">
      <j1 rule="para" parents="10 257"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      (x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(16(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="16 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(18(a,2),73(a,1,2,2))].">
      <j1 rule="para" parents="18 73"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(74(a,1),18(a,2,2))].">
      <j1 rule="para" parents="74 18"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(84(a,1),20(a,2,1))].">
      <j1 rule="para" parents="84 20"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[para(78(a,1),84(a,1,1,1,1))].">
      <j1 rule="para" parents="78 84"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),88(a,1,1))].">
      <j1 rule="para" parents="10 88"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),88(a,1,1))].">
      <j1 rule="para" parents="12 88"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="88 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(88(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="88 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      T(x * y,K(y,x)) = K(y,x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(88(a,1),22(a,2,2))].">
      <j1 rule="para" parents="88 22"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(88(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="88 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,110,a)].">
      <j1 rule="hyper" parents="63 110"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      T(x,x \ y) \ z = ((x \ y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,110,a)].">
      <j1 rule="hyper" parents="62 110"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(59,a,110,a)].">
      <j1 rule="hyper" parents="59 110"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,110,a)].">
      <j1 rule="hyper" parents="58 110"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(110(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      T(R(x,y,z),x \ u) = R((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(110(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      T(x / y,(x / y) \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(81(a,1),110(a,2,1))].">
      <j1 rule="para" parents="81 110"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),125(a,1))].">
      <j1 rule="para" parents="7 125"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(255,a,153,a),flip(a)].">
      <j1 rule="hyper" parents="255 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(297,a,155,a),flip(a)].">
      <j1 rule="hyper" parents="297 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(162(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="162 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(162(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="162 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(163(a,2),44(a,1))].">
      <j1 rule="para" parents="163 44"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(163(a,1),45(a,1))].">
      <j1 rule="para" parents="163 45"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(167(a,2),44(a,1))].">
      <j1 rule="para" parents="167 44"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(167(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="167 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(167(a,2),215(a,1))].">
      <j1 rule="para" parents="167 215"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(167(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="167 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(167(a,2),260(a,1))].">
      <j1 rule="para" parents="167 260"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,1),330(a,1,2))].">
      <j1 rule="para" parents="12 330"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(22(a,2),330(a,1))].">
      <j1 rule="para" parents="22 330"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(109(a,1),330(a,1,2))].">
      <j1 rule="para" parents="109 330"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(111(a,2),330(a,1))].">
      <j1 rule="para" parents="111 330"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(168(a,1),330(a,1,2))].">
      <j1 rule="para" parents="168 330"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(88(a,1),330(a,1,2))].">
      <j1 rule="para" parents="88 330"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(12(a,1),332(a,1,2))].">
      <j1 rule="para" parents="12 332"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(191(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="191 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(191(a,1),333(a,1,1))].">
      <j1 rule="para" parents="191 333"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(201(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="201 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      x * (((y / x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(261,a,202,a),flip(a)].">
      <j1 rule="hyper" parents="261 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),203(a,1,2,1,2))].">
      <j1 rule="para" parents="81 203"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(228(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="228 18"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(228(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="228 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(81(a,2),249(a,1,2))].">
      <j1 rule="para" parents="81 249"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,109,a,b,263,a)].">
      <j1 rule="hyper" parents="319 109 263"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,263,a(flip))].">
      <j1 rule="hyper" parents="134 263"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(263(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="263 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(304(a,1),20(a,2,1))].">
      <j1 rule="para" parents="304 20"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),321(a,1,1))].">
      <j1 rule="para" parents="20 321"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(270(a,1),343(a,1,2,1,1))].">
      <j1 rule="para" parents="270 343"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(344(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="344 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(270(a,1),344(a,1,2,1))].">
      <j1 rule="para" parents="270 344"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(350(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="350 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(216,a,93,a),flip(a)].">
      <j1 rule="hyper" parents="216 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,359,a)].">
      <j1 rule="hyper" parents="54 359"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,100,a,b,179,a),flip(a)].">
      <j1 rule="hyper" parents="126 100 179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      (x * y) / y = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(8(a,1),101(a,1,2))].">
      <j1 rule="para" parents="8 101"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,364,a),flip(a)].">
      <j1 rule="hyper" parents="257 364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(364(a,1),256(a,1))].">
      <j1 rule="para" parents="364 256"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(16(a,2),220(a,1)),flip(b)].">
      <j1 rule="para" parents="16 220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      L(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(319,a,275,a(flip),b,224,a),flip(a)].">
      <j1 rule="hyper" parents="319 275 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(319,a,172,a(flip),b,224,a),flip(a)].">
      <j1 rule="hyper" parents="319 172 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,159,a(flip),b,224,a),flip(a)].">
      <j1 rule="hyper" parents="319 159 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,224,a)].">
      <j1 rule="hyper" parents="62 224"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      x / L(y \ 1,y,z) = x / ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(61,a,224,a)].">
      <j1 rule="hyper" parents="61 224"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(59,a,224,a)].">
      <j1 rule="hyper" parents="59 224"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(207,a,224,a(flip))].">
      <j1 rule="hyper" parents="207 224"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,224,a(flip))].">
      <j1 rule="hyper" parents="145 224"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),224(a,2,1))].">
      <j1 rule="para" parents="12 224"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(224(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="224 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(110(a,2),224(a,1,1))].">
      <j1 rule="para" parents="110 224"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(199,a,225,a(flip))].">
      <j1 rule="hyper" parents="199 225"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),225(a,2,2))].">
      <j1 rule="para" parents="10 225"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),225(a,2,2))].">
      <j1 rule="para" parents="12 225"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="225 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),246(a,1,2))].">
      <j1 rule="para" parents="23 246"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,2),259(a,1,2))].">
      <j1 rule="para" parents="10 259"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(166(a,2),259(a,1))].">
      <j1 rule="para" parents="166 259"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(168(a,2),259(a,1))].">
      <j1 rule="para" parents="168 259"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),291(a,1,2))].">
      <j1 rule="para" parents="23 291"/>
    </justification>
  </clause>

  <clause id="390">
    <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),291(a,1,2))].">
      <j1 rule="para" parents="25 291"/>
    </justification>
  </clause>

  <clause id="391">
    <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),291(a,1,2))].">
      <j1 rule="para" parents="27 291"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(165(a,2),296(a,1,1))].">
      <j1 rule="para" parents="165 296"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),336(a,1,1,1))].">
      <j1 rule="para" parents="10 336"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      T(T(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(273(a,1),336(a,1,1))].">
      <j1 rule="para" parents="273 336"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      T(L(x \ 1,x,1 / x),x) = x \ 1
    ]]></literal>
    <justification jstring="[para(370(a,2),111(a,1,1))].">
      <j1 rule="para" parents="370 111"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      x \ (x / L(y \ 1,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,375,a(flip))].">
      <j1 rule="hyper" parents="134 375"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),375(a,1,2,1))].">
      <j1 rule="para" parents="81 375"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      (x * y) * z != x
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(375(a,1),135(a,1,1))].">
      <j1 rule="para" parents="375 135"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(375(a,1),333(a,1,1))].">
      <j1 rule="para" parents="375 333"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(376(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="376 18"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(78(a,1),381(a,1,1,1))].">
      <j1 rule="para" parents="78 381"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(381(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="381 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(78(a,1),393(a,1,1))].">
      <j1 rule="para" parents="78 393"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(198(a,1),393(a,1,1))].">
      <j1 rule="para" parents="198 393"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      T(x * y,K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(196(a,1),393(a,1,1))].">
      <j1 rule="para" parents="196 393"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      K(x,y) = (y * x) \ ((y \ (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),89(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(263(a,2),90(a,1,1))].">
      <j1 rule="para" parents="263 90"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),335(a,1))].">
      <j1 rule="para" parents="113 335"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,20,a,b,180,a(flip))].">
      <j1 rule="hyper" parents="127 20 180"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(127,a,18,a,b,172,a(flip))].">
      <j1 rule="hyper" parents="127 18 172"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(127,a,18,a,b,171,a(flip))].">
      <j1 rule="hyper" parents="127 18 171"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      (x / (y * y)) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,304,a(flip),b,34,a(flip))].">
      <j1 rule="hyper" parents="127 304 34"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      (x * x) \ (y * z) = ((x * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,152,a(flip),b,33,a(flip))].">
      <j1 rule="hyper" parents="127 152 33"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      ((x * x) * y) \ z = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,74,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="127 74 33"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(109(a,1),127(b,1)),flip(c)].">
      <j1 rule="para" parents="109 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      R(x,1 / y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,20,a,b,181,a(flip))].">
      <j1 rule="hyper" parents="128 20 181"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(128,a,20,a,b,180,a(flip))].">
      <j1 rule="hyper" parents="128 20 180"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = (x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,226,a(flip),b,192,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 226 192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      ((x * y) \ x) / L(y \ 1,y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(128,a,224,a(flip),b,7,a)].">
      <j1 rule="hyper" parents="128 224 7"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      (x * y) / ((z * z) \ y) = x * (z * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,153,a(flip),b,34,a)].">
      <j1 rule="hyper" parents="128 153 34"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      (x / y) / (z * z) = x / ((z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,84,a(flip),b,34,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 84 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,110,a,b,78,a),flip(a)].">
      <j1 rule="hyper" parents="129 110 78"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (((y * x) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,224,a(flip),b,78,a),flip(a)].">
      <j1 rule="hyper" parents="129 224 78"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      T(x,x \ y) \ (((x \ y) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,110,a(flip),b,78,a),flip(a)].">
      <j1 rule="hyper" parents="129 110 78"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(198(a,1),129(b,1)),flip(c)].">
      <j1 rule="para" parents="198 129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="130 31 20"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      ((x * y) \ x) * (L(y \ 1,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(130,a,224,a(flip),b,78,a)].">
      <j1 rule="hyper" parents="130 224 78"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 29 20"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 27 20"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,110,a,b,81,a)].">
      <j1 rule="hyper" parents="131 110 81"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="131 30 18"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="131 29 18"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,18,a,b,159,a(flip))].">
      <j1 rule="hyper" parents="131 18 159"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 25 18"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(206,a,110,a(flip),b,9,a)].">
      <j1 rule="hyper" parents="206 110 9"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),241(a,1,2,1))].">
      <j1 rule="para" parents="23 241"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(110(a,1),241(a,1,2,1))].">
      <j1 rule="para" parents="110 241"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(249(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="249 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(279,a,250,a)].">
      <j1 rule="hyper" parents="279 250"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(250(a,1),291(a,1,2))].">
      <j1 rule="para" parents="250 291"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      (x * x) \ (x * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,276,a)].">
      <j1 rule="hyper" parents="134 276"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      (1 / x) * (x \ y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,276,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      x * ((1 / x) \ y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,153,a(flip),b,276,a),flip(a)].">
      <j1 rule="hyper" parents="64 153 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      x \ ((x * x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,276,a(flip))].">
      <j1 rule="hyper" parents="127 153 276"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),277(a,1,1,2,1))].">
      <j1 rule="para" parents="231 277"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      ((x / y) * T(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(249(a,1),277(a,1,1,2,1))].">
      <j1 rule="para" parents="249 277"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(278(a,1),50(a,2)),flip(b)].">
      <j1 rule="para" parents="278 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,280,a)].">
      <j1 rule="hyper" parents="55 280"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(305(a,1),44(a,1))].">
      <j1 rule="para" parents="305 44"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(305(a,1),330(a,1,2))].">
      <j1 rule="para" parents="305 330"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(305(a,1),245(a,2))].">
      <j1 rule="para" parents="305 245"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a,b,449,a),flip(a)].">
      <j1 rule="hyper" parents="64 18 449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(127,a,18,a,b,449,a(flip))].">
      <j1 rule="hyper" parents="127 18 449"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      T(x * x,x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,233,a(flip),b,449,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 233 449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      (x * y) \ L(y,x,x) = T(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(285,a,461,a),flip(a)].">
      <j1 rule="hyper" parents="285 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      L(T(x,y),y,y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,229,a(flip),b,461,a),flip(a)].">
      <j1 rule="hyper" parents="64 229 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      L(x \ y,x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,153,a(flip),b,461,a),flip(a)].">
      <j1 rule="hyper" parents="64 153 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(462(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="462 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(319,a,193,a(flip),b,466,a),flip(a)].">
      <j1 rule="hyper" parents="319 193 466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(466(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="466 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      ((x * x) \ x) * y = L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(275(a,2),466(a,2,1)),flip(a)].">
      <j1 rule="para" parents="275 466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(285,a,94,a),flip(a)].">
      <j1 rule="hyper" parents="285 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(128,a,229,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="128 229 94"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(128,a,153,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="128 153 94"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,151,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="64 151 94"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      L(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,34,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="35 34 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      L(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,33,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="35 33 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(130,a,94,a(flip),b,196,a)].">
      <j1 rule="hyper" parents="130 94 196"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,L(z,y,x)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,94,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="128 94 109"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,152,a(flip),b,94,a(flip))].">
      <j1 rule="hyper" parents="127 152 94"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      (x * (y * (z * u))) \ ((x * (y * z)) * L(u,z,y)) = a(x,y * z,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(94(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="94 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(94(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="94 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="94 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(94(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="94 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      (x * (y * z)) / (y * L(z,y,x)) = R(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(94(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="94 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      (x * x) * (L(y,x,x) * z) = (x * (x * y)) * z
    ]]></literal>
    <justification jstring="[para(94(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="94 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="94 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),330(a,1,2))].">
      <j1 rule="para" parents="94 330"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(263(a,2),94(a,1,1))].">
      <j1 rule="para" parents="263 94"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),217(a,1))].">
      <j1 rule="para" parents="94 217"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      x * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(94(a,1),285(a,1))].">
      <j1 rule="para" parents="94 285"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(305(a,1),94(a,2,2))].">
      <j1 rule="para" parents="305 94"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),477(a,1,2))].">
      <j1 rule="para" parents="7 477"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      L(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(477(a,1),51(a,2))].">
      <j1 rule="para" parents="477 51"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(494(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="494 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      L(x,y * y,z) = L(x,u,w * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,477,a,b,478,a)].">
      <j1 rule="hyper" parents="319 477 478"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),478(a,1,3))].">
      <j1 rule="para" parents="7 478"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      L(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(478(a,1),51(a,2))].">
      <j1 rule="para" parents="478 51"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      L(x \ (y * x),x,y) = T(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,22,a,b,96,a),flip(a)].">
      <j1 rule="hyper" parents="319 22 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(319,a,233,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="319 233 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,172,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="319 172 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(319,a,171,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="319 171 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,159,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="319 159 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,91,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="319 91 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),96(a,2,1))].">
      <j1 rule="para" parents="12 96"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),96(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),96(a,2,1))].">
      <j1 rule="para" parents="109 96"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),96(a,2,2))].">
      <j1 rule="para" parents="109 96"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      (x * T(x,y)) \ (T(x,y) * z) = L(x \ z,x,T(x,y))
    ]]></literal>
    <justification jstring="[para(248(a,1),96(a,2,1)),flip(a)].">
      <j1 rule="para" parents="248 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(265(a,2),96(a,2,2))].">
      <j1 rule="para" parents="265 96"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(96(a,2),337(a,1))].">
      <j1 rule="para" parents="96 337"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(94(a,1),96(a,2,1))].">
      <j1 rule="para" parents="94 96"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(94(a,1),96(a,2,2))].">
      <j1 rule="para" parents="94 96"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(501(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="501 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[hyper(128,a,105,a,b,xx)].">
      <j1 rule="hyper" parents="128 105"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,304,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="127 304 105"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,230,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="127 230 105"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,152,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="127 152 105"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(127,a,151,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="127 151 105"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="127 10 105"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      R(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,34,a(flip),b,105,a),flip(a)].">
      <j1 rule="hyper" parents="36 34 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      R(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a(flip),b,105,a),flip(a)].">
      <j1 rule="hyper" parents="36 33 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,105,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="127 105 94"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),105(a,1,2))].">
      <j1 rule="para" parents="12 105"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="105 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(105(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="105 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),45(a,1))].">
      <j1 rule="para" parents="105 45"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * z
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(105(a,2),45(a,1))].">
      <j1 rule="para" parents="105 45"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="105 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(105(a,2),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="105 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(88(a,1),105(a,1,2))].">
      <j1 rule="para" parents="88 105"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),522(a,1,2))].">
      <j1 rule="para" parents="7 522"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      R(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(522(a,1),52(a,2))].">
      <j1 rule="para" parents="522 52"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(319,a,181,a(flip),b,106,a),flip(a)].">
      <j1 rule="hyper" parents="319 181 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,180,a(flip),b,106,a),flip(a)].">
      <j1 rule="hyper" parents="319 180 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),106(a,2,2))].">
      <j1 rule="para" parents="10 106"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),106(a,2,2))].">
      <j1 rule="para" parents="12 106"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="106 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[para(109(a,1),106(a,2,2))].">
      <j1 rule="para" parents="109 106"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(106(a,2),111(a,1,1))].">
      <j1 rule="para" parents="106 111"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(248(a,1),106(a,2,2))].">
      <j1 rule="para" parents="248 106"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      R(x / y,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),221(a,1)),flip(b)].">
      <j1 rule="para" parents="106 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(105(a,1),106(a,2,1))].">
      <j1 rule="para" parents="105 106"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),106(a,2,2))].">
      <j1 rule="para" parents="105 106"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(106(a,2),106(a,1,1))].">
      <j1 rule="para" parents="106 106"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(9(a,1),146(a,1,2,2))].">
      <j1 rule="para" parents="9 146"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(88(a,1),194(a,1,2,1))].">
      <j1 rule="para" parents="88 194"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(305(a,1),194(a,1,2,1))].">
      <j1 rule="para" parents="305 194"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(94(a,1),194(a,1,2,1))].">
      <j1 rule="para" parents="94 194"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),197(a,1,1,2))].">
      <j1 rule="para" parents="12 197"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,30,a,b,262,a)].">
      <j1 rule="hyper" parents="127 30 262"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      x \ R(L(y,x \ 1,x),z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,29,a,b,262,a)].">
      <j1 rule="hyper" parents="127 29 262"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,25,a(flip),b,262,a)].">
      <j1 rule="hyper" parents="127 25 262"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      (x * y) \ (x * L(z,y \ 1,y)) = L((y \ 1) * z,y,x)
    ]]></literal>
    <justification jstring="[para(262(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="262 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      x * K(x \ 1,x) = L(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(263(a,2),262(a,1,2))].">
      <j1 rule="para" parents="263 262"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,30,a,b,264,a)].">
      <j1 rule="hyper" parents="127 30 264"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(285,a,266,a),flip(a)].">
      <j1 rule="hyper" parents="285 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,29,a(flip),b,266,a)].">
      <j1 rule="hyper" parents="128 29 266"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,27,a(flip),b,266,a)].">
      <j1 rule="hyper" parents="128 27 266"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(266(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="266 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,29,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="128 29 267"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(302(a,1),25(a,2,1))].">
      <j1 rule="para" parents="302 25"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(302(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="302 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(302(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="302 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(78(a,1),324(a,1,1,1))].">
      <j1 rule="para" parents="78 324"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(198(a,1),324(a,1,1,1))].">
      <j1 rule="para" parents="198 324"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(190(a,2),324(a,1,1))].">
      <j1 rule="para" parents="190 324"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),326(a,1,1))].">
      <j1 rule="para" parents="11 326"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((x * y) * z) = w
    ]]></literal>
    <justification jstring="[para(20(a,2),326(a,1,1))].">
      <j1 rule="para" parents="20 326"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(162(a,1),326(a,1,1))].">
      <j1 rule="para" parents="162 326"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(9(a,1),327(a,1,2))].">
      <j1 rule="para" parents="9 327"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      x * T(y,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      (y * x) / u = z
    ]]></literal>
    <justification jstring="[para(22(a,2),327(a,1,2))].">
      <j1 rule="para" parents="22 327"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(81(a,1),327(a,1,2))].">
      <j1 rule="para" parents="81 327"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(172(a,1),327(a,1,2))].">
      <j1 rule="para" parents="172 327"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(167(a,1),327(a,1,2))].">
      <j1 rule="para" parents="167 327"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(167(a,2),327(a,1))].">
      <j1 rule="para" parents="167 327"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),328(a,1,2))].">
      <j1 rule="para" parents="109 328"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),329(a,2,2))].">
      <j1 rule="para" parents="22 329"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(81(a,1),329(a,2,2))].">
      <j1 rule="para" parents="81 329"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      x * (y * T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),331(a,1,2,2))].">
      <j1 rule="para" parents="22 331"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(68(a,1),331(a,1,2,2))].">
      <j1 rule="para" parents="68 331"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(167(a,2),331(a,1,2))].">
      <j1 rule="para" parents="167 331"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(201(a,2),331(a,1,2))].">
      <j1 rule="para" parents="201 331"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(262(a,1),331(a,1))].">
      <j1 rule="para" parents="262 331"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(96(a,2),341(a,1))].">
      <j1 rule="para" parents="96 341"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      x * T(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(109(a,2),358(a,1))].">
      <j1 rule="para" parents="109 358"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      ((x * x) \ y) \ 1 = y \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(499,a,371,a)].">
      <j1 rule="hyper" parents="499 371"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      1 / (x \ (y * y)) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(206,a,371,a(flip),b,478,a(flip))].">
      <j1 rule="hyper" parents="206 371 478"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(371(a,1),184(a,1,2))].">
      <j1 rule="para" parents="371 184"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(377(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="377 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      (x / y) \ (L(y \ 1,y,x / y) * x) = K(x \ (x / y),x)
    ]]></literal>
    <justification jstring="[para(377(a,2),89(a,1,2,1))].">
      <j1 rule="para" parents="377 89"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(130,a,382,a(flip),b,78,a)].">
      <j1 rule="hyper" parents="130 382 78"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(382(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="382 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(383(a,1),183(a,1,2))].">
      <j1 rule="para" parents="383 183"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),388(a,1,2))].">
      <j1 rule="para" parents="10 388"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(167(a,1),388(a,1,2))].">
      <j1 rule="para" parents="167 388"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(106(a,2),392(a,1))].">
      <j1 rule="para" parents="106 392"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,395,a)].">
      <j1 rule="hyper" parents="64 25 395"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      x / ((y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(402(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="402 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <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),404(a,1))].">
      <j1 rule="para" parents="27 404"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(413(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="413 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,1 / y,y) = x
    ]]></literal>
    <justification jstring="[para(418(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="418 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      x / (y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      R(z,y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(419(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="419 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      (((x * x) \ x) * y) * L(z,y,(x * x) \ x) = L(x \ (y * z),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,94,a,b,471,a)].">
      <j1 rule="hyper" parents="64 94 471"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(474(a,1),333(a,1,1))].">
      <j1 rule="para" parents="474 333"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),500(a,1,1))].">
      <j1 rule="para" parents="22 500"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a(flip),b,611,a)].">
      <j1 rule="hyper" parents="64 25 611"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      L(T(T(x,y),z),y,x) = T(T(x,x * y),z)
    ]]></literal>
    <justification jstring="[para(611(a,1),25(a,2,1))].">
      <j1 rule="para" parents="611 25"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(611(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="611 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      T(L(x,x \ 1,x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,211,a(flip),b,612,a),flip(a)].">
      <j1 rule="hyper" parents="319 211 612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(279,a,612,a)].">
      <j1 rule="hyper" parents="279 612"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,278,a,b,612,a)].">
      <j1 rule="hyper" parents="41 278 612"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,612,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 612 22"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(502(a,1),25(a,2,1))].">
      <j1 rule="para" parents="502 25"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(503(a,1),25(a,2,1))].">
      <j1 rule="para" parents="503 25"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x \ 1,x) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(503(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      T((x \ 1) \ y,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(503(a,1),184(a,1,2))].">
      <j1 rule="para" parents="503 184"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      (x * y) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / z,z,y) = u
    ]]></literal>
    <justification jstring="[para(520(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="520 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(537(a,1),27(a,2,1))].">
      <j1 rule="para" parents="537 27"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(538(a,1),27(a,2,1))].">
      <j1 rule="para" parents="538 27"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      (x * y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,x) = u
    ]]></literal>
    <justification jstring="[para(376(a,1),549(a,1,2))].">
      <j1 rule="para" parents="376 549"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(201(a,2),568(a,1,1))].">
      <j1 rule="para" parents="201 568"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      ((x \ 1) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(350(a,1),568(a,1,1,2))].">
      <j1 rule="para" parents="350 568"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(151(a,2),574(a,1))].">
      <j1 rule="para" parents="151 574"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(376(a,1),579(a,1,2))].">
      <j1 rule="para" parents="376 579"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),617(a,1,2))].">
      <j1 rule="para" parents="10 617"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),618(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      ((x \ y) \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(270(a,1),627(a,1,1,1))].">
      <j1 rule="para" parents="270 627"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(245,a,116,a),flip(a)].">
      <j1 rule="hyper" parents="245 116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      ((x * x) \ y) * T(z,y) = (x * x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(127,a,109,a(flip),b,116,a),flip(a)].">
      <j1 rule="hyper" parents="127 109 116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      ((x * x) \ y) \ z = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,116,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 153 116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      (x * x) * ((((x * x) \ y) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[para(116(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      (x * y) / (1 / y) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(226(a,1),122(a,1,1,2))].">
      <j1 rule="para" parents="226 122"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      (x / y) * (y * y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(392,a,640,a),flip(a)].">
      <j1 rule="hyper" parents="392 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      (x / (y * y)) * y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(323,a,640,a),flip(a)].">
      <j1 rule="hyper" parents="323 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      x * ((y \ 1) * (y \ 1)) = (x * (y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(78(a,1),640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      (x * (1 / y)) / y = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,11,a(flip),b,641,a),flip(a)].">
      <j1 rule="hyper" parents="128 11 641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      L(x,x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,461,a(flip),b,641,a)].">
      <j1 rule="hyper" parents="64 461 641"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,94,a(flip),b,242,a)].">
      <j1 rule="hyper" parents="64 94 242"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,242,a(flip),b,94,a(flip))].">
      <j1 rule="hyper" parents="127 242 94"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      (x * (L(y,z,u) * w)) \ ((x * w) * L(T(y,w),z,u)) = a(x,w,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(242(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="242 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),242(a,1,2,1))].">
      <j1 rule="para" parents="27 242"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(110(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="110 242"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,105,a(flip),b,243,a),flip(a)].">
      <j1 rule="hyper" parents="319 105 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,105,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="127 105 243"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      R(T(x,x * x),x,x) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,105,a(flip),b,243,a),flip(a)].">
      <j1 rule="hyper" parents="35 105 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(110(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="110 243"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(611(a,2),243(a,1,2,1))].">
      <j1 rule="para" parents="611 243"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      R(L(x,x,x),x,x) = x
    ]]></literal>
    <justification jstring="[para(112(a,1),655(a,1,1))].">
      <j1 rule="para" parents="112 655"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      L(R(x,x,x),x,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29,a(flip),b,661,a)].">
      <j1 rule="hyper" parents="64 29 661"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      x * R(x,x,x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,662,a(flip),b,461,a),flip(a)].">
      <j1 rule="hyper" parents="127 662 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(279,a,251,a)].">
      <j1 rule="hyper" parents="279 251"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(279,a,252,a)].">
      <j1 rule="hyper" parents="279 252"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),252(a,1,1))].">
      <j1 rule="para" parents="225 252"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),252(a,1,1))].">
      <j1 rule="para" parents="106 252"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(303(a,1),252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="303 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(383(a,1),252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="383 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,667,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 667 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(429,a,311,a,b,xx)].">
      <j1 rule="hyper" parents="429 311"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(311(a,1),48(a,1))].">
      <j1 rule="para" parents="311 48"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(127,a,313,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="127 313 88"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(314(a,2),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="314 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,(x \ y) \ y) = u
    ]]></literal>
    <justification jstring="[para(314(a,2),338(a,1,1))].">
      <j1 rule="para" parents="314 338"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(355(a,1),330(a,1,2))].">
      <j1 rule="para" parents="355 330"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(109(a,1),403(a,1,2))].">
      <j1 rule="para" parents="109 403"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,89,a(flip),b,407,a)].">
      <j1 rule="hyper" parents="319 89 407"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(70(a,1),682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),683(a,1,1,2))].">
      <j1 rule="para" parents="12 683"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x * x) * ((y * x) \ z) = R(y / x,x,x) \ z
    ]]></literal>
    <justification jstring="[para(106(a,2),414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      x / ((y * y) \ z) = (x / z) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(392,a,423,a)].">
      <j1 rule="hyper" parents="392 423"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      (x / (y * y)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(323,a,423,a),flip(a)].">
      <j1 rule="hyper" parents="323 423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      (x / ((y * y) * z)) \ u = (y * y) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[para(425(a,1),414(a,1,1))].">
      <j1 rule="para" parents="425 414"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(428(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="428 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      x / T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(434(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="434 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x = x * T(y,((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,314,a(flip),b,444,a)].">
      <j1 rule="hyper" parents="64 314 444"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(447(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="447 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(447(a,1),336(a,1,1))].">
      <j1 rule="para" parents="447 336"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(111(a,1),453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(453(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="453 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(453(a,1),336(a,1,1))].">
      <j1 rule="para" parents="453 336"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(55,a,622,a)].">
      <j1 rule="hyper" parents="55 622"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      T(x,y * y) * ((y * y) \ z) = ((y * y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,636,a(flip),b,423,a)].">
      <j1 rule="hyper" parents="130 636 423"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      ((x * x) \ y) * ((x * x) * z) = T(y,x * x) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,636,a(flip),b,122,a),flip(a)].">
      <j1 rule="hyper" parents="130 636 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      (((x * x) \ y) * z) * (x * x) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[para(415(a,1),636(a,1,1))].">
      <j1 rule="para" parents="415 636"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      (x / (y * z)) * (y * y) = x / ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(449(a,1),688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="449 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      x / (((y * y) \ z) * u) = (x / (z * u)) * (y * y)
    ]]></literal>
    <justification jstring="[para(415(a,1),688(a,1,2))].">
      <j1 rule="para" parents="415 688"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      ((x * ((y * y) \ z)) * u) / (z * u) = R(x / (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(689(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="689 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      ((x * y) * z) / a(y,T(x,y),z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,230,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="128 230 85"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,152,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="128 152 85"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,151,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="128 151 85"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),85(a,1,1,2))].">
      <j1 rule="para" parents="10 85"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      (x * y) * a(x,y / z,z) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),85(a,1,1,2))].">
      <j1 rule="para" parents="12 85"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = (x * y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),85(a,1,1))].">
      <j1 rule="para" parents="72 85"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      x * a(x,1 / y,y) = (x * (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(80(a,1),85(a,1,1))].">
      <j1 rule="para" parents="80 85"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(85(a,1),330(a,1,2))].">
      <j1 rule="para" parents="85 330"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      ((x * y) * z) * a(R(x,y,z),y,z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(105(a,1),85(a,1,1))].">
      <j1 rule="para" parents="105 85"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,30,a,b,95,a)].">
      <j1 rule="hyper" parents="131 30 95"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(109(a,1),97(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u / (z * y)) = u \ ((u / (z * y)) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[para(94(a,1),97(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="94 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      ((x * x) * y) / z = (x * x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,478,a(flip),b,98,a(flip))].">
      <j1 rule="hyper" parents="206 478 98"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      ((x * x) \ y) / z = (x * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(127,a,156,a(flip),b,719,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 156 719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      (((x * x) \ y) * z) / u = (x * x) \ ((y * z) / u)
    ]]></literal>
    <justification jstring="[para(415(a,1),720(a,1,1))].">
      <j1 rule="para" parents="415 720"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),102(a,2,2))].">
      <j1 rule="para" parents="10 102"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(130,a,29,a(flip),b,104,a)].">
      <j1 rule="hyper" parents="130 29 104"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(104(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="104 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a(flip),b,237,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(237(a,1),335(a,1))].">
      <j1 rule="para" parents="237 335"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (R(x,y,z) * z) \ ((x * y) * z) = L(T(y,z),z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),237(a,1,2))].">
      <j1 rule="para" parents="105 237"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(237(a,1),341(a,1))].">
      <j1 rule="para" parents="237 341"/>
    </justification>
  </clause>

  <clause id="729">
    <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(308(a,1),443(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="308 443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(417,a,151,a(flip),b,354,a)].">
      <j1 rule="hyper" parents="417 151 354"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,243,a,b,354,a)].">
      <j1 rule="hyper" parents="64 243 354"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,22,a,b,372,a),flip(a)].">
      <j1 rule="hyper" parents="319 22 372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,378,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="131 378 18"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(393,a,384,a),flip(a)].">
      <j1 rule="hyper" parents="393 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(110(a,1),385(a,1,2))].">
      <j1 rule="para" parents="110 385"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),389(a,1,2,1))].">
      <j1 rule="para" parents="22 389"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      ((x * y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(431(a,1),330(a,1,2))].">
      <j1 rule="para" parents="431 330"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,242,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="64 242 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,242,a(flip),b,437,a(flip))].">
      <j1 rule="hyper" parents="127 242 437"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(437(a,1),44(a,1))].">
      <j1 rule="para" parents="437 44"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(437(a,1),330(a,1,2))].">
      <j1 rule="para" parents="437 330"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      T(L(x,x,x),(1 / x) * y) = ((1 / x) * y) \ L(y,1 / x,1 / x)
    ]]></literal>
    <justification jstring="[para(645(a,2),464(a,2,1)),flip(a)].">
      <j1 rule="para" parents="645 464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(473(a,1),333(a,1,1))].">
      <j1 rule="para" parents="473 333"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(244,a,153,a(flip),b,476,a),flip(a)].">
      <j1 rule="hyper" parents="244 153 476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,242,a(flip),b,476,a),flip(a)].">
      <j1 rule="hyper" parents="64 242 476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,242,a(flip),b,476,a(flip))].">
      <j1 rule="hyper" parents="127 242 476"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(504(a,1),25(a,2,1))].">
      <j1 rule="para" parents="504 25"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(504(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="504 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(504(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="504 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,16,a,b,509,a)].">
      <j1 rule="hyper" parents="319 16 509"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(509(a,1),25(a,2,1))].">
      <j1 rule="para" parents="509 25"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      L(x \ T(x,y),x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(509(a,2),338(a,1))].">
      <j1 rule="para" parents="509 338"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),519(a,1,2))].">
      <j1 rule="para" parents="12 519"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(519(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="519 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(540(a,1),27(a,2,1))].">
      <j1 rule="para" parents="540 27"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(540(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="540 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(225(a,2),540(a,1,1,2))].">
      <j1 rule="para" parents="225 540"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(540(a,1),252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="540 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),580(a,1))].">
      <j1 rule="para" parents="22 580"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(131,a,613,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 613 18"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),668(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,266,a(flip),b,711,a),flip(a)].">
      <j1 rule="hyper" parents="319 266 711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,266,a(flip),b,711,a)].">
      <j1 rule="hyper" parents="127 266 711"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      (x * y) * (y \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(711(a,1),44(a,1))].">
      <j1 rule="para" parents="711 44"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(767(a,1),330(a,1,2))].">
      <j1 rule="para" parents="767 330"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(767(a,1),96(a,2,2))].">
      <j1 rule="para" parents="767 96"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      x \ R(x,1 / y,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,267,a(flip),b,712,a)].">
      <j1 rule="hyper" parents="127 267 712"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      (1 / x) \ T(L(y,x,1 / x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(127,a,725,a(flip),b,172,a(flip))].">
      <j1 rule="hyper" parents="127 725 172"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(765(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="765 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(180(a,1),765(a,2,1)),flip(a)].">
      <j1 rule="para" parents="180 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(765(a,2),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="765 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(765(a,2),278(a,1,1))].">
      <j1 rule="para" parents="765 278"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,779,a)].">
      <j1 rule="hyper" parents="64 27 779"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(779(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="779 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(779(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="779 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),780(a,1,1,2))].">
      <j1 rule="para" parents="12 780"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(780(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="780 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(783(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="783 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(208(a,1),783(a,1,1))].">
      <j1 rule="para" parents="208 783"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,786,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="128 786 267"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,265,a,b,787,a),flip(a)].">
      <j1 rule="hyper" parents="319 265 787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(502(a,1),774(a,1,2,1))].">
      <j1 rule="para" parents="502 774"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(279,a,777,a)].">
      <j1 rule="hyper" parents="279 777"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,27,a,b,115,a)].">
      <j1 rule="hyper" parents="319 27 115"/>
    </justification>
  </clause>

  <clause id="793">
    <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),300(a,1,2))].">
      <j1 rule="para" parents="25 300"/>
    </justification>
  </clause>

  <clause id="794">
    <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),300(a,1,2))].">
      <j1 rule="para" parents="29 300"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,317,a)].">
      <j1 rule="hyper" parents="64 27 317"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) != (y * x) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,K(y,x),x * y) = u
    ]]></literal>
    <justification jstring="[para(88(a,1),488(a,1,1)),flip(a)].">
      <j1 rule="para" parents="88 488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(x,y),y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),489(a,1,1))].">
      <j1 rule="para" parents="109 489"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      (x * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ (x \ z),y,x) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),489(a,1,2))].">
      <j1 rule="para" parents="74 489"/>
    </justification>
  </clause>

  <clause id="801">
    <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(94(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="94 489"/>
    </justification>
  </clause>

  <clause id="802">
    <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(85(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="85 489"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),531(a,1,1))].">
      <j1 rule="para" parents="84 531"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),601(a,1,1,1))].">
      <j1 rule="para" parents="11 601"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      ((x \ 1) \ y) / y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,x \ 1,(x \ 1) \ y) = z
    ]]></literal>
    <justification jstring="[para(10(a,1),604(a,1,2))].">
      <j1 rule="para" parents="10 604"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      (x * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      R(x / (z / y),z / y,y) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),623(a,1,2))].">
      <j1 rule="para" parents="12 623"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      ((x * x) \ y) * T(z,y) = ((x * x) \ z) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,415,a(flip),b,637,a),flip(a)].">
      <j1 rule="hyper" parents="319 415 637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(127,a,156,a(flip),b,643,a),flip(a)].">
      <j1 rule="hyper" parents="127 156 643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      (x \ 1) / x = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,421,a(flip),b,809,a)].">
      <j1 rule="hyper" parents="64 421 809"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      L(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(809(a,1),478(a,1,3))].">
      <j1 rule="para" parents="809 478"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      R(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(809(a,1),522(a,1,2))].">
      <j1 rule="para" parents="809 522"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ z) = x
    ]]></literal>
    <justification jstring="[para(78(a,1),811(a,1,3,2))].">
      <j1 rule="para" parents="78 811"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      R(x,(y \ 1) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(78(a,1),812(a,1,2,2))].">
      <j1 rule="para" parents="78 812"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      (((x \ 1) \ x) * y) * z = ((x \ 1) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,813,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 813 18"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      (x \ 1) \ (x * y) = ((x \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[para(814(a,1),519(a,1,1))].">
      <j1 rule="para" parents="814 519"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      ((x \ 1) \ x) * (x \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,374,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="128 374 650"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),818(a,1,1,2,1))].">
      <j1 rule="para" parents="10 818"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,651,a),flip(a)].">
      <j1 rule="hyper" parents="142 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,374,a(flip),b,651,a),flip(a)].">
      <j1 rule="hyper" parents="128 374 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,94,a(flip),b,651,a),flip(a)].">
      <j1 rule="hyper" parents="128 94 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(290,a,657,a)].">
      <j1 rule="hyper" parents="290 657"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,657,a),flip(a)].">
      <j1 rule="hyper" parents="142 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,657,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="128 657 105"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(665(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="665 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(665(a,1),336(a,1,1))].">
      <j1 rule="para" parents="665 336"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(96(a,1),665(a,1,1,2))].">
      <j1 rule="para" parents="96 665"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(302(a,1),665(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="302 665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(502(a,1),665(a,1,1,2))].">
      <j1 rule="para" parents="502 665"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(751(a,2),665(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="751 665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      ((x * y) * R(L(z,y,x),u,w)) / (x * y) = R((x * (y * z)) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),666(a,1,1,2,1))].">
      <j1 rule="para" parents="18 666"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(666(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="666 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(279,a,696,a)].">
      <j1 rule="hyper" parents="279 696"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,696,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 696 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      (x * x) \ (y / ((1 / x) * z)) = T(y / (x * z),x * x)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,703,a),flip(a)].">
      <j1 rule="hyper" parents="417 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,789,a)].">
      <j1 rule="hyper" parents="145 789"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),791(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(z,z \ u),w,v5) = ((x \ y) \ y) \ R((z \ u) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(127,a,796,a,b,355,a)].">
      <j1 rule="hyper" parents="127 796 355"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(78(a,1),805(a,1,1))].">
      <j1 rule="para" parents="78 805"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      ((x * x) \ y) * ((x * x) * z) = z * T(y,(x * x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      ((x * x) \ y) * x = (1 / x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(275(a,1),808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="275 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      x \ ((1 / x) * T(y,x)) = T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,842,a),flip(a)].">
      <j1 rule="hyper" parents="417 842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(131,a,820,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 820 18"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(820(a,2),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="820 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(377(a,1),820(a,2,1,2))].">
      <j1 rule="para" parents="377 820"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(502(a,1),820(a,2,1,2))].">
      <j1 rule="para" parents="502 820"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(504(a,1),820(a,2,1,2))].">
      <j1 rule="para" parents="504 820"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,824,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 824 20"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(824(a,2),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="824 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(303(a,1),824(a,2,1,2))].">
      <j1 rule="para" parents="303 824"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(537(a,1),824(a,2,1,2))].">
      <j1 rule="para" parents="537 824"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(538(a,1),824(a,2,1,2))].">
      <j1 rule="para" parents="538 824"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(824(a,1),290(a,1,1))].">
      <j1 rule="para" parents="824 290"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(87(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="87 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (z * y)) * z = u
    ]]></literal>
    <justification jstring="[para(99(a,2),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="99 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      (x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,30,a,b,236,a)].">
      <j1 rule="hyper" parents="131 30 236"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,453,a(flip),b,239,a)].">
      <j1 rule="hyper" parents="64 453 239"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[para(779(a,1),281(a,1,2))].">
      <j1 rule="para" parents="779 281"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(324,a,859,a),flip(a)].">
      <j1 rule="hyper" parents="324 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,71,a(flip),b,859,a)].">
      <j1 rule="hyper" parents="127 71 859"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(263(a,2),862(a,1,1))].">
      <j1 rule="para" parents="263 862"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,110,a(flip),b,863,a)].">
      <j1 rule="hyper" parents="131 110 863"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,96,a(flip),b,379,a),flip(a)].">
      <j1 rule="hyper" parents="319 96 379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,379,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 379 18"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      L((x * y) \ x,y,1 / y) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(370(a,1),379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="370 379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),867(a,1,1,1))].">
      <j1 rule="para" parents="10 867"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(22(a,1),390(a,1,2,1))].">
      <j1 rule="para" parents="22 390"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      (T(x * x,y) * z) * u = T(x * x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(523(a,1),433(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="523 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(303(a,1),433(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="303 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(96(a,1),438(a,1,2,1))].">
      <j1 rule="para" parents="96 438"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(302(a,1),438(a,1,2,1))].">
      <j1 rule="para" parents="302 438"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      (1 / x) \ R((1 / x) * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,470,a(flip),b,461,a)].">
      <j1 rule="hyper" parents="127 470 461"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,85,a(flip),b,487,a),flip(a)].">
      <j1 rule="hyper" parents="35 85 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,877,a)].">
      <j1 rule="hyper" parents="134 877"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(508(a,1),25(a,2,1))].">
      <j1 rule="para" parents="508 25"/>
    </justification>
  </clause>

  <clause id="881">
    <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(508(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="508 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),518(a,1,2))].">
      <j1 rule="para" parents="109 518"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(393,a,541,a),flip(a)].">
      <j1 rule="hyper" parents="393 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(541(a,1),393(a,1))].">
      <j1 rule="para" parents="541 393"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(503(a,1),556(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="503 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[para(538(a,1),562(a,1,1,1))].">
      <j1 rule="para" parents="538 562"/>
    </justification>
  </clause>

  <clause id="887">
    <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(565(a,1),300(a,1,2))].">
      <j1 rule="para" parents="565 300"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,594,a,b,97,a),flip(a)].">
      <j1 rule="hyper" parents="131 594 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(130,a,597,a,b,104,a)].">
      <j1 rule="hyper" parents="130 597 104"/>
    </justification>
  </clause>

  <clause id="890">
    <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),614(a,1,1))].">
      <j1 rule="para" parents="27 614"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,619,a(flip),b,264,a)].">
      <j1 rule="hyper" parents="127 619 264"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,624,a(flip),b,267,a),flip(a)].">
      <j1 rule="hyper" parents="128 624 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[para(224(a,1),646(a,2,1)),flip(a)].">
      <j1 rule="para" parents="224 646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,85,a(flip),b,653,a),flip(a)].">
      <j1 rule="hyper" parents="127 85 653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      (x * y) * z != (u * x) * y
    ]]></literal>
    <literal><![CDATA[
      R(T(u,x * y),x,y) = z
    ]]></literal>
    <justification jstring="[para(653(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="653 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x / y) = z
    ]]></literal>
    <justification jstring="[para(670(a,2),291(a,1,2))].">
      <j1 rule="para" parents="670 291"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * T((x \ z) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(78(a,1),694(a,1,1,1))].">
      <j1 rule="para" parents="78 694"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),697(a,1,1,1,1))].">
      <j1 rule="para" parents="12 697"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(633(a,1),697(a,1,1))].">
      <j1 rule="para" parents="633 697"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(109(a,1),707(a,1,1))].">
      <j1 rule="para" parents="109 707"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,x / z) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,646,a(flip),b,708,a),flip(a)].">
      <j1 rule="hyper" parents="319 646 708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,709,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="128 709 109"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,730,a)].">
      <j1 rule="hyper" parents="64 27 730"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      R(T(x / y,x),y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,151,a(flip),b,731,a),flip(a)].">
      <j1 rule="hyper" parents="35 151 731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(371(a,1),739(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="371 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(504(a,1),739(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="504 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(z,x) = u
    ]]></literal>
    <justification jstring="[para(745(a,1),330(a,1,2))].">
      <j1 rule="para" parents="745 330"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(506(a,1),775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="506 775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),829(a,2,1,2,1))].">
      <j1 rule="para" parents="12 829"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(235(a,1),829(a,2,1,2))].">
      <j1 rule="para" parents="235 829"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(890(a,1),242(a,1,2))].">
      <j1 rule="para" parents="890 242"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(130,a,903,a(flip),b,104,a)].">
      <j1 rule="hyper" parents="130 903 104"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      (((x * x) \ y) * x) * x = R(T(y,x * x),x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,653,a,b,639,a),flip(a)].">
      <j1 rule="hyper" parents="35 653 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) * z) = y * ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,701,a(flip),b,415,a)].">
      <j1 rule="hyper" parents="131 701 415"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      R(x,(y * y) \ z,u) / (y * y) = ((x * ((y * y) \ z)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,20,a,b,704,a(flip))].">
      <j1 rule="hyper" parents="128 20 704"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      ((x \ 1) \ x) * ((x \ y) * z) = ((x \ 1) \ y) * z
    ]]></literal>
    <justification jstring="[para(817(a,1),815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="817 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),834(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 834"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(834(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="834 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,419,a,b,835,a)].">
      <j1 rule="hyper" parents="64 419 835"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),835(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(106(a,2),835(a,1,1,1,2))].">
      <j1 rule="para" parents="106 835"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),838(a,1,1,1))].">
      <j1 rule="para" parents="106 838"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(543(a,1),838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="543 838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,872,a)].">
      <j1 rule="hyper" parents="488 872"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = L(x,w,v5 * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,478,a,b,927,a),flip(a)].">
      <j1 rule="hyper" parents="319 478 927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      L(x,y,(1 / z) \ z) = x
    ]]></literal>
    <justification jstring="[para(463(a,1),927(a,1,3))].">
      <j1 rule="para" parents="463 927"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      x * ((((1 / y) \ y) * x) \ z) = ((1 / y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(131,a,302,a(flip),b,929,a(flip))].">
      <j1 rule="hyper" parents="131 302 929"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(736,a,885,a),flip(a)].">
      <j1 rule="hyper" parents="736 885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(291,a,885,a),flip(a)].">
      <j1 rule="hyper" parents="291 885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,885,a)].">
      <j1 rule="hyper" parents="134 885"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(582,a,885,a(flip))].">
      <j1 rule="hyper" parents="582 885"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),885(a,2,2,1))].">
      <j1 rule="para" parents="8 885"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),885(a,2,2,1))].">
      <j1 rule="para" parents="10 885"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,445,a(flip),b,935,a)].">
      <j1 rule="hyper" parents="64 445 935"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,935,a(flip),b,445,a(flip))].">
      <j1 rule="hyper" parents="127 935 445"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(938(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="938 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(445(a,2),939(a,1))].">
      <j1 rule="para" parents="445 939"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,443,a(flip),b,886,a),flip(a)].">
      <j1 rule="hyper" parents="319 443 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),891(a,1,2,1))].">
      <j1 rule="para" parents="8 891"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(697,a,892,a),flip(a)].">
      <j1 rule="hyper" parents="697 892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(694,a,892,a)].">
      <j1 rule="hyper" parents="694 892"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),892(a,2,1,1))].">
      <j1 rule="para" parents="7 892"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(111(a,1),892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(694,a,946,a)].">
      <j1 rule="hyper" parents="694 946"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,446,a(flip),b,946,a)].">
      <j1 rule="hyper" parents="64 446 946"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(417,a,946,a(flip),b,446,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="417 946 446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,946,a(flip),b,446,a(flip))].">
      <j1 rule="hyper" parents="128 946 446"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      (1 / x) \ (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,946,a(flip),b,446,a(flip))].">
      <j1 rule="hyper" parents="127 946 446"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(946(a,1),694(a,1))].">
      <j1 rule="para" parents="946 694"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(570,a,949,a),flip(a)].">
      <j1 rule="hyper" parents="570 949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,313,a(flip),b,949,a),flip(a)].">
      <j1 rule="hyper" parents="64 313 949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(949(a,1),570(a,1))].">
      <j1 rule="para" parents="949 570"/>
    </justification>
  </clause>

  <clause id="957">
    <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(949(a,1),617(a,1,2))].">
      <j1 rule="para" parents="949 617"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x
    ]]></literal>
    <justification jstring="[para(110(a,1),955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,407,a,b,905,a)].">
      <j1 rule="hyper" parents="319 407 905"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,407,a,b,905,a),flip(a)].">
      <j1 rule="hyper" parents="127 407 905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) \ z) = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(600,a,916,a),flip(a)].">
      <j1 rule="hyper" parents="600 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,919,a(flip),b,816,a)].">
      <j1 rule="hyper" parents="131 919 816"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (((x / y) \ 1) \ (x / y)) * (y * z) = (((x / y) \ 1) \ x) * z
    ]]></literal>
    <justification jstring="[para(81(a,1),919(a,1,2,1))].">
      <j1 rule="para" parents="81 919"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),932(a,1,2,1))].">
      <j1 rule="para" parents="12 932"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(933(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="933 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,936,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="128 936 443"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(945(a,1),291(a,1))].">
      <j1 rule="para" parents="945 291"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),947(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) / u = z
    ]]></literal>
    <justification jstring="[para(960(a,2),327(a,1,2))].">
      <j1 rule="para" parents="960 327"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ K(y,x) = z
    ]]></literal>
    <justification jstring="[para(960(a,2),737(a,1))].">
      <j1 rule="para" parents="960 737"/>
    </justification>
  </clause>

  <clause id="973">
    <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(960(a,1),954(a,1,1))].">
      <j1 rule="para" parents="960 954"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      (x * x) \ (y \ ((x * x) * z)) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[hyper(134,a,961,a)].">
      <j1 rule="hyper" parents="134 961"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      L(x \ (((1 / x) \ y) * z),x,x) = ((1 / x) \ 1) * ((((1 / x) \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,466,a,b,962,a)].">
      <j1 rule="hyper" parents="319 466 962"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      (x * x) \ ((y \ ((x * x) * z)) / u) = (T(y,x * x) \ z) / u
    ]]></literal>
    <justification jstring="[para(974(a,1),720(a,1,1)),flip(a)].">
      <j1 rule="para" parents="974 720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(106(a,1),430(a,1,1,1))].">
      <j1 rule="para" parents="106 430"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,432,a(flip),b,646,a)].">
      <j1 rule="hyper" parents="127 432 646"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(303(a,1),432(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="303 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (x * z),u,w) = x * (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(96(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="96 435"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(302(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="302 435"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(611(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="611 435"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(224(a,1),436(a,1,2,1))].">
      <j1 rule="para" parents="224 436"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(302(a,1),436(a,1,2,1))].">
      <j1 rule="para" parents="302 436"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z))
    ]]></literal>
    <justification jstring="[para(565(a,1),490(a,1,2))].">
      <j1 rule="para" parents="565 490"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,T(x,y)),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(937(a,1),550(a,1,1,1))].">
      <j1 rule="para" parents="937 550"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) != (x \ 1) * w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(554(a,2),44(a,1))].">
      <j1 rule="para" parents="554 44"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(503(a,1),554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="503 554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(1 \ x,y,z)
    ]]></literal>
    <justification jstring="[para(371(a,1),555(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="371 555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(503(a,1),555(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="503 555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(370(a,1),559(a,1,2,1))].">
      <j1 rule="para" parents="370 559"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(502(a,1),559(a,1,2,1))].">
      <j1 rule="para" parents="502 559"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(602(a,1),559(a,1,2,1))].">
      <j1 rule="para" parents="602 559"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(538(a,1),561(a,1,1,1))].">
      <j1 rule="para" parents="538 561"/>
    </justification>
  </clause>

  <clause id="995">
    <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(384(a,2),564(a,1,1,1))].">
      <j1 rule="para" parents="384 564"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(786(a,1),564(a,1,1,1))].">
      <j1 rule="para" parents="786 564"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      K(x \ 1,x) * R(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(566(a,1),490(a,1,2))].">
      <j1 rule="para" parents="566 490"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(567(a,1),300(a,1,2))].">
      <j1 rule="para" parents="567 300"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(567(a,1),490(a,1,2))].">
      <j1 rule="para" parents="567 490"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      x \ (y * (((y \ x) \ z) * (y \ x))) = T(x \ (y * z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,716,a(flip),b,747,a)].">
      <j1 rule="hyper" parents="64 716 747"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(747(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="747 481"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,758,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="130 758 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,27,a,b,778,a),flip(a)].">
      <j1 rule="hyper" parents="319 27 778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(131,a,821,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 821 18"/>
    </justification>
  </clause>

  <clause id="1005">
    <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(447(a,1),845(a,1,1,1))].">
      <j1 rule="para" parents="447 845"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),926(a,2,1,2))].">
      <j1 rule="para" parents="7 926"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ ((x * (y \ 1)) * y) = u
    ]]></literal>
    <justification jstring="[para(263(a,2),572(a,1,2))].">
      <j1 rule="para" parents="263 572"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(389,a,764,a),flip(a)].">
      <j1 rule="hyper" parents="389 764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(241(a,1),1008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="241 1008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(600,a,1009,a)].">
      <j1 rule="hyper" parents="600 1009"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(584,a,1009,a),flip(a)].">
      <j1 rule="hyper" parents="584 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(578,a,1009,a)].">
      <j1 rule="hyper" parents="578 1009"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(331,a,1009,a),flip(a)].">
      <j1 rule="hyper" parents="331 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(319,a,153,a(flip),b,1009,a),flip(a)].">
      <j1 rule="hyper" parents="319 153 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      (x * y) / (x * (T(x,z) \ y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,153,a(flip),b,1009,a)].">
      <j1 rule="hyper" parents="128 153 1009"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,1009,a)].">
      <j1 rule="hyper" parents="127 153 1009"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,74,a(flip),b,1009,a),flip(a)].">
      <j1 rule="hyper" parents="127 74 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,1009,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1009(a,2),44(a,1))].">
      <j1 rule="para" parents="1009 44"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),1009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,1018,a)].">
      <j1 rule="hyper" parents="142 1018"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,1018,a)].">
      <j1 rule="hyper" parents="134 1018"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1018,a(flip),b,412,a),flip(a)].">
      <j1 rule="hyper" parents="131 1018 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1018(a,1),336(a,1,1,1))].">
      <j1 rule="para" parents="1018 336"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = z
    ]]></literal>
    <justification jstring="[para(1022(a,1),393(a,1,1))].">
      <j1 rule="para" parents="1022 393"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1022(a,1),966(a,2,1))].">
      <j1 rule="para" parents="1022 966"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1023(a,1),837(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1023 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x \ y) \ (x \ (T(x,z) * y)) = T(T(x,z),x \ y)
    ]]></literal>
    <justification jstring="[hyper(417,a,1010,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="417 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1012(a,1),135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1012 135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(244,a,109,a,b,1014,a),flip(a)].">
      <j1 rule="hyper" parents="244 109 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1014(a,1),330(a,1,2))].">
      <j1 rule="para" parents="1014 330"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (T(x,y) \ z)) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(1015(a,1),393(a,1,1))].">
      <j1 rule="para" parents="1015 393"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1017,a),flip(a)].">
      <j1 rule="hyper" parents="134 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1035(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1035 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1035(a,2),388(a,1,2))].">
      <j1 rule="para" parents="1035 388"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,437,a,b,1011,a),flip(a)].">
      <j1 rule="hyper" parents="35 437 1011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,1027,a)].">
      <j1 rule="hyper" parents="144 1027"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ x) = z
    ]]></literal>
    <justification jstring="[para(240(a,1),1032(a,1))].">
      <j1 rule="para" parents="240 1032"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),1036(a,1,2,2))].">
      <j1 rule="para" parents="9 1036"/>
    </justification>
  </clause>

  <clause id="1045">
    <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(96(a,1),793(a,1,2,1))].">
      <j1 rule="para" parents="96 793"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(244,a,701,a(flip),b,841,a(flip))].">
      <j1 rule="hyper" parents="244 701 841"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,(z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(410,a,1047,a)].">
      <j1 rule="hyper" parents="410 1047"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      T(x,(((y * y) \ y) * ((y * y) \ y)) * z) = T(T(x,z),L(y \ ((y * y) \ y),y,y))
    ]]></literal>
    <justification jstring="[para(471(a,1),1048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="471 1048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),876(a,1,2,1))].">
      <j1 rule="para" parents="8 876"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) = a(1 / x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(771,a,1050,a),flip(a)].">
      <j1 rule="hyper" parents="771 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,671,a,b,1050,a)].">
      <j1 rule="hyper" parents="131 671 1050"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(383(a,1),1050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="383 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1050(a,1),771(a,1))].">
      <j1 rule="para" parents="1050 771"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(417,a,225,a(flip),b,1053,a),flip(a)].">
      <j1 rule="hyper" parents="417 225 1053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(348(a,1),888(a,1,2))].">
      <j1 rule="para" parents="348 888"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(694,a,889,a),flip(a)].">
      <j1 rule="hyper" parents="694 889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(457,a,893,a)].">
      <j1 rule="hyper" parents="457 893"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,1059,a,b,443,a)].">
      <j1 rule="hyper" parents="128 1059 443"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(443(a,1),912(a,2,1))].">
      <j1 rule="para" parents="443 912"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),978(a,2,2))].">
      <j1 rule="para" parents="27 978"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),988(a,2,2,1))].">
      <j1 rule="para" parents="8 988"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      x \ L(x * (y \ z),x \ 1,y) = (x \ 1) * ((y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(302(a,1),988(a,1,2)),flip(a)].">
      <j1 rule="para" parents="302 988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,652,a(flip),b,1063,a)].">
      <j1 rule="hyper" parents="64 652 1063"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,1063,a(flip),b,652,a(flip))].">
      <j1 rule="hyper" parents="127 1063 652"/>
    </justification>
  </clause>

  <clause id="1067">
    <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(1065(a,1),671(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1065 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1065(a,1),931(a,1,2,1,2))].">
      <j1 rule="para" parents="1065 931"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ L((y \ x) \ 1,y \ x,y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(371(a,1),1066(a,1,1))].">
      <j1 rule="para" parents="371 1066"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(66(a,1),989(a,2,2,1))].">
      <j1 rule="para" parents="66 989"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,658,a(flip),b,1070,a)].">
      <j1 rule="hyper" parents="64 658 1070"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,1071,a(flip),b,196,a)].">
      <j1 rule="hyper" parents="130 1071 196"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,1071,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="128 1071 243"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1071(a,1),671(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1071 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <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),990(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,242,a(flip),b,993,a)].">
      <j1 rule="hyper" parents="131 242 993"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,224,a(flip),b,1077,a)].">
      <j1 rule="hyper" parents="319 224 1077"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(127,a,371,a(flip),b,1077,a),flip(a)].">
      <j1 rule="hyper" parents="127 371 1077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(224(a,1),1078(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 1078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1080(a,1),992(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1080 992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,650,a(flip),b,994,a),flip(a)].">
      <j1 rule="hyper" parents="319 650 994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),1021(a,1,2,1))].">
      <j1 rule="para" parents="111 1021"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(231(a,1),1021(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 1021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(600,a,1083,a)].">
      <j1 rule="hyper" parents="600 1083"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(386,a,1083,a),flip(a)].">
      <j1 rule="hyper" parents="386 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,80,a(flip),b,1083,a),flip(a)].">
      <j1 rule="hyper" parents="319 80 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ 1) = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,1083,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(81(a,1),1087(a,1,2,1))].">
      <j1 rule="para" parents="81 1087"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(263(a,2),1087(a,1,2))].">
      <j1 rule="para" parents="263 1087"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,958,a(flip),b,1086,a)].">
      <j1 rule="hyper" parents="64 958 1086"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (x / y) \ (y \ x) != (y \ x) * z
    ]]></literal>
    <literal><![CDATA[
      (x / y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1088(a,1),44(a,1))].">
      <j1 rule="para" parents="1088 44"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,81,a(flip),b,1089,a),flip(a)].">
      <j1 rule="hyper" parents="319 81 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(265(a,2),1093(a,1,2))].">
      <j1 rule="para" parents="265 1093"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(443(a,1),1058(a,1,1))].">
      <j1 rule="para" parents="443 1058"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(81(a,1),1082(a,1,1,1,2))].">
      <j1 rule="para" parents="81 1082"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1096(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1096 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(348(a,1),1096(a,1,1))].">
      <j1 rule="para" parents="348 1096"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(935(a,1),1096(a,1,1))].">
      <j1 rule="para" parents="935 1096"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      ((x * x) * ((y * z) * u)) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),121(a,1,1))].">
      <j1 rule="para" parents="33 121"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(907,a,595,a),flip(a)].">
      <j1 rule="hyper" parents="907 595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,595,a(flip),b,746,a(flip))].">
      <j1 rule="hyper" parents="127 595 746"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,948,a(flip),b,1102,a),flip(a)].">
      <j1 rule="hyper" parents="319 948 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,935,a(flip),b,1102,a),flip(a)].">
      <j1 rule="hyper" parents="319 935 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(130,a,1102,a,b,948,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 1102 948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,1102,a,b,443,a)].">
      <j1 rule="hyper" parents="128 1102 443"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(396(a,1),1102(a,1,1))].">
      <j1 rule="para" parents="396 1102"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(950(a,1),1102(a,1,1))].">
      <j1 rule="para" parents="950 1102"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1102(a,2),1011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1102 1011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y / x),y) = z
    ]]></literal>
    <justification jstring="[para(1103(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1103 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(231(a,1),1106(a,2,2))].">
      <j1 rule="para" parents="231 1106"/>
    </justification>
  </clause>

  <clause id="1115">
    <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(1114(a,2),404(a,1,2))].">
      <j1 rule="para" parents="1114 404"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      K((x / y) \ ((x / y) / (T(x / (x / y),z) \ 1)),x / y) = (((x / y) * T(y,z)) / (x / y)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(454(a,1),1114(a,1,1,2,2,1))].">
      <j1 rule="para" parents="454 1114"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,436,a(flip),b,660,a)].">
      <j1 rule="hyper" parents="64 436 660"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(243(a,1),1117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="243 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(600,a,1118,a)].">
      <j1 rule="hyper" parents="600 1118"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(584,a,1118,a),flip(a)].">
      <j1 rule="hyper" parents="584 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(578,a,1118,a)].">
      <j1 rule="hyper" parents="578 1118"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(134,a,1118,a)].">
      <j1 rule="hyper" parents="134 1118"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,1118,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1124">
    <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(417,a,153,a(flip),b,1118,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="417 153 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(292,a,1123,a)].">
      <j1 rule="hyper" parents="292 1123"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1123,a(flip),b,412,a),flip(a)].">
      <j1 rule="hyper" parents="131 1123 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <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(1123(a,1),931(a,1,2,1,2))].">
      <j1 rule="para" parents="1123 931"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),1119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(354(a,1),1119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="354 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1121(a,1),333(a,1,1))].">
      <j1 rule="para" parents="1121 333"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(142,a,1128,a),flip(a)].">
      <j1 rule="hyper" parents="142 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(244,a,105,a(flip),b,1120,a),flip(a)].">
      <j1 rule="hyper" parents="244 105 1120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1132,a)].">
      <j1 rule="hyper" parents="134 1132"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(722(a,1),1129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="722 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(382(a,1),723(a,1,1,1))].">
      <j1 rule="para" parents="382 723"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,748,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="131 748 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(748(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="748 481"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(749(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="749 481"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,759,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="130 759 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,432,a(flip),b,781,a),flip(a)].">
      <j1 rule="hyper" parents="64 432 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,430,a(flip),b,782,a),flip(a)].">
      <j1 rule="hyper" parents="64 430 782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(822(a,2),47(a,1))].">
      <j1 rule="para" parents="822 47"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(96(a,1),844(a,1,2,1,2))].">
      <j1 rule="para" parents="96 844"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(302(a,1),844(a,1,2,1,2))].">
      <j1 rule="para" parents="302 844"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,846,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="131 846 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(127,a,847,a(flip),b,264,a)].">
      <j1 rule="hyper" parents="127 847 264"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(225(a,1),849(a,1,1,1,2))].">
      <j1 rule="para" parents="225 849"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,852,a(flip),b,267,a),flip(a)].">
      <j1 rule="hyper" parents="128 852 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,880,a(flip),b,236,a)].">
      <j1 rule="hyper" parents="131 880 236"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(946(a,1),898(a,1))].">
      <j1 rule="para" parents="946 898"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,738,a(flip),b,900,a),flip(a)].">
      <j1 rule="hyper" parents="319 738 900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(199,a,1152,a)].">
      <j1 rule="hyper" parents="199 1152"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1010(a,1),910(a,1,1,1))].">
      <j1 rule="para" parents="1010 910"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      ((x * x) * ((y * z) * T(u,z))) / (u * z) = R((x * x) * y,z,T(u,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),1101(a,1,2))].">
      <j1 rule="para" parents="109 1101"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(693(a,2),44(a,1))].">
      <j1 rule="para" parents="693 44"/>
    </justification>
  </clause>

  <clause id="1159">
    <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(96(a,1),794(a,1,2,1))].">
      <j1 rule="para" parents="96 794"/>
    </justification>
  </clause>

  <clause id="1161">
    <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(868(a,1),1065(a,1,1)),flip(a)].">
      <j1 rule="para" parents="868 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,443,a(flip),b,873,a),flip(a)].">
      <j1 rule="hyper" parents="319 443 873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(390,a,982,a),flip(a)].">
      <j1 rule="hyper" parents="390 982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(242(a,1),1163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="242 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(600,a,1164,a)].">
      <j1 rule="hyper" parents="600 1164"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(331,a,1164,a),flip(a)].">
      <j1 rule="hyper" parents="331 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(134,a,1164,a)].">
      <j1 rule="hyper" parents="134 1164"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,1164,a)].">
      <j1 rule="hyper" parents="127 153 1164"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,1164,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ (L(x,y,z) * u) = T(x,L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(417,a,153,a(flip),b,1164,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="417 153 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      ((x * y) * L(x,z,u)) \ (x * (L(x,z,u) * y)) = K(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(127,a,1164,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="127 1164 88"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * (L(x,y,z) * u)) = L(T(x,u),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1164(a,1),237(a,1,2))].">
      <j1 rule="para" parents="1164 237"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,1169,a)].">
      <j1 rule="hyper" parents="134 1169"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1169,a(flip),b,412,a),flip(a)].">
      <j1 rule="hyper" parents="131 1169 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1169(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1169 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      T((1 / x) * (L(x,y,z) \ x),x) = (1 / x) * ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1173(a,1),837(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1173 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1177">
    <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(569,a,983,a)].">
      <j1 rule="hyper" parents="569 983"/>
    </justification>
  </clause>

  <clause id="1178">
    <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(94(a,1),983(a,1,1))].">
      <j1 rule="para" parents="94 983"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((((x * y) \ (x * (y * z))) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(14(a,2),1000(a,2,1))].">
      <j1 rule="para" parents="14 1000"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1001(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,1059,a,b,1180,a)].">
      <j1 rule="hyper" parents="64 1059 1180"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1102,a,b,1180,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 1102 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,348,a(flip),b,1180,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 348 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,945,a(flip),b,1184,a)].">
      <j1 rule="hyper" parents="64 945 1184"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,936,a(flip),b,1184,a),flip(a)].">
      <j1 rule="hyper" parents="64 936 1184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <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),1184(a,2,2,1,2,2))].">
      <j1 rule="para" parents="16 1184"/>
    </justification>
  </clause>

  <clause id="1189">
    <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),1184(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 1184"/>
    </justification>
  </clause>

  <clause id="1190">
    <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),1185(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1186(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,443,a(flip),b,1002,a),flip(a)].">
      <j1 rule="hyper" parents="319 443 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1068(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),1193(a,2,2))].">
      <j1 rule="para" parents="25 1193"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),1195(a,1,1))].">
      <j1 rule="para" parents="25 1195"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(600,a,1197,a)].">
      <j1 rule="hyper" parents="600 1197"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(386,a,1197,a),flip(a)].">
      <j1 rule="hyper" parents="386 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(331,a,1197,a),flip(a)].">
      <j1 rule="hyper" parents="331 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,1197,a)].">
      <j1 rule="hyper" parents="127 153 1197"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,1197,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,923,a,b,1199,a)].">
      <j1 rule="hyper" parents="64 923 1199"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      x \ (((y * x) / y) \ x) = ((y * x) / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,1202,a)].">
      <j1 rule="hyper" parents="134 1202"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      (((x / y) * T(y,z)) / (x / y)) \ T(y,z) = T(y,z) * (T(x / (x / y),z) \ 1)
    ]]></literal>
    <justification jstring="[para(454(a,1),1202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="454 1202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(741,a,1198,a),flip(a)].">
      <j1 rule="hyper" parents="741 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(244,a,12,a(flip),b,1200,a)].">
      <j1 rule="hyper" parents="244 12 1200"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,1207,a,b,154,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 1207 154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,1207,a,b,xx)].">
      <j1 rule="hyper" parents="128 1207"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[para(381(a,1),1207(a,2,2)),flip(a)].">
      <j1 rule="para" parents="381 1207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(402(a,1),1207(a,2,2)),flip(a)].">
      <j1 rule="para" parents="402 1207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(1210(a,2),231(a,1,1))].">
      <j1 rule="para" parents="1210 231"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(81(a,1),1213(a,1,1,2))].">
      <j1 rule="para" parents="81 1213"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(411(a,1),1213(a,1,1,2))].">
      <j1 rule="para" parents="411 1213"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1214(a,1),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1214 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,1216,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(279,a,1217,a),flip(a)].">
      <j1 rule="hyper" parents="279 1217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),1217(a,1,1,2,2))].">
      <j1 rule="para" parents="78 1217"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1218,a)].">
      <j1 rule="hyper" parents="145 1218"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(131,a,829,a,b,1218,a)].">
      <j1 rule="hyper" parents="131 829 1218"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1218(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1218 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1218(a,1),388(a,1,2))].">
      <j1 rule="para" parents="1218 388"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(81(a,1),1220(a,1,2,1,2))].">
      <j1 rule="para" parents="81 1220"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1209(a,1),858(a,1,1))].">
      <j1 rule="para" parents="1209 858"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(393,a,1225,a)].">
      <j1 rule="hyper" parents="393 1225"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(1226(a,1),501(a,1,1))].">
      <j1 rule="para" parents="1226 501"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      R(z,y,T(z,y)) = x
    ]]></literal>
    <justification jstring="[para(1227(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1227 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(232(a,1),1224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(835(a,2),1222(a,1))].">
      <j1 rule="para" parents="835 1222"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(300,a,1221,a)].">
      <j1 rule="hyper" parents="300 1221"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(1221(a,1),300(a,1))].">
      <j1 rule="para" parents="1221 300"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(826,a,1136,a),flip(a)].">
      <j1 rule="hyper" parents="826 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(1230,a,1149,a),flip(a)].">
      <j1 rule="hyper" parents="1230 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(921,a,1149,a)].">
      <j1 rule="hyper" parents="921 1149"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1234(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1162(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),1162(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 1162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(443(a,1),1162(a,1,1))].">
      <j1 rule="para" parents="443 1162"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,875,a(flip),b,1238,a)].">
      <j1 rule="hyper" parents="64 875 1238"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,874,a(flip),b,1238,a),flip(a)].">
      <j1 rule="hyper" parents="64 874 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,733,a(flip),b,1238,a),flip(a)].">
      <j1 rule="hyper" parents="64 733 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(78(a,1),1242(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 1242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(945(a,1),1240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="945 1240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1099(a,2),1240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1099 1240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(232(a,1),1241(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(244,a,1246,a(flip),b,229,a(flip))].">
      <j1 rule="hyper" parents="244 1246 229"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,1247,a,b,xx)].">
      <j1 rule="hyper" parents="128 1247"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1247(a,2),77(a,1,2,1))].">
      <j1 rule="para" parents="1247 77"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),1248(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 1248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      x * (T(y * x,x) / x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1249(a,1,2,1,1,1))].">
      <j1 rule="para" parents="9 1249"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),1249(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(820(a,2),1250(a,1,2,1,2))].">
      <j1 rule="para" parents="820 1250"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(944(a,1),1251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="944 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),1245(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(628,a,1255,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="628 1255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(1255(a,2),628(a,1))].">
      <j1 rule="para" parents="1255 628"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1256(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (x * (K(x \ 1,x) * y)) = L(T(x,y),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1259(a,1),237(a,1,2))].">
      <j1 rule="para" parents="1259 237"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(127,a,1191,a(flip),b,1184,a),flip(a)].">
      <j1 rule="hyper" parents="127 1191 1184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(443(a,1),1192(a,1,1))].">
      <j1 rule="para" parents="443 1192"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,849,a(flip),b,1211,a)].">
      <j1 rule="hyper" parents="64 849 1211"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[para(835(a,1),1264(a,1,1))].">
      <j1 rule="para" parents="835 1264"/>
    </justification>
  </clause>

  <clause id="1266">
    <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(1018(a,1),1265(a,1,1,2,1))].">
      <j1 rule="para" parents="1018 1265"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(650(a,1),1233(a,1,1))].">
      <j1 rule="para" parents="650 1233"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1235(a,2,1,1,2))].">
      <j1 rule="para" parents="7 1235"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),1268(a,1,2,1,2))].">
      <j1 rule="para" parents="81 1268"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(443(a,1),1237(a,2,1))].">
      <j1 rule="para" parents="443 1237"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(444(a,1),1270(a,1,1))].">
      <j1 rule="para" parents="444 1270"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(630,a,1272,a)].">
      <j1 rule="hyper" parents="630 1272"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(577,a,1272,a),flip(a)].">
      <j1 rule="hyper" parents="577 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      (x * T(T(y,x),z)) * T(y,x) = (y * x) * T(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,230,a(flip),b,1272,a),flip(a)].">
      <j1 rule="hyper" parents="319 230 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,151,a(flip),b,1272,a),flip(a)].">
      <j1 rule="hyper" parents="319 151 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(244,a,1272,a,b,109,a(flip))].">
      <j1 rule="hyper" parents="244 1272 109"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1272,a)].">
      <j1 rule="hyper" parents="134 1272"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,151,a(flip),b,1272,a)].">
      <j1 rule="hyper" parents="128 151 1272"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,109,a(flip),b,1272,a)].">
      <j1 rule="hyper" parents="128 109 1272"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,84,a(flip),b,1272,a),flip(a)].">
      <j1 rule="hyper" parents="128 84 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(111(a,1),1272(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,1274,a)].">
      <j1 rule="hyper" parents="134 1274"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (1 / T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1283(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1283 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1283(a,1),969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1283 969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1283(a,1),1262(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1283 1262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(130,a,1229,a,b,1273,a)].">
      <j1 rule="hyper" parents="130 1229 1273"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1273(a,2),245(a,2)),flip(a)].">
      <j1 rule="para" parents="1273 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      T((x / y) * T(y,x),y) = x
    ]]></literal>
    <justification jstring="[hyper(244,a,1276,a,b,109,a(flip))].">
      <j1 rule="hyper" parents="244 1276 109"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,109,a(flip),b,1276,a),flip(a)].">
      <j1 rule="hyper" parents="128 109 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      T(x * T(x \ y,y),x \ y) = y
    ]]></literal>
    <justification jstring="[para(78(a,1),1289(a,1,1,1))].">
      <j1 rule="para" parents="78 1289"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      T(x * T(T(y,x),y * x),T(y,x)) = y * x
    ]]></literal>
    <justification jstring="[para(198(a,1),1289(a,1,1,1))].">
      <j1 rule="para" parents="198 1289"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(570,a,1290,a),flip(a)].">
      <j1 rule="hyper" parents="570 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(142,a,1290,a)].">
      <j1 rule="hyper" parents="142 1290"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,232,a(flip),b,1290,a)].">
      <j1 rule="hyper" parents="127 232 1290"/>
    </justification>
  </clause>

  <clause id="1296">
    <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(375(a,1),1290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="375 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y)
    ]]></literal>
    <justification jstring="[para(398(a,1),1290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="398 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1278(a,1),1003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1278 1003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1299(a,1,1,2))].">
      <j1 rule="para" parents="109 1299"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(207,a,1286,a)].">
      <j1 rule="hyper" parents="207 1286"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1287(a,1),1011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1287 1011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[para(241(a,1),1292(a,1,1))].">
      <j1 rule="para" parents="241 1292"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,12,a(flip),b,1304,a),flip(a)].">
      <j1 rule="hyper" parents="319 12 1304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1303,a),flip(a)].">
      <j1 rule="hyper" parents="142 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1229,a(flip),b,1306,a),flip(a)].">
      <j1 rule="hyper" parents="64 1229 1306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(804,a,1307,a)].">
      <j1 rule="hyper" parents="804 1307"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      (x / T(y,x)) * y != z
    ]]></literal>
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = z
    ]]></literal>
    <justification jstring="[para(1308(a,1),601(a,1))].">
      <j1 rule="para" parents="1308 601"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1234(a,1),1308(a,1,1))].">
      <j1 rule="para" parents="1234 1308"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(241(a,1),1275(a,1,1))].">
      <j1 rule="para" parents="241 1275"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,71,a(flip),b,1311,a)].">
      <j1 rule="hyper" parents="128 71 1311"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(111(a,1),1282(a,1,2))].">
      <j1 rule="para" parents="111 1282"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(231(a,1),1282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 1282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(630,a,1313,a)].">
      <j1 rule="hyper" parents="630 1313"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(577,a,1313,a),flip(a)].">
      <j1 rule="hyper" parents="577 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      (x * (1 / x)) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(319,a,71,a(flip),b,1313,a),flip(a)].">
      <j1 rule="hyper" parents="319 71 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,1316,a),flip(a)].">
      <j1 rule="hyper" parents="417 1316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,937,a(flip),b,1312,a),flip(a)].">
      <j1 rule="hyper" parents="319 937 1312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1318(a,1),1105(a,1,1))].">
      <j1 rule="para" parents="1318 1105"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(319,a,875,a(flip),b,1239,a),flip(a)].">
      <j1 rule="hyper" parents="319 875 1239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),1239(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1239(a,1),569(a,1))].">
      <j1 rule="para" parents="1239 569"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,875,a(flip),b,1322,a)].">
      <j1 rule="hyper" parents="64 875 1322"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(244,a,733,a(flip),b,1322,a(flip))].">
      <j1 rule="hyper" parents="244 733 1322"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(109(a,1),1325(a,1,2))].">
      <j1 rule="para" parents="109 1325"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      T(x,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(348(a,1),1325(a,1,2))].">
      <j1 rule="para" parents="348 1325"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1325(a,1),783(a,1,1))].">
      <j1 rule="para" parents="1325 783"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(445(a,1),1325(a,1,2))].">
      <j1 rule="para" parents="445 1325"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(935(a,1),1325(a,1,2))].">
      <j1 rule="para" parents="935 1325"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(948(a,1),1325(a,1,2))].">
      <j1 rule="para" parents="948 1325"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1326(a,1),780(a,1,1))].">
      <j1 rule="para" parents="1326 780"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1332(a,1),402(a,1,1))].">
      <j1 rule="para" parents="1332 402"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,1330,a)].">
      <j1 rule="hyper" parents="55 1330"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1331(a,1),453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1331 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      T(x,x \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,263,a,b,1333,a)].">
      <j1 rule="hyper" parents="131 263 1333"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(244,a,1333,a(flip),b,1018,a),flip(a)].">
      <j1 rule="hyper" parents="244 1333 1018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1329(a,1),780(a,1,1))].">
      <j1 rule="para" parents="1329 780"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1334(a,1),752(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1334 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,751,a,b,1340,a)].">
      <j1 rule="hyper" parents="319 751 1340"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),1341(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(55,a,1342,a)].">
      <j1 rule="hyper" parents="55 1342"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1342,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 1342 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      x * T(x \ 1,K(x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,1343,a,b,xx)].">
      <j1 rule="hyper" parents="131 1343"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,1345,a(flip),b,443,a),flip(a)].">
      <j1 rule="hyper" parents="128 1345 443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1346(a,1),758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1346 758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(319,a,383,a(flip),b,1347,a),flip(a)].">
      <j1 rule="hyper" parents="319 383 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1348(a,1,1,1))].">
      <j1 rule="para" parents="7 1348"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1349(a,1),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1349 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,1350,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(905(a,1),1243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="905 1243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(89(a,1),1352(a,2,2))].">
      <j1 rule="para" parents="89 1352"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1353(a,1,1,1))].">
      <j1 rule="para" parents="9 1353"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1354(a,2,2,1))].">
      <j1 rule="para" parents="9 1354"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,304,a,b,1355,a)].">
      <j1 rule="hyper" parents="35 304 1355"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,875,a(flip),b,1263,a)].">
      <j1 rule="hyper" parents="128 875 1263"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,109,a(flip),b,1263,a),flip(a)].">
      <j1 rule="hyper" parents="128 109 1263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1263(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1263"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,1360,a),flip(a)].">
      <j1 rule="hyper" parents="142 1360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(1112,a,1361,a)].">
      <j1 rule="hyper" parents="1112 1361"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,1059,a,b,1361,a)].">
      <j1 rule="hyper" parents="64 1059 1361"/>
    </justification>
  </clause>

  <clause id="1364">
    <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),1362(a,1,1,2,2))].">
      <j1 rule="para" parents="20 1362"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,875,a(flip),b,1271,a)].">
      <j1 rule="hyper" parents="64 875 1271"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,733,a(flip),b,1271,a),flip(a)].">
      <j1 rule="hyper" parents="64 733 1271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,1271,a(flip),b,875,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="244 1271 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1367(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(762,a,1368,a)].">
      <j1 rule="hyper" parents="762 1368"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1369(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1250(a,1),1370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1250 1370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1371,a),flip(a)].">
      <j1 rule="hyper" parents="145 1371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(210(a,1),1372(a,2,2,1,1))].">
      <j1 rule="para" parents="210 1372"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1314(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(630,a,1374,a)].">
      <j1 rule="hyper" parents="630 1374"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(577,a,1374,a),flip(a)].">
      <j1 rule="hyper" parents="577 1374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1224(a,1),1374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1224 1374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      (x / ((y * x) / y)) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,1376,a)].">
      <j1 rule="hyper" parents="142 1376"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(324,a,1378,a),flip(a)].">
      <j1 rule="hyper" parents="324 1378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1030,a,1380,a)].">
      <j1 rule="hyper" parents="1030 1380"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / (x / y)) = z
    ]]></literal>
    <justification jstring="[para(1381(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1381 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(1383,a,1236,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1383 1236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1384(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(78(a,1),1321(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1321(a,1),569(a,1))].">
      <j1 rule="para" parents="1321 569"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(885(a,1),1321(a,1,1)),flip(a)].">
      <j1 rule="para" parents="885 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1057(a,2),1321(a,1,1))].">
      <j1 rule="para" parents="1057 1321"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1254,a,b,1365,a)].">
      <j1 rule="hyper" parents="64 1254 1365"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(68(a,1),1389(a,2,2,2,1,2))].">
      <j1 rule="para" parents="68 1389"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,229,a(flip),b,1391,a),flip(a)].">
      <j1 rule="hyper" parents="319 229 1391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(348(a,1),1391(a,2,2))].">
      <j1 rule="para" parents="348 1391"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,105,a(flip),b,1392,a),flip(a)].">
      <j1 rule="hyper" parents="36 105 1392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(818(a,1),1394(a,1,1,1))].">
      <j1 rule="para" parents="818 1394"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,848,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="131 848 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(848(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="848 481"/>
    </justification>
  </clause>

  <clause id="1399">
    <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(508(a,1),857(a,1,2,1))].">
      <j1 rule="para" parents="508 857"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(371(a,1),1079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="371 1079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,1400,a)].">
      <j1 rule="hyper" parents="145 1400"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,1401,a)].">
      <j1 rule="hyper" parents="417 1401"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(447(a,1),1328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="447 1328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(447(a,1),1403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="447 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(T(1 / x,y),x) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(1404(a,1),1132(a,1,1))].">
      <j1 rule="para" parents="1404 1132"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / (y \ 1))) * x) * (y \ 1) = u
    ]]></literal>
    <justification jstring="[para(885(a,1),1387(a,1,2))].">
      <j1 rule="para" parents="885 1387"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      L(x \ y,x,x) * L(z,y,(x * x) \ x) = L(x \ (y * z),x,x)
    ]]></literal>
    <justification jstring="[para(471(a,1),609(a,1,1))].">
      <j1 rule="para" parents="471 609"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      (1 / (x / y)) \ (y / x) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(896,a,1054,a),flip(a)].">
      <j1 rule="hyper" parents="896 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = (1 / ((y \ x) / x)) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),1408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 1408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      (1 / ((x \ y) / y)) * (x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,193,a(flip),b,1409,a(flip))].">
      <j1 rule="hyper" parents="131 193 1409"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = (x * ((x \ y) / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,1410,a)].">
      <j1 rule="hyper" parents="417 1410"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(833,a,977,a)].">
      <j1 rule="hyper" parents="833 977"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,650,a(flip),b,979,a),flip(a)].">
      <j1 rule="hyper" parents="319 650 979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1223,a,1004,a)].">
      <j1 rule="hyper" parents="1223 1004"/>
    </justification>
  </clause>

  <clause id="1415">
    <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(94(a,1),1004(a,1,1))].">
      <j1 rule="para" parents="94 1004"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1414(a,2),1265(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1414 1265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,243,a(flip),b,1076,a),flip(a)].">
      <j1 rule="hyper" parents="319 243 1076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <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(1018(a,1),1417(a,1,2,1,2))].">
      <j1 rule="para" parents="1018 1417"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),1097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="81 1097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1419(a,2,1,1))].">
      <j1 rule="para" parents="7 1419"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),1420(a,1,2,1))].">
      <j1 rule="para" parents="81 1420"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(142,a,1421,a)].">
      <j1 rule="hyper" parents="142 1421"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,193,a(flip),b,1421,a(flip))].">
      <j1 rule="hyper" parents="130 193 1421"/>
    </justification>
  </clause>

  <clause id="1424">
    <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(1421(a,1),96(a,2,1))].">
      <j1 rule="para" parents="1421 96"/>
    </justification>
  </clause>

  <clause id="1425">
    <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(1421(a,1),617(a,1,2))].">
      <j1 rule="para" parents="1421 617"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(224(a,1),1423(a,1,1,2))].">
      <j1 rule="para" parents="224 1423"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ L(x \ 1,x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,1426,a)].">
      <j1 rule="hyper" parents="134 1426"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1426(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1426 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ L((x \ y) \ 1,x \ y,x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1427(a,1,1,2,1))].">
      <j1 rule="para" parents="10 1427"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(371(a,1),1429(a,1,2))].">
      <j1 rule="para" parents="371 1429"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(207,a,1430,a)].">
      <j1 rule="hyper" parents="207 1430"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1138(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1139(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1434">
    <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),1433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1140(a,2,1,1,1))].">
      <j1 rule="para" parents="7 1140"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,656,a(flip),b,1435,a),flip(a)].">
      <j1 rule="hyper" parents="319 656 1435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(656(a,1),1436(a,1,1))].">
      <j1 rule="para" parents="656 1436"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,1437,a),flip(a)].">
      <j1 rule="hyper" parents="142 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),1438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1146,a)].">
      <j1 rule="hyper" parents="134 1146"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(331,a,1148,a)].">
      <j1 rule="hyper" parents="331 1148"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      ((x * ((y * z) / (R(u,y,z) * (y * z)))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),1148(a,1,2))].">
      <j1 rule="para" parents="105 1148"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1172,a),flip(a)].">
      <j1 rule="hyper" parents="335 1172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(854,a,1212,a)].">
      <j1 rule="hyper" parents="854 1212"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1199(a,1),1444(a,1,1))].">
      <j1 rule="para" parents="1199 1444"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(232(a,1),1445(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ 1 = x \ (((T(y,x) \ y) * x) \ x)
    ]]></literal>
    <justification jstring="[para(1446(a,1),1023(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1446 1023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(562(a,1),1215(a,1,1))].">
      <j1 rule="para" parents="562 1215"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1448(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1448 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1305(a,1),1449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1305 1449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(538(a,1),1450(a,2,2))].">
      <j1 rule="para" parents="538 1450"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),1451(a,1,1))].">
      <j1 rule="para" parents="12 1451"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(111(a,1),1452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(733(a,1),1366(a,1,1))].">
      <j1 rule="para" parents="733 1366"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(250(a,1),1405(a,1,2))].">
      <j1 rule="para" parents="250 1405"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,1373,a(flip),b,1455,a),flip(a)].">
      <j1 rule="hyper" parents="319 1373 1455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(656(a,1),1412(a,2,1))].">
      <j1 rule="para" parents="656 1412"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1413(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(650(a,1),1413(a,1,1))].">
      <j1 rule="para" parents="650 1413"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1440(a,1,2,2,1))].">
      <j1 rule="para" parents="10 1440"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,91,a(flip),b,1460,a)].">
      <j1 rule="hyper" parents="64 91 1460"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,1203,a(flip),b,1461,a),flip(a)].">
      <j1 rule="hyper" parents="319 1203 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(131,a,1461,a,b,1414,a)].">
      <j1 rule="hyper" parents="131 1461 1414"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      x * K(y,(y / (x \ 1)) / y) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1461,a,b,1203,a(flip))].">
      <j1 rule="hyper" parents="131 1461 1203"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(78(a,1),1461(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(951(a,1),1461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="951 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1467">
    <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(1302(a,1),1461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1302 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      ((x * y) / x) * ((y * (((x * y) / x) \ 1)) / y) = K(y,1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1379(a,1),1461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1379 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1422(a,1),1461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1422 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(1018(a,1),1462(a,2,2,1))].">
      <j1 rule="para" parents="1018 1462"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(445(a,2),1466(a,1,2,1))].">
      <j1 rule="para" parents="445 1466"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,984,a(flip),b,1457,a)].">
      <j1 rule="hyper" parents="64 984 1457"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,1457,a(flip),b,1137,a),flip(a)].">
      <j1 rule="hyper" parents="244 1457 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,1457,a(flip),b,984,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="244 1457 984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,1457,a(flip),b,1137,a),flip(a)].">
      <j1 rule="hyper" parents="127 1457 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1457(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1457"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = (R(x,y,z) * z) * R(L(T(y,z),z,R(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(727(a,1),1457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="727 1457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1478(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1478"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(577,a,1480,a),flip(a)].">
      <j1 rule="hyper" parents="577 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(324,a,1480,a),flip(a)].">
      <j1 rule="hyper" parents="324 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      ((1 / x) * R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,79,a(flip),b,1480,a),flip(a)].">
      <j1 rule="hyper" parents="319 79 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1480,a)].">
      <j1 rule="hyper" parents="134 1480"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,151,a(flip),b,1480,a)].">
      <j1 rule="hyper" parents="128 151 1480"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,79,a(flip),b,1480,a),flip(a)].">
      <j1 rule="hyper" parents="128 79 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1488">
    <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(1486(a,1),245(a,2)),flip(a)].">
      <j1 rule="para" parents="1486 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1482(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1482 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      T(R(x,y,R(x,z,u)),y * R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1484(a,1),778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1484 778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,543,a(flip),b,1491,a)].">
      <j1 rule="hyper" parents="64 543 1491"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1491(a,1),281(a,1,2))].">
      <j1 rule="para" parents="1491 281"/>
    </justification>
  </clause>

  <clause id="1498">
    <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),1475(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(762,a,1498,a)].">
      <j1 rule="hyper" parents="762 1498"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,1498,a,b,656,a)].">
      <j1 rule="hyper" parents="128 1498 656"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(210(a,1),1498(a,2,2,1,2))].">
      <j1 rule="para" parents="210 1498"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,1501,a)].">
      <j1 rule="hyper" parents="55 1501"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1501(a,1),1252(a,2,2,1))].">
      <j1 rule="para" parents="1501 1252"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(658(a,1),1502(a,1,2))].">
      <j1 rule="para" parents="658 1502"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1070(a,1),1502(a,1,2))].">
      <j1 rule="para" parents="1070 1502"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1507(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1507 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1506(a,1),780(a,1,1))].">
      <j1 rule="para" parents="1506 780"/>
    </justification>
  </clause>

  <clause id="1511">
    <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),1500(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,984,a(flip),b,1477,a)].">
      <j1 rule="hyper" parents="64 984 1477"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      (x * R(y / x,z,u)) * (x \ y) = y * R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,111,a(flip),b,1492,a)].">
      <j1 rule="hyper" parents="131 111 1492"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      R(1 / x,y,z) / (x \ 1) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,7,a(flip),b,1513,a)].">
      <j1 rule="hyper" parents="128 7 1513"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      (x / y) * R(1 / (x / y),x / y,y) = (y / x) / ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(383(a,1),1514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="383 1514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1512(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 1512"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      (x / y) / ((y / x) \ 1) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(383(a,1),1515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="383 1515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((x / y) \ 1) = y / x
    ]]></literal>
    <justification jstring="[hyper(144,a,1517,a)].">
      <j1 rule="hyper" parents="144 1517"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = ((y \ x) / x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),1517(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,193,a(flip),b,1519,a(flip))].">
      <j1 rule="hyper" parents="130 193 1519"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,382,a,b,1520,a),flip(a)].">
      <j1 rule="hyper" parents="319 382 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1458(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(650(a,1),1458(a,2,1))].">
      <j1 rule="para" parents="650 1458"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(651(a,1),1522(a,1,1))].">
      <j1 rule="para" parents="651 1522"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(630,a,1524,a)].">
      <j1 rule="hyper" parents="630 1524"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(577,a,1524,a),flip(a)].">
      <j1 rule="hyper" parents="577 1524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(573,a,1524,a)].">
      <j1 rule="hyper" parents="573 1524"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,151,a(flip),b,1524,a),flip(a)].">
      <j1 rule="hyper" parents="319 151 1524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(217,a,1524,a),flip(a)].">
      <j1 rule="hyper" parents="217 1524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1524,a)].">
      <j1 rule="hyper" parents="134 1524"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(127,a,151,a(flip),b,1524,a)].">
      <j1 rule="hyper" parents="127 151 1524"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) \ (y * (x * L(y,z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(1524(a,1),338(a,1,1))].">
      <j1 rule="para" parents="1524 338"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = x \ (x / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,1526,a)].">
      <j1 rule="hyper" parents="417 1526"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      x * L(y,z,u) != y
    ]]></literal>
    <literal><![CDATA[
      (1 / L(y,z,u)) * y = x
    ]]></literal>
    <justification jstring="[para(1529(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1529 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1527(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1527 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,94,a(flip),b,1528,a),flip(a)].">
      <j1 rule="hyper" parents="128 94 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1530(a,1),1003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1530 1003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      T(x \ (x / L(x,y,z)),L(x,y,z)) = T(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1533(a,1),250(a,1,1))].">
      <j1 rule="para" parents="1533 250"/>
    </justification>
  </clause>

  <clause id="1539">
    <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(1536(a,1),245(a,2)),flip(a)].">
      <j1 rule="para" parents="1536 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,1537,a(flip),b,654,a)].">
      <j1 rule="hyper" parents="131 1537 654"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),1459(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,981,a(flip),b,1541,a)].">
      <j1 rule="hyper" parents="64 981 1541"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,980,a(flip),b,1541,a)].">
      <j1 rule="hyper" parents="64 980 1541"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(244,a,866,a(flip),b,1541,a(flip))].">
      <j1 rule="hyper" parents="244 866 1541"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,1544,a)].">
      <j1 rule="hyper" parents="56 1544"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      T(x,x * ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[para(224(a,1),1544(a,1,2,2))].">
      <j1 rule="para" parents="224 1544"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(371(a,1),1544(a,1,2,2))].">
      <j1 rule="para" parents="371 1544"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(652(a,1),1544(a,1,2))].">
      <j1 rule="para" parents="652 1544"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      T(x \ 1,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1063(a,1),1544(a,1,2))].">
      <j1 rule="para" parents="1063 1544"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1420(a,1),1544(a,1,2))].">
      <j1 rule="para" parents="1420 1544"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      (((x * y) \ x) * y) / ((x * y) \ x) = L(y,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(1546(a,1),616(a,1,1,2))].">
      <j1 rule="para" parents="1546 616"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(T(x,y),T(x,y) * ((T(x,y) / x) \ (1 / x))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(949(a,1),1546(a,1,2,2,1))].">
      <j1 rule="para" parents="949 1546"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1551(a,1),453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1551 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1549(a,1),780(a,1,1))].">
      <j1 rule="para" parents="1549 780"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(55,a,1553,a)].">
      <j1 rule="hyper" parents="55 1553"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(((x / y) * y) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(324,a,1523,a),flip(a)].">
      <j1 rule="hyper" parents="324 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,981,a(flip),b,1523,a)].">
      <j1 rule="hyper" parents="64 981 1523"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,866,a(flip),b,1523,a),flip(a)].">
      <j1 rule="hyper" parents="64 866 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,1523,a(flip),b,981,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="244 1523 981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1561">
    <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),1560(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(762,a,1561,a)].">
      <j1 rule="hyper" parents="762 1561"/>
    </justification>
  </clause>

  <clause id="1563">
    <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),1562(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1250(a,1),1563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1250 1563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,1253,a(flip),b,1564,a),flip(a)].">
      <j1 rule="hyper" parents="64 1253 1564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      ((x * x) * (y * z)) \ ((x * x) * (y * (z * u))) = L(u,z,(x * x) * y)
    ]]></literal>
    <justification jstring="[para(33(a,1),119(a,1,2))].">
      <j1 rule="para" parents="33 119"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(34(a,1),124(a,1,2))].">
      <j1 rule="para" parents="34 124"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,14,a,b,513,a)].">
      <j1 rule="hyper" parents="319 14 513"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      R(x,(y * y) \ z,u) / (y * y) = R(x / (y * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,705,a(flip),b,917,a),flip(a)].">
      <j1 rule="hyper" parents="319 705 917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (x * x) * R((x * x) \ y,z,u) = R(y,(x * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(38,a,666,a,b,1569,a)].">
      <j1 rule="hyper" parents="38 666 1569"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      R(x,(y * y) \ 1,z) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,535,a(flip),b,1569,a),flip(a)].">
      <j1 rule="hyper" parents="38 535 1569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(853(a,1),922(a,1,1))].">
      <j1 rule="para" parents="853 922"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(864(a,1),1572(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="864 1572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(544(a,1),1266(a,2,2))].">
      <j1 rule="para" parents="544 1266"/>
    </justification>
  </clause>

  <clause id="1575">
    <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),1574(a,2,2,1))].">
      <j1 rule="para" parents="7 1574"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      x \ (((T(y,x) \ y) * x) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(1446(a,1),1447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1446 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u * u) = L(x,y,(u * u) * z)
    ]]></literal>
    <justification jstring="[hyper(801,a,1566,a)].">
      <j1 rule="hyper" parents="801 1566"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      L(x,y,(z * z) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(499,a,1577,a),flip(a)].">
      <j1 rule="hyper" parents="499 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1578(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(226(a,1),1578(a,1,3)),flip(a)].">
      <j1 rule="para" parents="226 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      L(x,y,(1 / z) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(276(a,1),1578(a,1,3)),flip(a)].">
      <j1 rule="para" parents="276 1578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      L(x \ ((1 / y) \ z),x,y) = ((1 / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,1581,a),flip(a)].">
      <j1 rule="hyper" parents="64 302 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      L(x,y,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),1581(a,1,3)),flip(a)].">
      <j1 rule="para" parents="78 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(592(a,1),1581(a,1,3))].">
      <j1 rule="para" parents="592 1581"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      T(L(x,x,x),(1 / x) * y) = ((1 / x) * y) \ L(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(1581(a,1),742(a,2,2))].">
      <j1 rule="para" parents="1581 742"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,1581,a,b,1584,a)].">
      <j1 rule="hyper" parents="319 1581 1584"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,461,a,b,1584,a)].">
      <j1 rule="hyper" parents="319 461 1584"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,1584,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="319 1584 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      L(x,y,(z * z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,478,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="319 478 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,466,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="319 466 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,465,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="319 465 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(319,a,369,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="319 369 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(127,a,1584,a,b,461,a)].">
      <j1 rule="hyper" parents="127 1584 461"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      L(x \ ((y \ 1) \ z),x,y) = ((y \ 1) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="64 302 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(206,a,1593,a(flip),b,224,a(flip))].">
      <j1 rule="hyper" parents="206 1593 224"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1593(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1593 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1593(a,1),1267(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1593 1267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1593(a,1),1542(a,2,1,2))].">
      <j1 rule="para" parents="1593 1542"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      L(L(x,y,z),u,(w * w) \ 1) = L(x,y,(v5 * v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,1590,a,b,1580,a)].">
      <j1 rule="hyper" parents="319 1590 1580"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      L(x \ y,x,x) * L(z,y,x) = L(x \ (y * z),x,x)
    ]]></literal>
    <justification jstring="[para(1580(a,1),1407(a,1,2))].">
      <j1 rule="para" parents="1580 1407"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(130,a,263,a,b,1596,a)].">
      <j1 rule="hyper" parents="130 263 1596"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(244,a,1316,a,b,1596,a(flip))].">
      <j1 rule="hyper" parents="244 1316 1596"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1596(a,2),358(a,1))].">
      <j1 rule="para" parents="1596 358"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(41,a,615,a,b,1603,a)].">
      <j1 rule="hyper" parents="41 615 1603"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1603(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1603 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1603(a,1),149(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1603 149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      T(x,x \ 1) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1603(a,1),946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1603 946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1603(a,1),1320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1603 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,558,a,b,1605,a)].">
      <j1 rule="hyper" parents="64 558 1605"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,1605,a(flip),b,558,a)].">
      <j1 rule="hyper" parents="127 1605 558"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      R(x,K(y \ 1,y),1 / y) * (y \ 1) = (x * K(y \ 1,y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1602,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="131 1602 194"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,265,a,b,1608,a),flip(a)].">
      <j1 rule="hyper" parents="319 265 1608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(130,a,265,a,b,1608,a)].">
      <j1 rule="hyper" parents="130 265 1608"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,787,a,b,1608,a)].">
      <j1 rule="hyper" parents="38 787 1608"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(244,a,1608,a(flip),b,955,a(flip))].">
      <j1 rule="hyper" parents="244 1608 955"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      T(1 / x,1 / (1 / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,318,a(flip),b,1618,a),flip(a)].">
      <j1 rule="hyper" parents="319 318 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1618(a,1),453(a,1,1,2))].">
      <j1 rule="para" parents="1618 453"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      R(x,1 / x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,786,a,b,1619,a)].">
      <j1 rule="hyper" parents="64 786 1619"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(1619(a,1),788(a,1,1))].">
      <j1 rule="para" parents="1619 788"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1619(a,1),996(a,1,1,1))].">
      <j1 rule="para" parents="1619 996"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      a(x,1 / x,x) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1622(a,1),773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1622 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,1609,a)].">
      <j1 rule="hyper" parents="144 1609"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1608,a(flip),b,1609,a),flip(a)].">
      <j1 rule="hyper" parents="64 1608 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(127,a,1609,a(flip),b,1608,a(flip))].">
      <j1 rule="hyper" parents="127 1609 1608"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(110(a,1),1609(a,1,1))].">
      <j1 rule="para" parents="110 1609"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,265,a,b,1628,a)].">
      <j1 rule="hyper" parents="319 265 1628"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(131,a,1628,a,b,1167,a)].">
      <j1 rule="hyper" parents="131 1628 1167"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1628,a,b,194,a)].">
      <j1 rule="hyper" parents="131 1628 194"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1628(a,2),92(a,1,1))].">
      <j1 rule="para" parents="1628 92"/>
    </justification>
  </clause>

  <clause id="1635">
    <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(1628(a,2),875(a,1,1))].">
      <j1 rule="para" parents="1628 875"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1628(a,2),1168(a,1,2))].">
      <j1 rule="para" parents="1628 1168"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(1628(a,2),1317(a,1,1))].">
      <j1 rule="para" parents="1628 1317"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      x \ y != z * (1 / z)
    ]]></literal>
    <literal><![CDATA[
      x * K(z,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(1629(a,1),329(a,2,2))].">
      <j1 rule="para" parents="1629 329"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      K((x / y) \ x,1 / y) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,684,a,b,1631,a)].">
      <j1 rule="hyper" parents="64 684 1631"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(78(a,1),1631(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1631(a,1),368(a,1))].">
      <j1 rule="para" parents="1631 368"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      x * (T(x,y) \ K(x \ 1,x)) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(127,a,1610,a(flip),b,1014,a),flip(a)].">
      <j1 rule="hyper" parents="127 1610 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      x * K(x \ 1,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ (1 / (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(1611(a,1),388(a,1,2))].">
      <j1 rule="para" parents="1611 388"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(318(a,1),1616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="318 1616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      K(x,1 / x) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a(flip),b,1617,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 1617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1620(a,1),996(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1620 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(130,a,1631,a(flip),b,1623,a)].">
      <j1 rule="hyper" parents="130 1631 1623"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1630,a(flip),b,1091,a(flip))].">
      <j1 rule="hyper" parents="131 1630 1091"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1647(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1647 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(1588(a,1),219(a,1))].">
      <j1 rule="para" parents="1588 219"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      L((x \ 1) * y,x,x \ 1) = (1 / x) * L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(262(a,1),1588(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 1588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(1588(a,1),307(a,1,1))].">
      <j1 rule="para" parents="1588 307"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1591(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1591 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1594(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1594 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      x \ (K(x,1 / x) * x) = a(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(1645(a,2),1626(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1645 1626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      L(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(499,a,1582,a),flip(a)].">
      <j1 rule="hyper" parents="499 1582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      ((x * (1 / x)) \ y) \ z = y \ ((x * (1 / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(589,a,1659,a),flip(a)].">
      <j1 rule="hyper" parents="589 1659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      ((x * (1 / x)) * y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,1659,a)].">
      <j1 rule="hyper" parents="64 302 1659"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      ((x * (1 / x)) * y) / z = (x * (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,1659,a(flip),b,98,a(flip))].">
      <j1 rule="hyper" parents="206 1659 98"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(265(a,2),1659(a,1,3))].">
      <j1 rule="para" parents="265 1659"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1628(a,2),1659(a,1,3))].">
      <j1 rule="para" parents="1628 1659"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1143,a,1663,a),flip(a)].">
      <j1 rule="hyper" parents="1143 1663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(206,a,1663,a(flip),b,227,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 1663 227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(78(a,1),1663(a,1,3,2))].">
      <j1 rule="para" parents="78 1663"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(1663(a,1),300(a,1,2))].">
      <j1 rule="para" parents="1663 300"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1143,a,1664,a),flip(a)].">
      <j1 rule="hyper" parents="1143 1664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,96,a(flip),b,1664,a)].">
      <j1 rule="hyper" parents="64 96 1664"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,1664,a(flip),b,98,a(flip))].">
      <j1 rule="hyper" parents="206 1664 98"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1143,a,1667,a),flip(a)].">
      <j1 rule="hyper" parents="1143 1667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,96,a(flip),b,1667,a)].">
      <j1 rule="hyper" parents="64 96 1667"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,1667,a(flip),b,98,a(flip))].">
      <j1 rule="hyper" parents="206 1667 98"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(1667(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1667 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1667(a,1),51(a,2))].">
      <j1 rule="para" parents="1667 51"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1592(a,1),242(a,1,2))].">
      <j1 rule="para" parents="1592 242"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1623(a,1),1650(a,1))].">
      <j1 rule="para" parents="1623 1650"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      T(K(x,1 / x),x) = a(x,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1658,a)].">
      <j1 rule="hyper" parents="335 1658"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1580,a(flip),b,1585,a),flip(a)].">
      <j1 rule="hyper" parents="64 1580 1585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      L(x,y,(z * z) / u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(81(a,1),1680(a,1,3)),flip(a)].">
      <j1 rule="para" parents="81 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,(z \ u) \ u)
    ]]></literal>
    <justification jstring="[para(426(a,1),1680(a,1,3))].">
      <j1 rule="para" parents="426 1680"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1644(a,2),1604(a,1))].">
      <j1 rule="para" parents="1644 1604"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      L(x \ ((1 / y) \ L(x,1 / y,1 / y)),x,y) = T(1 / (1 / y),(1 / y) * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,464,a(flip),b,1583,a),flip(a)].">
      <j1 rule="hyper" parents="319 464 1583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(589,a,1595,a),flip(a)].">
      <j1 rule="hyper" parents="589 1595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) \ (y / ((1 / (x \ 1)) * z))),x \ 1,x) = T(y / ((x \ 1) * z),(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,836,a(flip),b,1595,a),flip(a)].">
      <j1 rule="hyper" parents="319 836 1595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      x \ L((y \ 1) \ ((y \ 1) \ z),y \ 1,y) = (((y \ 1) * (y \ 1)) * x) \ z
    ]]></literal>
    <justification jstring="[para(1595(a,2),416(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1595 416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) \ y),x \ 1,x) \ z = y \ (((x \ 1) * (x \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(1595(a,2),638(a,1,1))].">
      <j1 rule="para" parents="1595 638"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      R(x,L((y \ 1) \ ((y \ 1) \ 1),y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(1595(a,2),1571(a,1,2))].">
      <j1 rule="para" parents="1595 1571"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1597(a,1),490(a,1,2))].">
      <j1 rule="para" parents="1597 490"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1684,a,1631,a),flip(a)].">
      <j1 rule="hyper" parents="1684 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(81(a,1),1693(a,1,2))].">
      <j1 rule="para" parents="81 1693"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      x * K(1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1694,a,b,1611,a)].">
      <j1 rule="hyper" parents="131 1694 1611"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1634,a,b,1694,a)].">
      <j1 rule="hyper" parents="64 1634 1694"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,453,a(flip),b,1621,a),flip(a)].">
      <j1 rule="hyper" parents="64 453 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1624(a,1),111(a,1,1))].">
      <j1 rule="para" parents="1624 111"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(529,a,1669,a)].">
      <j1 rule="hyper" parents="529 1669"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1627(a,1),1669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1627 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1637(a,1),1669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1637 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1647(a,1),1669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1647 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = u
    ]]></literal>
    <justification jstring="[para(1701(a,1),290(a,1,1))].">
      <j1 rule="para" parents="1701 290"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      T(x,x \ 1) \ (K(x,x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(600,a,1703,a)].">
      <j1 rule="hyper" parents="600 1703"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(331,a,1704,a),flip(a)].">
      <j1 rule="hyper" parents="331 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x * ((1 / y) * z)) / L((y \ 1) * z,K(y,y \ 1),x) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1704(a,1),197(a,1,1,2))].">
      <j1 rule="para" parents="1704 197"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ 1) * z,K(y,y \ 1),x) = u
    ]]></literal>
    <justification jstring="[para(1704(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="1704 489"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[para(1704(a,1),1669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1704 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,1708,a(flip),b,1085,a)].">
      <j1 rule="hyper" parents="131 1708 1085"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      (x \ 1) \ (K(x,x \ 1) * y) = K(x,x \ 1) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,1708,a(flip),b,1712,a)].">
      <j1 rule="hyper" parents="127 1708 1712"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,1712,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1712,a(flip),b,413,a),flip(a)].">
      <j1 rule="hyper" parents="131 1712 413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(1637(a,1),1671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1637 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1672(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1672 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(864(a,1),1672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="864 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1602(a,1),1672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1602 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(331,a,1721,a),flip(a)].">
      <j1 rule="hyper" parents="331 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1259,a,b,1721,a),flip(a)].">
      <j1 rule="hyper" parents="35 1259 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(331,a,1722,a),flip(a)].">
      <j1 rule="hyper" parents="331 1722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      ((x * K(y \ 1,y)) * ((1 / y) * z)) / ((y \ 1) * z) = R(x,K(y \ 1,y),(1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(206,a,1722,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="206 1722 194"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(1722(a,1),473(a,1,1))].">
      <j1 rule="para" parents="1722 473"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,1256,a,b,1723,a)].">
      <j1 rule="hyper" parents="35 1256 1723"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      (x * y) \ ((K(x \ 1,x) * y) * ((x \ 1) \ 1)) = K(K(x \ 1,x) * y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1724(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1724 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * ((1 / x) * z)) / y) = (x \ 1) * (x * ((y * (x \ z)) / y))
    ]]></literal>
    <justification jstring="[para(1147(a,1),1725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1147 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1099,a(flip),b,1728,a)].">
      <j1 rule="hyper" parents="64 1099 1728"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(1722(a,1),1673(a,1,1))].">
      <j1 rule="para" parents="1722 1673"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      T(K(x \ 1,x) * (y / z),z) = z \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(1674(a,1),111(a,1,1))].">
      <j1 rule="para" parents="1674 111"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) / y) = x / y
    ]]></literal>
    <justification jstring="[para(864(a,1),1674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="864 1674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      R(x,y * ((y \ 1) \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(503(a,1),1690(a,1,2))].">
      <j1 rule="para" parents="503 1690"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(232(a,1),1699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 1699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1600(a,1),496(a,1)),flip(b)].">
      <j1 rule="para" parents="1600 496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(275(a,1),1738(a,1,3))].">
      <j1 rule="para" parents="275 1738"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(78(a,1),1739(a,1,3))].">
      <j1 rule="para" parents="78 1739"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      L(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1587(a,1),1739(a,1))].">
      <j1 rule="para" parents="1587 1739"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(1581(a,2),1740(a,1))].">
      <j1 rule="para" parents="1581 1740"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,1 / z) = u
    ]]></literal>
    <justification jstring="[para(81(a,1),1741(a,1,3))].">
      <j1 rule="para" parents="81 1741"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      L(x \ y,x,x) \ L(x \ (y * z),x,x) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1601,a)].">
      <j1 rule="hyper" parents="134 1601"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      (x \ 1) \ (L((1 / x) * y,z,u) * ((x \ 1) * x)) = x * T(L(x \ y,z,u),(x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1656(a,1),647(a,1,2,1))].">
      <j1 rule="para" parents="1656 647"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(232(a,1),1736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 1736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1747(a,1),1285(a,1,1))].">
      <j1 rule="para" parents="1747 1285"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1748(a,1),1281(a,1,1,1))].">
      <j1 rule="para" parents="1748 1281"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1628(a,2),1598(a,2,1))].">
      <j1 rule="para" parents="1628 1598"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1751(a,1),1599(a,1,2))].">
      <j1 rule="para" parents="1751 1599"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,94,a(flip),b,1752,a),flip(a)].">
      <j1 rule="hyper" parents="35 94 1752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1628(a,2),1752(a,2,1))].">
      <j1 rule="para" parents="1628 1752"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1754(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(1754(a,1),44(a,1))].">
      <j1 rule="para" parents="1754 44"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x
    ]]></literal>
    <justification jstring="[hyper(128,a,1703,a(flip),b,1755,a(flip))].">
      <j1 rule="hyper" parents="128 1703 1755"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * (K(x,x \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(1755(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1755 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1704,a,b,1753,a),flip(a)].">
      <j1 rule="hyper" parents="35 1704 1753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(987,a,1760,a)].">
      <j1 rule="hyper" parents="987 1760"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),1762(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(588,a,1763,a),flip(a)].">
      <j1 rule="hyper" parents="588 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(921,a,1749,a)].">
      <j1 rule="hyper" parents="921 1749"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(131,a,1767,a(flip),b,1414,a)].">
      <j1 rule="hyper" parents="131 1767 1414"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1018(a,1),1767(a,1,2,1))].">
      <j1 rule="para" parents="1018 1767"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1769(a,1),1575(a,1,1))].">
      <j1 rule="para" parents="1769 1575"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(1770(a,1),254(a,1)),flip(b)].">
      <j1 rule="para" parents="1770 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1771,a,1768,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1771 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1769(a,2),1772(a,1,2))].">
      <j1 rule="para" parents="1769 1772"/>
    </justification>
  </clause>

  <clause id="1774">
    <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(1655(a,2),1742(a,1))].">
      <j1 rule="para" parents="1655 1742"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u * (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,120,a(flip),b,1567,a)].">
      <j1 rule="hyper" parents="64 120 1567"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      L(x,T(y,z * z) * u,w * (z * z)) = L(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[para(916(a,1),1775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="916 1775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      L(x,T(y,z * z) * u,T(w,z * z)) = L(x,y * ((z * z) * u),(z * z) \ w)
    ]]></literal>
    <justification jstring="[para(636(a,1),1776(a,1,3))].">
      <j1 rule="para" parents="636 1776"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1672(a,1),1720(a,1,1))].">
      <j1 rule="para" parents="1672 1720"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(1667(a,1),1727(a,1,2))].">
      <j1 rule="para" parents="1667 1727"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1674,a(flip),b,1779,a)].">
      <j1 rule="hyper" parents="64 1674 1779"/>
    </justification>
  </clause>

  <clause id="1783">
    <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),1782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 1782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(869,a,1081,a),flip(a)].">
      <j1 rule="hyper" parents="869 1081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1134(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(244,a,1239,a,b,1150,a(flip))].">
      <j1 rule="hyper" parents="244 1239 1150"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(244,a,1271,a(flip),b,1150,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="244 1271 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),x) = y * L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[para(1038(a,1),1150(a,2,2))].">
      <j1 rule="para" parents="1038 1150"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(232(a,1),1789(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(210(a,1),1792(a,1,2,1,2))].">
      <j1 rule="para" parents="210 1792"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(1112,a,1793,a),flip(a)].">
      <j1 rule="hyper" parents="1112 1793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(291,a,1793,a),flip(a)].">
      <j1 rule="hyper" parents="291 1793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1793,a)].">
      <j1 rule="hyper" parents="134 1793"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1794,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 1794 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[para(270(a,1),1794(a,2,1,2))].">
      <j1 rule="para" parents="270 1794"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(348(a,1),1794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="348 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1109(a,2),1794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1109 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      T(L(x,y,z) * T(L(x,y,z) \ 1,x),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(1169(a,2),1798(a,1,2))].">
      <j1 rule="para" parents="1169 1798"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(371(a,1),1800(a,1,1,2,2,1))].">
      <j1 rule="para" parents="371 1800"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x)
    ]]></literal>
    <justification jstring="[para(110(a,1),1802(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="110 1802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1330(a,1),1796(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1330 1796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1805">
    <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(1780(a,1),1797(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1780 1797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1804(a,2,2,1))].">
      <j1 rule="para" parents="10 1804"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(210(a,1),1806(a,2,2))].">
      <j1 rule="para" parents="210 1806"/>
    </justification>
  </clause>

  <clause id="1810">
    <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),1791(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y))
    ]]></literal>
    <justification jstring="[para(1547(a,1),1183(a,2,2,2))].">
      <j1 rule="para" parents="1547 1183"/>
    </justification>
  </clause>

  <clause id="1812">
    <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),1188(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(1102(a,1),1812(a,1,2))].">
      <j1 rule="para" parents="1102 1812"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1813,a)].">
      <j1 rule="hyper" parents="134 1813"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(584,a,1388,a),flip(a)].">
      <j1 rule="hyper" parents="584 1388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(1100(a,2),1388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1100 1388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1247,a,b,1815,a)].">
      <j1 rule="hyper" parents="64 1247 1815"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(82(a,1),1817(a,1,1))].">
      <j1 rule="para" parents="82 1817"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(762,a,1818,a),flip(a)].">
      <j1 rule="hyper" parents="762 1818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1818(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,1820,a(flip),b,493,a)].">
      <j1 rule="hyper" parents="127 1820 493"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(81(a,1),1820(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 1820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(89(a,1),1820(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="89 1820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y)
    ]]></literal>
    <justification jstring="[para(1461(a,2),1397(a,1,2))].">
      <j1 rule="para" parents="1461 1397"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1825(a,2,2,1,2,2))].">
      <j1 rule="para" parents="8 1825"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1826(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1398(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1418(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <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(1040(a,1),1467(a,1,2,1))].">
      <j1 rule="para" parents="1040 1467"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      ((x * y) / x) * ((((x * y) / x) \ y) / y) = K(y,1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1202(a,1),1468(a,1,2,1))].">
      <j1 rule="para" parents="1202 1468"/>
    </justification>
  </clause>

  <clause id="1832">
    <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),1474(a,1,1))].">
      <j1 rule="para" parents="22 1474"/>
    </justification>
  </clause>

  <clause id="1833">
    <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),1832(a,1,2,1,1))].">
      <j1 rule="para" parents="22 1832"/>
    </justification>
  </clause>

  <clause id="1834">
    <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),1833(a,2,1,2,1))].">
      <j1 rule="para" parents="9 1833"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(666(a,1),1503(a,2,2))].">
      <j1 rule="para" parents="666 1503"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(666(a,1),1835(a,1,1,2))].">
      <j1 rule="para" parents="666 1835"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),1836(a,1,1,2))].">
      <j1 rule="para" parents="225 1836"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(225(a,1),1837(a,2,2))].">
      <j1 rule="para" parents="225 1837"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,1838,a)].">
      <j1 rule="hyper" parents="55 1838"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      T(x,x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),1839(a,1,2,2,2))].">
      <j1 rule="para" parents="10 1839"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1839(a,1,2,2,2))].">
      <j1 rule="para" parents="12 1839"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      T((x \ y) \ y,x * ((x \ z) / z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1840(a,1),315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1840 315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1841(a,1),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1841 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,1843,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1844(a,1),1363(a,2,1,2))].">
      <j1 rule="para" parents="1844 1363"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = ((x \ y) * T(x,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(1842(a,1),1363(a,2,1,2))].">
      <j1 rule="para" parents="1842 1363"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1477(a,1),1516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1477 1516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * R((x \ 1) \ 1,y,z)) * u) = (x \ R(x,y,z)) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1070(a,1),1847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1070 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1541(a,1),1543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1541 1543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * L((x \ 1) \ 1,y,z)) * u) = (x \ L(x,y,z)) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1063(a,1),1849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1063 1849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(866(a,1),1559(a,1,1))].">
      <j1 rule="para" parents="866 1559"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,151,a(flip),b,1851,a)].">
      <j1 rule="hyper" parents="128 151 1851"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,258,a(flip),b,1811,a),flip(a)].">
      <j1 rule="hyper" parents="319 258 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(1853(a,1),1060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1853 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1402,a(flip),b,1855,a)].">
      <j1 rule="hyper" parents="64 1402 1855"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (1 / (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(131,a,1855,a(flip),b,1402,a(flip))].">
      <j1 rule="hyper" parents="131 1855 1402"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(400,a,1856,a)].">
      <j1 rule="hyper" parents="400 1856"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1856(a,1,1,2))].">
      <j1 rule="para" parents="9 1856"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(1859(a,1),1433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1859 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1860(a,2,2))].">
      <j1 rule="para" parents="9 1860"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(207,a,1862,a)].">
      <j1 rule="hyper" parents="207 1862"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,1862,a)].">
      <j1 rule="hyper" parents="145 1862"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1863(a,1),1107(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1863 1107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(224(a,2),1864(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="224 1864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(632,a,1866,a)].">
      <j1 rule="hyper" parents="632 1866"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      x * L(x \ y,y \ x,x \ y) = y * K(y \ x,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1638,a,1861,a),flip(a)].">
      <j1 rule="hyper" parents="1638 1861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * 1,y)) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),1816(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8(a,1),1869(a,2,1,2,1))].">
      <j1 rule="para" parents="8 1869"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,10,a(flip),b,1870,a),flip(a)].">
      <j1 rule="hyper" parents="126 10 1870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(319,a,156,a(flip),b,1845,a),flip(a)].">
      <j1 rule="hyper" parents="319 156 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,75,a(flip),b,1873,a),flip(a)].">
      <j1 rule="hyper" parents="319 75 1873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      ((x * x) * (y * (z * u))) \ (((x * x) * (y * z)) * u) = a((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),118(a,1,2,1))].">
      <j1 rule="para" parents="33 118"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(34(a,1),123(a,1,2,1))].">
      <j1 rule="para" parents="34 123"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      R((x * (y * z)) / (x * y),u,w) = (x * (y * R(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(436(a,1),832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(38,a,20,a(flip),b,1879,a(flip))].">
      <j1 rule="hyper" parents="38 20 1879"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),1880(a,1,1,1,1,2))].">
      <j1 rule="para" parents="109 1880"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(243(a,1),1881(a,2,2))].">
      <j1 rule="para" parents="243 1881"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1335,a(flip),b,957,a)].">
      <j1 rule="hyper" parents="64 1335 957"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1883(a,1),696(a,1,1))].">
      <j1 rule="para" parents="1883 696"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(827,a,1885,a),flip(a)].">
      <j1 rule="hyper" parents="827 1885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1886(a,1),1466(a,1,2))].">
      <j1 rule="para" parents="1886 1466"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      L(x \ (((1 / x) \ y) * z),x,x) = x * ((((1 / x) \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,202,a(flip),b,975,a),flip(a)].">
      <j1 rule="hyper" parents="319 202 975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      L(x \ (((1 / x) \ y) * z),x,x) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),1888(a,2,2,1,1))].">
      <j1 rule="para" parents="81 1888"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,466,a(flip),b,1890,a)].">
      <j1 rule="hyper" parents="64 466 1890"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      (1 / x) * (x * y) = x * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(81(a,1),1891(a,1,2,1))].">
      <j1 rule="para" parents="81 1891"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(177(a,1),1891(a,2,2))].">
      <j1 rule="para" parents="177 1891"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(491,a,1892,a),flip(a)].">
      <j1 rule="hyper" parents="491 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(468,a,1892,a),flip(a)].">
      <j1 rule="hyper" parents="468 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,262,a(flip),b,1892,a),flip(a)].">
      <j1 rule="hyper" parents="319 262 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      (1 / x) \ (x * y) = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,1892,a)].">
      <j1 rule="hyper" parents="127 153 1892"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      x * ((x \ 1) \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,1892,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      x \ L(y,x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(127,a,461,a(flip),b,1892,a(flip))].">
      <j1 rule="hyper" parents="127 461 1892"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      L(x,y \ 1,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(606,a,1895,a)].">
      <j1 rule="hyper" parents="606 1895"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1762,a,b,1900,a)].">
      <j1 rule="hyper" parents="64 1762 1900"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      L(x,1 / y,1 / y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(1743,a,1902,a)].">
      <j1 rule="hyper" parents="1743 1902"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      T(L(x,x,x),(1 / x) * y) = ((1 / x) * y) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(1902(a,1),1586(a,2,2))].">
      <j1 rule="para" parents="1902 1586"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      R(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,663,a,b,1898,a)].">
      <j1 rule="hyper" parents="35 663 1898"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      R(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(1898(a,1),1735(a,1,2))].">
      <j1 rule="para" parents="1898 1735"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      R(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(78(a,1),1907(a,1,2,1))].">
      <j1 rule="para" parents="78 1907"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      (1 / x) \ (x * y) = ((1 / x) \ x) * y
    ]]></literal>
    <justification jstring="[para(1907(a,1),519(a,1,1))].">
      <j1 rule="para" parents="1907 519"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = x \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(600,a,1893,a),flip(a)].">
      <j1 rule="hyper" parents="600 1893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      ((1 / x) \ x) * y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1897,a(flip),b,1909,a),flip(a)].">
      <j1 rule="hyper" parents="64 1897 1909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      x * ((((1 / y) \ y) * x) \ z) = y \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,930,a,b,1910,a)].">
      <j1 rule="hyper" parents="64 930 1910"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      x * ((y * ((y \ 1) \ x)) \ z) = y \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(1911(a,1),1912(a,1,2,1))].">
      <j1 rule="para" parents="1911 1912"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ (x \ y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(371(a,1),1069(a,1,2,2))].">
      <j1 rule="para" parents="371 1069"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      (x \ y) * (((y \ x) \ 1) \ 1) = ((y \ x) \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,1914,a)].">
      <j1 rule="hyper" parents="145 1914"/>
    </justification>
  </clause>

  <clause id="1916">
    <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(1915(a,1),923(a,1,2,1))].">
      <j1 rule="para" parents="1915 923"/>
    </justification>
  </clause>

  <clause id="1917">
    <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(1915(a,1),1461(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1915 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      L(T(x,y),y,K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = z
    ]]></literal>
    <justification jstring="[para(1261(a,1),335(a,1))].">
      <j1 rule="para" parents="1261 335"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1918,a,1667,a)].">
      <j1 rule="hyper" parents="1918 1667"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1722(a,1),1919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1722 1919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      T(x \ 1,((x \ 1) \ 1) * y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(78(a,1),1920(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 1920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,438,a(flip),b,1296,a),flip(a)].">
      <j1 rule="hyper" parents="319 438 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(1922(a,1),456(a,1,2))].">
      <j1 rule="para" parents="1922 456"/>
    </justification>
  </clause>

  <clause id="1924">
    <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(1922(a,1),1199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1922 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) \ 1 = y \ ((y * (x * T(x \ 1,y))) \ y)
    ]]></literal>
    <justification jstring="[para(1922(a,1),1204(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1922 1204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <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(1922(a,1),1269(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1922 1269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(959(a,2),1923(a,1,2,2))].">
      <j1 rule="para" parents="959 1923"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1180(a,1),1923(a,1,2,2))].">
      <j1 rule="para" parents="1180 1923"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(55,a,1927,a)].">
      <j1 rule="hyper" parents="55 1927"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1219(a,1),1928(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1219 1928"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),1930(a,1,2,2,2))].">
      <j1 rule="para" parents="10 1930"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1931(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1931 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1034,a,1932,a)].">
      <j1 rule="hyper" parents="1034 1932"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(207,a,1933,a)].">
      <j1 rule="hyper" parents="207 1933"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = T(x,R(T(y,x),T(y,x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(1446(a,1),1933(a,1,1,2,1))].">
      <j1 rule="para" parents="1446 1933"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1288,a,1934,a)].">
      <j1 rule="hyper" parents="1288 1934"/>
    </justification>
  </clause>

  <clause id="1937">
    <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(1934(a,2),617(a,1,2))].">
      <j1 rule="para" parents="1934 617"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1936,a(flip),b,447,a),flip(a)].">
      <j1 rule="hyper" parents="130 1936 447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      x \ L((y \ 1) \ ((y \ 1) \ z),y \ 1,y) = (((y \ 1) / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(421(a,1),1688(a,2,1,1))].">
      <j1 rule="para" parents="421 1688"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      (((x \ 1) / x) * y) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(503(a,1),1939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 1939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      ((x \ (1 / x)) * y) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(810(a,1),1940(a,1,1,1))].">
      <j1 rule="para" parents="810 1940"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      (x \ (1 / x)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(40,a,1686,a,b,1941,a),flip(a)].">
      <j1 rule="hyper" parents="40 1686 1941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      x \ (((y \ 1) * (y \ 1)) * z) = (y * ((y \ 1) \ x)) \ z
    ]]></literal>
    <justification jstring="[para(503(a,1),1689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 1689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) \ z = y \ (((x \ 1) / x) * z)
    ]]></literal>
    <justification jstring="[para(421(a,1),1943(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="421 1943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      x * (x \ (((y \ 1) / y) * z)) = y \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(1944(a,1),1913(a,1,2))].">
      <j1 rule="para" parents="1944 1913"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      x \ ((1 / x) * y) = ((x \ 1) / x) * y
    ]]></literal>
    <justification jstring="[hyper(586,a,1945,a),flip(a)].">
      <j1 rule="hyper" parents="586 1945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      ((x \ 1) / x) * T(y,x) = T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,843,a(flip),b,1946,a),flip(a)].">
      <j1 rule="hyper" parents="64 843 1946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      (x \ (1 / x)) * T(y,x) = T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(810(a,1),1947(a,1,1))].">
      <j1 rule="para" parents="810 1947"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      (x \ 1) * (x \ T(y,x)) = T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1942,a(flip),b,1948,a)].">
      <j1 rule="hyper" parents="64 1942 1948"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      ((x * x) * (y * (z * u))) \ ((x * x) * ((y * z) * u)) = a((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),1877(a,1,2))].">
      <j1 rule="para" parents="33 1877"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,117,a(flip),b,1878,a),flip(a)].">
      <j1 rule="hyper" parents="64 117 1878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,1446,a(flip),b,1935,a),flip(a)].">
      <j1 rule="hyper" parents="319 1446 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),u * u) = a((u * u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,507,a(flip),b,1950,a)].">
      <j1 rule="hyper" parents="64 507 1950"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(499,a,1953,a),flip(a)].">
      <j1 rule="hyper" parents="499 1953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(226(a,1),1954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="226 1954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      a(1 / x,x,y) = L(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,879,a,b,1957,a),flip(a)].">
      <j1 rule="hyper" parents="319 879 1957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),1957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 1957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,1957,a,b,1960,a)].">
      <j1 rule="hyper" parents="319 1957 1960"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(96(a,2),1956(a,1,1))].">
      <j1 rule="para" parents="96 1956"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(1584(a,2),1959(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1584 1959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,1961,a(flip),b,1963,a),flip(a)].">
      <j1 rule="hyper" parents="319 1961 1963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,1961,a(flip),b,1963,a)].">
      <j1 rule="hyper" parents="131 1961 1963"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(1965(a,1),330(a,1,2))].">
      <j1 rule="para" parents="1965 330"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      a(L(((x * x) * y) \ z,(x * x) * y,(x * x) * y),u,w) = a((x * x) * (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(33(a,1),1962(a,2,1))].">
      <j1 rule="para" parents="33 1962"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      (L(x,y,z) * u) \ ((x * (x \ u)) * L(T(x,x \ u),y,z)) = a(x,x \ u,L(T(x,x \ u),y,z))
    ]]></literal>
    <justification jstring="[para(1166(a,1),648(a,1,1))].">
      <j1 rule="para" parents="1166 648"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) * (1 / x) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(181(a,1),995(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="181 995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      (1 / x) * L(T((1 / x) \ 1,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(1005,a,1969,a)].">
      <j1 rule="hyper" parents="1005 1969"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),1970(a,1,2,1,1))].">
      <j1 rule="para" parents="81 1970"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1127(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(111(a,1),1972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 1972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),1973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 1973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <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),1974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),1975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <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(109(a,1),1177(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(244,a,1477,a(flip),b,1977,a),flip(a)].">
      <j1 rule="hyper" parents="244 1477 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,671,a,b,1978,a),flip(a)].">
      <j1 rule="hyper" parents="64 671 1978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = T(x \ 1,x \ L(x,u,w)) * R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1550(a,1),1978(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1550 1978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <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(937(a,1),1979(a,2,1,2))].">
      <j1 rule="para" parents="937 1979"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1339(a,1),1981(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1339 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,1795,a(flip),b,1982,a),flip(a)].">
      <j1 rule="hyper" parents="36 1795 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1983(a,1),111(a,1,1))].">
      <j1 rule="para" parents="1983 111"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,1808,a(flip),b,1984,a),flip(a)].">
      <j1 rule="hyper" parents="64 1808 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ ((1 / x) \ 1) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(942(a,1),1985(a,1,1))].">
      <j1 rule="para" parents="942 1985"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1985(a,1),1872(a,1,2,2))].">
      <j1 rule="para" parents="1985 1872"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,1988,a),flip(a)].">
      <j1 rule="hyper" parents="134 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ x = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(81(a,1),1987(a,1,2))].">
      <j1 rule="para" parents="81 1987"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      x / (T(1 / x,y) \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(207,a,1990,a)].">
      <j1 rule="hyper" parents="207 1990"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      K(x \ (x / y),x) \ y = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[para(1102(a,2),1990(a,1,1))].">
      <j1 rule="para" parents="1102 1990"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      T(x,y) * (T(z / (z / x),y) \ 1) = T(z / (z / x),y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(454(a,1),1205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="454 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1994">
    <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(244,a,1459,a,b,1399,a(flip))].">
      <j1 rule="hyper" parents="244 1459 1399"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(244,a,1523,a(flip),b,1399,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="244 1523 1399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1997">
    <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(232(a,1),1994(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      T(L((x \ 1) * ((1 / x) \ ((y * z) / y)),x,x \ 1),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1654(a,2),1994(a,1,1))].">
      <j1 rule="para" parents="1654 1994"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(210(a,1),1997(a,1,2,1,2))].">
      <j1 rule="para" parents="210 1997"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,y),u,w) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ T(x * L(x \ z,u,w),y) = v6
    ]]></literal>
    <justification jstring="[para(1997(a,2),762(a,1))].">
      <j1 rule="para" parents="1997 762"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,1999,a)].">
      <j1 rule="hyper" parents="134 1999"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,374,a(flip),b,1999,a),flip(a)].">
      <j1 rule="hyper" parents="64 374 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(744(a,1),1999(a,2,1,2))].">
      <j1 rule="para" parents="744 1999"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * L(x \ 1,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(2001(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2001 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = L(T(x \ y,z) \ 1,x \ y,x)
    ]]></literal>
    <justification jstring="[para(371(a,1),2001(a,1,2,1,2))].">
      <j1 rule="para" parents="371 2001"/>
    </justification>
  </clause>

  <clause id="2006">
    <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(949(a,1),2002(a,2,2,1))].">
      <j1 rule="para" parents="949 2002"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1024(a,1),2003(a,1,2))].">
      <j1 rule="para" parents="1024 2003"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(208(a,1),2007(a,2,1,2))].">
      <j1 rule="para" parents="208 2007"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1887(a,1),2006(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1887 2006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1441(a,1,1,1,2,2))].">
      <j1 rule="para" parents="10 1441"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(576,a,2010,a)].">
      <j1 rule="hyper" parents="576 2010"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,835,a(flip),b,2011,a),flip(a)].">
      <j1 rule="hyper" parents="319 835 2011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      (x \ ((y \ x) * z)) * R((x \ ((y \ x) * z)) \ z,u,w) = x \ ((R(y,u,w) * (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(658(a,1),1476(a,2,2,1))].">
      <j1 rule="para" parents="658 1476"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),1557(a,2,2,1,1))].">
      <j1 rule="para" parents="12 1557"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(142,a,2014,a)].">
      <j1 rule="hyper" parents="142 2014"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2015(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L((((x * y) * z) / (y * z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),2016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 2016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(350(a,1),1573(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="350 1573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(232(a,1),2018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 2018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(232(a,1),2019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 2019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x)
    ]]></literal>
    <justification jstring="[para(2020(a,1),1470(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2020 1470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),2021(a,2,2))].">
      <j1 rule="para" parents="11 2021"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,2022,a)].">
      <j1 rule="hyper" parents="145 2022"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      L(x \ ((1 / y) \ L(x,y,y)),x,y) = T(1 / (1 / y),(1 / y) * x)
    ]]></literal>
    <justification jstring="[para(1903(a,1),1685(a,1,1,2,2))].">
      <j1 rule="para" parents="1903 1685"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / x) * y) = L(y \ (x * y),y,x)
    ]]></literal>
    <justification jstring="[para(462(a,1),2026(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="462 2026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / x) * y) = L(T(x,y),y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2027(a,2,1))].">
      <j1 rule="para" parents="22 2027"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * (x \ z)) / y)),y) = y \ (K(x \ 1,x) * (y * ((1 / x) * z)))
    ]]></literal>
    <justification jstring="[para(1730(a,1),1733(a,1,1))].">
      <j1 rule="para" parents="1730 1733"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      L(x,T(y,z * z) * u,T(w,z * z)) = L(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,1580,a(flip),b,1777,a),flip(a)].">
      <j1 rule="hyper" parents="319 1580 1777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      L(x,T(1,y * y) * z,T(u,y * y)) = L(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),2030(a,2,2))].">
      <j1 rule="para" parents="7 2030"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      L(x,1 * y,T(z,u * u)) = L(x,(u * u) * y,z)
    ]]></literal>
    <justification jstring="[para(210(a,1),2032(a,1,2,1))].">
      <j1 rule="para" parents="210 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,T(u,y * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),2033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = y / y
    ]]></literal>
    <justification jstring="[para(228(a,1),1846(a,2,1))].">
      <j1 rule="para" parents="228 1846"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,75,a(flip),b,2036,a),flip(a)].">
      <j1 rule="hyper" parents="319 75 2036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(2037(a,1),1060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2037 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ x = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1411,a(flip),b,2039,a)].">
      <j1 rule="hyper" parents="64 1411 2039"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (((x / y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),2040(a,1,1,2,1))].">
      <j1 rule="para" parents="81 2040"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),2041(a,2,2,1))].">
      <j1 rule="para" parents="81 2041"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[para(2042(a,1),1875(a,1,1))].">
      <j1 rule="para" parents="2042 1875"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2043(a,1,1,2))].">
      <j1 rule="para" parents="11 2043"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2044(a,1,2,2))].">
      <j1 rule="para" parents="11 2044"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(57,a,2045,a)].">
      <j1 rule="hyper" parents="57 2045"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      ((x / (y * x)) * y) * (1 / y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,2046,a(flip),b,1056,a)].">
      <j1 rule="hyper" parents="131 2046 1056"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(399,a,2047,a)].">
      <j1 rule="hyper" parents="399 2047"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(225(a,2),2048(a,1,3))].">
      <j1 rule="para" parents="225 2048"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(206,a,2049,a(flip),b,224,a(flip))].">
      <j1 rule="hyper" parents="206 2049 224"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1488,a,2050,a)].">
      <j1 rule="hyper" parents="1488 2050"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(225(a,1),2051(a,1,2))].">
      <j1 rule="para" parents="225 2051"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2052(a,1),1606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2052 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a(flip),b,2053,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 2053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),2054(a,1,2,2))].">
      <j1 rule="para" parents="12 2054"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(130,a,2055,a(flip),b,453,a)].">
      <j1 rule="hyper" parents="130 2055 453"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2055(a,1,2))].">
      <j1 rule="para" parents="11 2055"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,667,a(flip),b,2057,a)].">
      <j1 rule="hyper" parents="64 667 2057"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(1158,a,2056,a)].">
      <j1 rule="hyper" parents="1158 2056"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1865(a,1,1,1))].">
      <j1 rule="para" parents="9 1865"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),x) = x \ T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,2060,a)].">
      <j1 rule="hyper" parents="417 2060"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(854,a,924,a),flip(a)].">
      <j1 rule="hyper" parents="854 924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2063(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(835(a,1),2063(a,2,1))].">
      <j1 rule="para" parents="835 2063"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(324,a,2064,a),flip(a)].">
      <j1 rule="hyper" parents="324 2064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(2064(a,1),324(a,1))].">
      <j1 rule="para" parents="2064 324"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1222,a,2066,a),flip(a)].">
      <j1 rule="hyper" parents="1222 2066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1145,a(flip),b,2066,a)].">
      <j1 rule="hyper" parents="64 1145 2066"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(2068(a,1),285(a,1))].">
      <j1 rule="para" parents="2068 285"/>
    </justification>
  </clause>

  <clause id="2071">
    <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(353(a,2),2069(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="353 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1220(a,1),2067(a,1))].">
      <j1 rule="para" parents="1220 2067"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(324,a,2065,a),flip(a)].">
      <j1 rule="hyper" parents="324 2065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ (u * y)))) / z)) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1145,a(flip),b,2065,a)].">
      <j1 rule="hyper" parents="64 1145 2065"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,2065,a(flip),b,1397,a),flip(a)].">
      <j1 rule="hyper" parents="244 2065 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),2065(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 2065"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1144,a(flip),b,2076,a)].">
      <j1 rule="hyper" parents="64 1144 2076"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1004,a(flip),b,2076,a),flip(a)].">
      <j1 rule="hyper" parents="64 1004 2076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(244,a,2076,a(flip),b,1827,a(flip))].">
      <j1 rule="hyper" parents="244 2076 1827"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(2076(a,1),2069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2076 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,1461,a(flip),b,2079,a)].">
      <j1 rule="hyper" parents="319 1461 2079"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      K(x,(x / T(x,y)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2079(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1465(a,1),2079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1465 2079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1461,a(flip),b,2083,a)].">
      <j1 rule="hyper" parents="64 1461 2083"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1351(a,1),2084(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1351 2084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1018(a,1),2085(a,1,2,1))].">
      <j1 rule="para" parents="1018 2085"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(35,a,2008,a,b,2087,a)].">
      <j1 rule="hyper" parents="35 2008 2087"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1628(a,2),2087(a,2,1))].">
      <j1 rule="para" parents="1628 2087"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2088(a,1),1028(a,1,1))].">
      <j1 rule="para" parents="2088 1028"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2089(a,1),1773(a,1,2))].">
      <j1 rule="para" parents="2089 1773"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2091(a,1),44(a,1))].">
      <j1 rule="para" parents="2091 44"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(78(a,1),2086(a,2,2,1))].">
      <j1 rule="para" parents="78 2086"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2093(a,1,1,2))].">
      <j1 rule="para" parents="11 2093"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2094(a,1,2,1))].">
      <j1 rule="para" parents="11 2094"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2095(a,2,2))].">
      <j1 rule="para" parents="11 2095"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,2096,a)].">
      <j1 rule="hyper" parents="55 2096"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2096,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2096 22"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2096(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2096 291"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2096(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2096 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2096(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2096 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      K(x,y) * L(K(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,x),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2096(a,1),390(a,1,2,1))].">
      <j1 rule="para" parents="2096 390"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2098(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2098 291"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2098(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2098 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      K(x,y) * R(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(y,z),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2098(a,1),391(a,1,2,1))].">
      <j1 rule="para" parents="2098 391"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1025,a,2090,a),flip(a)].">
      <j1 rule="hyper" parents="1025 2090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1268(a,1),2078(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1268 2078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2109">
    <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(445(a,2),2082(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="445 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) * y = x * (y * ((x \ (z * y)) / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),2074(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * z = (x * y) * (z * (L(y \ z,y,x) / z))
    ]]></literal>
    <justification jstring="[para(96(a,2),2110(a,2,2,2,1))].">
      <j1 rule="para" parents="96 2110"/>
    </justification>
  </clause>

  <clause id="2112">
    <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),2075(a,1,1))].">
      <j1 rule="para" parents="22 2075"/>
    </justification>
  </clause>

  <clause id="2113">
    <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),2112(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 2112"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(2076(a,1),2077(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2076 2077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((y * ((x * (y \ 1)) / x)) * z)
    ]]></literal>
    <justification jstring="[para(1461(a,2),2114(a,1,1))].">
      <j1 rule="para" parents="1461 2114"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1268(a,1),2108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1268 2108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,2116,a)].">
      <j1 rule="hyper" parents="142 2116"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2117(a,1),851(a,1,1))].">
      <j1 rule="para" parents="2117 851"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(601,a,2118,a),flip(a)].">
      <j1 rule="hyper" parents="601 2118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2119(a,1),696(a,1,1))].">
      <j1 rule="para" parents="2119 696"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(393,a,2120,a),flip(a)].">
      <j1 rule="hyper" parents="393 2120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,16,a,b,2121,a)].">
      <j1 rule="hyper" parents="319 16 2121"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),2122(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(272,a,2123,a)].">
      <j1 rule="hyper" parents="272 2123"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(1095(a,1),2123(a,1,1))].">
      <j1 rule="para" parents="1095 2123"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,2124,a)].">
      <j1 rule="hyper" parents="56 2124"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2124(a,1),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2124 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(78(a,1),2126(a,1,1))].">
      <j1 rule="para" parents="78 2126"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,2128,a)].">
      <j1 rule="hyper" parents="57 2128"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,2129,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2129 22"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(130,a,1631,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="130 1631 2125"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,2127,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 2127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      T(K(x,y),y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,2133,a)].">
      <j1 rule="hyper" parents="55 2133"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2133(a,1),378(a,2,1))].">
      <j1 rule="para" parents="2133 378"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      T(K(x,1 / y),y) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),2134(a,1,2))].">
      <j1 rule="para" parents="81 2134"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      L(1 / (1 / x),K(x,x \ 1),y) = (y * K(x,x \ 1)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2132(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="2132 18"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2132(a,1),1669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2132 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      a(x,1 / x,x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1679,a(flip),b,2136,a)].">
      <j1 rule="hyper" parents="64 1679 2136"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1626,a(flip),b,2140,a)].">
      <j1 rule="hyper" parents="64 1626 2140"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,265,a(flip),b,2141,a),flip(a)].">
      <j1 rule="hyper" parents="319 265 2141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,1631,a(flip),b,2141,a)].">
      <j1 rule="hyper" parents="131 1631 2141"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      x * (x * (1 / x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,2142,a(flip),b,311,a)].">
      <j1 rule="hyper" parents="131 2142 311"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a,b,2143,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 2143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      T(x,x \ 1) \ (x * L(y,(x * (1 / x)) \ 1,x * (1 / x))) = L(((x * (1 / x)) \ 1) * y,x * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2144(a,1),557(a,1,1))].">
      <j1 rule="para" parents="2144 557"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2145(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="2145 531"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2135(a,1,1,1))].">
      <j1 rule="para" parents="10 2135"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(1759,a,2139,a),flip(a)].">
      <j1 rule="hyper" parents="1759 2139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(305(a,1),2139(a,1,2))].">
      <j1 rule="para" parents="305 2139"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,2149,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 2149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1631(a,2),2151(a,1,1))].">
      <j1 rule="para" parents="1631 2151"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,371,a(flip),b,2148,a),flip(a)].">
      <j1 rule="hyper" parents="319 371 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,2153,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2153 22"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(2147,a,1758,a)].">
      <j1 rule="hyper" parents="2147 1758"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      R(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1693(a,1),2155(a,1,2))].">
      <j1 rule="para" parents="1693 2155"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,438,a(flip),b,1297,a),flip(a)].">
      <j1 rule="hyper" parents="319 438 1297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(949(a,1),2157(a,2,2))].">
      <j1 rule="para" parents="949 2157"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z) = (x * (T(y,x) / y)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(2158(a,1),1201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2158 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1168,a(flip),b,1428,a)].">
      <j1 rule="hyper" parents="64 1168 1428"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(39,a,427,a,b,1428,a)].">
      <j1 rule="hyper" parents="39 427 1428"/>
    </justification>
  </clause>

  <clause id="2162">
    <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(1293(a,1),1937(a,1,1))].">
      <j1 rule="para" parents="1293 1937"/>
    </justification>
  </clause>

  <clause id="2163">
    <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(1038(a,1),2162(a,1,1))].">
      <j1 rule="para" parents="1038 2162"/>
    </justification>
  </clause>

  <clause id="2164">
    <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(1934(a,1),2163(a,1,2))].">
      <j1 rule="para" parents="1934 2163"/>
    </justification>
  </clause>

  <clause id="2165">
    <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(64,a,25,a,b,2164,a)].">
      <j1 rule="hyper" parents="64 25 2164"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(1931(a,1),2165(a,1,1))].">
      <j1 rule="para" parents="1931 2165"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1038,a,b,2166,a)].">
      <j1 rule="hyper" parents="64 1038 2166"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2166(a,1),1810(a,1,2))].">
      <j1 rule="para" parents="2166 1810"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1938,a(flip),b,2167,a),flip(a)].">
      <j1 rule="hyper" parents="64 1938 2167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(732(a,1),2160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="732 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2171">
    <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(263(a,2),985(a,1,2,1,1))].">
      <j1 rule="para" parents="263 985"/>
    </justification>
  </clause>

  <clause id="2172">
    <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),1358(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(74(a,1),1390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 1390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(569,a,2173,a)].">
      <j1 rule="hyper" parents="569 2173"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2174(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2174(a,1),45(a,1))].">
      <j1 rule="para" parents="2174 45"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2176(a,2),45(a,1))].">
      <j1 rule="para" parents="2176 45"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1105(a,2),1556(a,2,2,1))].">
      <j1 rule="para" parents="1105 1556"/>
    </justification>
  </clause>

  <clause id="2180">
    <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(1628(a,2),1635(a,1,2,1,1))].">
      <j1 rule="para" parents="1628 1635"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1070(a,1),1848(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1070 1848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,2181,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1063(a,1),1850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1063 1850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,2183,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) != (x \ 1) * u
    ]]></literal>
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = u
    ]]></literal>
    <justification jstring="[para(2184(a,1),44(a,1))].">
      <j1 rule="para" parents="2184 44"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(1922(a,1),1924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1922 1924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,9,a(flip),b,2186,a),flip(a)].">
      <j1 rule="hyper" parents="319 9 2186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(935(a,1),2187(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="935 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = (x * K(y,x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(959(a,2),2187(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="959 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(940,a,2189,a),flip(a)].">
      <j1 rule="hyper" parents="940 2189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      K(x,y) / (y \ 1) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(971,a,2190,a)].">
      <j1 rule="hyper" parents="971 2190"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) / u = z
    ]]></literal>
    <justification jstring="[para(2190(a,1),971(a,1))].">
      <j1 rule="para" parents="2190 971"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),2192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="81 2192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      x \ ((x * (y * T(y \ 1,x))) \ x) = (x * (y * T(y \ 1,x))) \ 1
    ]]></literal>
    <justification jstring="[para(1922(a,1),1925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1922 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2196">
    <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(319,a,264,a(flip),b,1926,a),flip(a)].">
      <j1 rule="hyper" parents="319 264 1926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(1922(a,1),2196(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1922 2196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(959(a,2),2197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="959 2197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(959(a,2),2198(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="959 2198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),2073(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 2073"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,2200,a)].">
      <j1 rule="hyper" parents="142 2200"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2201(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      ((x * y) * ((y * ((x * y) \ x)) / y)) / x = ((x * y) / x) * ((((x * y) / x) \ y) / y)
    ]]></literal>
    <justification jstring="[para(1202(a,1),2202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1202 2202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2158(a,1),2159(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2158 2159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,1388,a(flip),b,2171,a),flip(a)].">
      <j1 rule="hyper" parents="319 1388 2171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(945(a,1),2180(a,2,2))].">
      <j1 rule="para" parents="945 2180"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(177(a,1),2206(a,2,2,1,1))].">
      <j1 rule="para" parents="177 2206"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(130,a,2207,a(flip),b,941,a)].">
      <j1 rule="hyper" parents="130 2207 941"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1696(a,1),2208(a,1,2))].">
      <j1 rule="para" parents="1696 2208"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1696(a,1),2209(a,2,1,2))].">
      <j1 rule="para" parents="1696 2209"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1610(a,1),2210(a,2,1))].">
      <j1 rule="para" parents="1610 2210"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      ((x * y) / x) * ((((x * y) / x) \ y) / y) = ((x * y) * L(1 / y,y,x)) / x
    ]]></literal>
    <justification jstring="[para(818(a,1),2203(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="818 2203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      ((x * y) / x) * ((((x * y) / x) \ y) / y) = (x * (y * (1 / y))) / x
    ]]></literal>
    <justification jstring="[para(94(a,1),2212(a,2,1))].">
      <j1 rule="para" parents="94 2212"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      ((x * y) / x) * ((((x * y) / x) \ y) / y) = (x * K(y,y \ 1)) / x
    ]]></literal>
    <justification jstring="[para(1628(a,2),2213(a,2,1,2))].">
      <j1 rule="para" parents="1628 2213"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      K(x,1 / ((y * x) / y)) = (y * K(x,x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,1831,a(flip),b,2214,a)].">
      <j1 rule="hyper" parents="64 1831 2214"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      (x * K(x \ y,(x \ y) \ 1)) / x = K(x \ y,1 / (y / x))
    ]]></literal>
    <justification jstring="[para(10(a,1),2215(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2217">
    <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(319,a,433,a(flip),b,729,a),flip(a)].">
      <j1 rule="hyper" parents="319 433 729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1045,a,2217,a)].">
      <j1 rule="hyper" parents="1045 2217"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      (T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(584,a,2218,a),flip(a)].">
      <j1 rule="hyper" parents="584 2218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(1045,a,1189,a),flip(a)].">
      <j1 rule="hyper" parents="1045 1189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(733(a,1),2220(a,2,2))].">
      <j1 rule="para" parents="733 2220"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(488,a,2221,a)].">
      <j1 rule="hyper" parents="488 2221"/>
    </justification>
  </clause>

  <clause id="2223">
    <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(319,a,1102,a(flip),b,2222,a)].">
      <j1 rule="hyper" parents="319 1102 2222"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(935(a,1),2222(a,1,1))].">
      <j1 rule="para" parents="935 2222"/>
    </justification>
  </clause>

  <clause id="2225">
    <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),2224(a,2,1,2))].">
      <j1 rule="para" parents="11 2224"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      L(x \ T(x,(y * x) \ y),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(422(a,1),2224(a,2,1,2))].">
      <j1 rule="para" parents="422 2224"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      L(x * T(x \ 1,L(x,y,z)),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(2223(a,1),590(a,1))].">
      <j1 rule="para" parents="2223 590"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      L(T(K(x,(y * x) \ y),x),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2061(a,2),2226(a,1,1))].">
      <j1 rule="para" parents="2061 2226"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1271(a,1),1364(a,2,1))].">
      <j1 rule="para" parents="1271 1364"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1322(a,1),2229(a,2,1,1))].">
      <j1 rule="para" parents="1322 2229"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,2230,a)].">
      <j1 rule="hyper" parents="319 20 2230"/>
    </justification>
  </clause>

  <clause id="2232">
    <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(319,a,1102,a(flip),b,2231,a)].">
      <j1 rule="hyper" parents="319 1102 2231"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      R(T(x,x \ 1) * T(T(x,x \ 1) \ 1,x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1073(a,1),2231(a,2,1,2))].">
      <j1 rule="para" parents="1073 2231"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) = (R(x,y,z) \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(291,a,2232,a),flip(a)].">
      <j1 rule="hyper" parents="291 2232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T(R(1 / x,K(x \ 1,x),z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2156(a,1),2232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2156 2232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2237">
    <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(64,a,1554,a(flip),b,1425,a)].">
      <j1 rule="hyper" parents="64 1554 1425"/>
    </justification>
  </clause>

  <clause id="2239">
    <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(2237(a,1),921(a,1,1))].">
      <j1 rule="para" parents="2237 921"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      a(L(x \ ((y * y) \ z),(y * y) * x,(y * y) * x),u,w) = a((y * y) * (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(416(a,1),1967(a,1,1,1))].">
      <j1 rule="para" parents="416 1967"/>
    </justification>
  </clause>

  <clause id="2241">
    <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(2239,a,650,a)].">
      <j1 rule="hyper" parents="2239 650"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1469,a(flip),b,2241,a),flip(a)].">
      <j1 rule="hyper" parents="64 1469 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      a(L(x \ ((y * y) \ z),(y * y) * x,x),u,w) = a((y * y) * (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(1578(a,1),2240(a,1,1))].">
      <j1 rule="para" parents="1578 2240"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,959,a,b,973,a),flip(a)].">
      <j1 rule="hyper" parents="319 959 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2246">
    <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(2245(a,1),393(a,1,1))].">
      <j1 rule="para" parents="2245 393"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(263(a,2),997(a,1,2,1,1))].">
      <j1 rule="para" parents="263 997"/>
    </justification>
  </clause>

  <clause id="2248">
    <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(263(a,2),999(a,1,2,1,1))].">
      <j1 rule="para" parents="263 999"/>
    </justification>
  </clause>

  <clause id="2249">
    <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(868(a,1),1161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="868 1161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      (x \ 1) \ (L((1 / x) * y,z,u) * K(x \ 1,x)) = x * T(L(x \ y,z,u),(x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(263(a,2),1746(a,1,2,2))].">
      <j1 rule="para" parents="263 1746"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      T(L(x * T(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(2223(a,1),1801(a,1,1))].">
      <j1 rule="para" parents="2223 1801"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      T(L(K(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(348(a,1),2251(a,1,1,1))].">
      <j1 rule="para" parents="348 2251"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      T(L(K(x \ 1,x),y,z),L(x,y,z) \ x) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(1169(a,1),2252(a,1,2))].">
      <j1 rule="para" parents="1169 2252"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,2253,a)].">
      <j1 rule="hyper" parents="64 25 2253"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1173(a,1),2254(a,2,1))].">
      <j1 rule="para" parents="1173 2254"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      K(x \ y,x) * R((y \ ((x \ y) * x)) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(89(a,1),2013(a,1,1))].">
      <j1 rule="para" parents="89 2013"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      K(x \ y,x) * R(K(x \ y,x) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(89(a,1),2256(a,1,2,1,1))].">
      <j1 rule="para" parents="89 2256"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * R((x \ 1) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,1473,a(flip),b,2247,a),flip(a)].">
      <j1 rule="hyper" parents="319 1473 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2259">
    <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(319,a,1558,a(flip),b,2248,a),flip(a)].">
      <j1 rule="hyper" parents="319 1558 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(990(a,1),2258(a,2,1))].">
      <j1 rule="para" parents="990 2258"/>
    </justification>
  </clause>

  <clause id="2261">
    <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(988(a,1),2259(a,2,1))].">
      <j1 rule="para" parents="988 2259"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      a(x,x \ y,L(T(x,x \ y),z,u)) = (L(x,z,u) * y) \ (y * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),1968(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x)) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1556,a(flip),b,2179,a),flip(a)].">
      <j1 rule="hyper" parents="64 1556 2179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      T(x,y) * (T(1 / (1 / x),y) \ 1) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1992(a,1),2271(a,1,2))].">
      <j1 rule="para" parents="1992 2271"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(1 / (1 / x),y) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1993,a(flip),b,2272,a),flip(a)].">
      <j1 rule="hyper" parents="64 1993 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2274">
    <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(1544(a,1),2225(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1544 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(68(a,1),2274(a,2,1))].">
      <j1 rule="para" parents="68 2274"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,359,a(flip),b,2275,a),flip(a)].">
      <j1 rule="hyper" parents="319 359 2275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x * 1
    ]]></literal>
    <justification jstring="[hyper(131,a,2276,a(flip),b,89,a),flip(a)].">
      <j1 rule="hyper" parents="131 2276 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a(flip),b,2279,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 2279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      K((1 / x) \ ((1 / x) * T((1 / x) \ 1,y)),1 / x) = (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1991(a,1),1116(a,1,1,2))].">
      <j1 rule="para" parents="1991 1116"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K((1 / x) \ (T(x,y) / x),1 / x)
    ]]></literal>
    <justification jstring="[para(948(a,1),2285(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="948 2285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(952(a,1),2286(a,2,1))].">
      <j1 rule="para" parents="952 2286"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ T(x,y) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(454(a,1),2287(a,1,1))].">
      <j1 rule="para" parents="454 2287"/>
    </justification>
  </clause>

  <clause id="2289">
    <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(819(a,1),1916(a,2,1))].">
      <j1 rule="para" parents="819 1916"/>
    </justification>
  </clause>

  <clause id="2290">
    <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(319,a,2249,a(flip),b,2289,a),flip(a)].">
      <j1 rule="hyper" parents="319 2249 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2291">
    <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(1431(a,1),1917(a,2,2,1))].">
      <j1 rule="para" parents="1431 1917"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2291(a,2,2))].">
      <j1 rule="para" parents="11 2291"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2292,a(flip),b,2290,a(flip))].">
      <j1 rule="hyper" parents="131 2292 2290"/>
    </justification>
  </clause>

  <clause id="2295">
    <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(1040(a,1),2109(a,2,2,1))].">
      <j1 rule="para" parents="1040 2109"/>
    </justification>
  </clause>

  <clause id="2296">
    <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(1472(a,1),2295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1472 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1830,a(flip),b,2296,a)].">
      <j1 rule="hyper" parents="64 1830 2296"/>
    </justification>
  </clause>

  <clause id="2298">
    <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(2297(a,1),1678(a,1))].">
      <j1 rule="para" parents="2297 1678"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2298,a,2009,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2298 2009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2009(a,2),2298(a,1))].">
      <j1 rule="para" parents="2009 2298"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1628,a(flip),b,2299,a),flip(a)].">
      <j1 rule="hyper" parents="35 1628 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      (T(x,y) / x) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(145,a,2301,a)].">
      <j1 rule="hyper" parents="145 2301"/>
    </justification>
  </clause>

  <clause id="2303">
    <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(270(a,1),2301(a,1,2))].">
      <j1 rule="para" parents="270 2301"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2273(a,1),2300(a,1))].">
      <j1 rule="para" parents="2273 2300"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(2304,a,2288,a)].">
      <j1 rule="hyper" parents="2304 2288"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1319(a,1),2303(a,1,1))].">
      <j1 rule="para" parents="1319 2303"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,1985,a(flip),b,2306,a),flip(a)].">
      <j1 rule="hyper" parents="64 1985 2306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(199,a,2307,a),flip(a)].">
      <j1 rule="hyper" parents="199 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      1 / T(x \ 1,y) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(318(a,1),2307(a,1,2,1))].">
      <j1 rule="para" parents="318 2307"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(347(a,1),2307(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="347 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(110(a,1),2308(a,1,1))].">
      <j1 rule="para" parents="110 2308"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(318(a,1),2308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="318 2308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(207,a,2310,a)].">
      <j1 rule="hyper" parents="207 2310"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,2311,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2311 22"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,1 / x,1 / x) = 1 / (1 / T(x,(1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,464,a,b,2313,a)].">
      <j1 rule="hyper" parents="319 464 2313"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1610,a,b,2313,a)].">
      <j1 rule="hyper" parents="64 1610 2313"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(111(a,1),2313(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 2313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(735,a,2315,a)].">
      <j1 rule="hyper" parents="735 2315"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(111(a,1),2315(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="111 2315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1026,a,2319,a)].">
      <j1 rule="hyper" parents="1026 2319"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,2143,a,b,2319,a),flip(a)].">
      <j1 rule="hyper" parents="319 2143 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2092,a,2322,a)].">
      <j1 rule="hyper" parents="2092 2322"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,2323,a)].">
      <j1 rule="hyper" parents="55 2323"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,2323,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 2323 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(127,a,2323,a(flip),b,2089,a)].">
      <j1 rule="hyper" parents="127 2323 2089"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2323(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2323 291"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      T(x,y * (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(1628(a,1),2324(a,1,2))].">
      <j1 rule="para" parents="1628 2324"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      T(x,K(y,1 / y)) = x
    ]]></literal>
    <justification jstring="[para(1631(a,2),2324(a,1,2))].">
      <j1 rule="para" parents="1631 2324"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1640(a,1),2324(a,1,2))].">
      <j1 rule="para" parents="1640 2324"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      x / (y * (1 / y)) = (y * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,2330,a),flip(a)].">
      <j1 rule="hyper" parents="393 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(78(a,1),2330(a,1,2,2))].">
      <j1 rule="para" parents="78 2330"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(2178,a,2331,a),flip(a)].">
      <j1 rule="hyper" parents="2178 2331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2178,a,2332,a),flip(a)].">
      <j1 rule="hyper" parents="2178 2332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(55,a,2332,a)].">
      <j1 rule="hyper" parents="55 2332"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      K(x \ 1,x) * y != z * K(x \ 1,x)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2332(a,1),246(a,1,2))].">
      <j1 rule="para" parents="2332 246"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2332(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2332 291"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2332(a,1),229(a,1,2,2))].">
      <j1 rule="para" parents="2332 229"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      x \ y != K(z \ 1,z) * u
    ]]></literal>
    <literal><![CDATA[
      x * (u * K(z \ 1,z)) = y
    ]]></literal>
    <justification jstring="[para(2332(a,1),582(a,2,2))].">
      <j1 rule="para" parents="2332 582"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(2178,a,2336,a),flip(a)].">
      <j1 rule="hyper" parents="2178 2336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1799,a,b,2340,a)].">
      <j1 rule="hyper" parents="64 1799 2340"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(263(a,1),2340(a,1,1))].">
      <j1 rule="para" parents="263 2340"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(2340(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2340 291"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2340(a,1),2255(a,1,1))].">
      <j1 rule="para" parents="2340 2255"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,1632,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="319 1632 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1715,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="64 1715 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (((x \ 1) * y) * z) * K(x,x \ 1) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,1711,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="64 1711 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1705,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="64 1705 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1704,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="64 1704 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2325(a,1),1669(a,1,1))].">
      <j1 rule="para" parents="2325 1669"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1665,a,b,2337,a)].">
      <j1 rule="hyper" parents="64 1665 2337"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2152,a(flip),b,2337,a),flip(a)].">
      <j1 rule="hyper" parents="64 2152 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,1610,a(flip),b,2339,a),flip(a)].">
      <j1 rule="hyper" parents="319 1610 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y * T(y \ (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,1057,a(flip),b,2339,a),flip(a)].">
      <j1 rule="hyper" parents="319 1057 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1725,a,b,2339,a)].">
      <j1 rule="hyper" parents="64 1725 2339"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1723,a,b,2339,a)].">
      <j1 rule="hyper" parents="64 1723 2339"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1728,a(flip),b,2339,a),flip(a)].">
      <j1 rule="hyper" parents="64 1728 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1722,a(flip),b,2339,a),flip(a)].">
      <j1 rule="hyper" parents="64 1722 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1691,a(flip),b,2339,a),flip(a)].">
      <j1 rule="hyper" parents="64 1691 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1007,a,2339,a(flip))].">
      <j1 rule="hyper" parents="1007 2339"/>
    </justification>
  </clause>

  <clause id="2366">
    <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(2339(a,2),654(a,1,1))].">
      <j1 rule="para" parents="2339 654"/>
    </justification>
  </clause>

  <clause id="2367">
    <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(2339(a,1),743(a,1,2))].">
      <j1 rule="para" parents="2339 743"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((y * (x \ 1)) * x) = a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2339(a,2),351(a,1,1))].">
      <j1 rule="para" parents="2339 351"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(2339(a,1),1672(a,1,1))].">
      <j1 rule="para" parents="2339 1672"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(769,a,2345,a)].">
      <j1 rule="hyper" parents="769 2345"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,263,a,b,2370,a),flip(a)].">
      <j1 rule="hyper" parents="319 263 2370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2346(a,1),1108(a,1,1))].">
      <j1 rule="para" parents="2346 1108"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (1 / (1 / x)) = u
    ]]></literal>
    <justification jstring="[para(2346(a,2),1643(a,1,2))].">
      <j1 rule="para" parents="2346 1643"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(279,a,2318,a)].">
      <j1 rule="hyper" parents="279 2318"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,2321,a)].">
      <j1 rule="hyper" parents="145 2321"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,2349,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 2349 18"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2380(a,1),1764(a,1,1))].">
      <j1 rule="para" parents="2380 1764"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2380(a,1),2361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2380 2361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1158,a,2320,a)].">
      <j1 rule="hyper" parents="1158 2320"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,2320,a)].">
      <j1 rule="hyper" parents="142 2320"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,151,a(flip),b,2356,a)].">
      <j1 rule="hyper" parents="128 151 2356"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) * (x / L(x,y,z)) = x * T(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1538(a,1),2359(a,2,2))].">
      <j1 rule="para" parents="1538 2359"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ ((y * K(x \ 1,x)) * (z * u)) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2369(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2369 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * K(z \ 1,z),x) = u
    ]]></literal>
    <justification jstring="[para(2369(a,1),338(a,1,2))].">
      <j1 rule="para" parents="2369 338"/>
    </justification>
  </clause>

  <clause id="2391">
    <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(2369(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="2369 489"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * ((1 / x) * z))) / ((x \ 1) * z) = R(y,K(x \ 1,x),(1 / x) * z)
    ]]></literal>
    <justification jstring="[para(2369(a,1),1726(a,1,1))].">
      <j1 rule="para" parents="2369 1726"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),2375(a,1,1,2,2,2))].">
      <j1 rule="para" parents="9 2375"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,2382,a)].">
      <j1 rule="hyper" parents="529 2382"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      x * ((T(x,y) \ 1) * K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1018(a,1),2382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1018 2382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2394(a,1),27(a,2,1))].">
      <j1 rule="para" parents="2394 27"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x \ 1,x) = T(x,y) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2396(a,1),402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2396 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2384(a,2,1,1))].">
      <j1 rule="para" parents="9 2384"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2059,a(flip),b,2398,a)].">
      <j1 rule="hyper" parents="64 2059 2398"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a,b,2399,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 2399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),2399(a,1,2,2))].">
      <j1 rule="para" parents="10 2399"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1607,a,2401,a(flip))].">
      <j1 rule="hyper" parents="1607 2401"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),2403(a,1,2,2))].">
      <j1 rule="para" parents="12 2403"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(2404(a,1),233(a,1,2,2))].">
      <j1 rule="para" parents="2404 233"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2402(a,1,2))].">
      <j1 rule="para" parents="11 2402"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(78(a,1),2402(a,1,2))].">
      <j1 rule="para" parents="78 2402"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2407(a,1),1731(a,1,2))].">
      <j1 rule="para" parents="2407 1731"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      R(x / (y / K(z,1 / z)),y / K(z,1 / z),K(z,1 / z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(807,a,2386,a)].">
      <j1 rule="hyper" parents="807 2386"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ (((x / (x * L(x \ 1,y,z))) * (x * L(x \ 1,y,z))) / x) = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(1852(a,2),2405(a,1,2))].">
      <j1 rule="para" parents="1852 2405"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,2408,a(flip),b,2320,a)].">
      <j1 rule="hyper" parents="128 2408 2320"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(81(a,1),2408(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="81 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(207,a,2412,a)].">
      <j1 rule="hyper" parents="207 2412"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(206,a,2320,a,b,2412,a)].">
      <j1 rule="hyper" parents="206 2320 2412"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2414(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9 2414"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2415(a,1,2,1,1,1))].">
      <j1 rule="para" parents="11 2415"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2058,a,b,2417,a)].">
      <j1 rule="hyper" parents="319 2058 2417"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,223,a,b,2418,a)].">
      <j1 rule="hyper" parents="319 223 2418"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      T(R(x \ 1,x,y),((x \ 1) \ 1) * y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2418(a,2),111(a,1,1))].">
      <j1 rule="para" parents="2418 111"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(110(a,2),2418(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="110 2418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      L((x \ 1) * ((1 / x) \ y),x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(2360(a,2),2381(a,1,1))].">
      <j1 rule="para" parents="2360 2381"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1757,a,2350,a)].">
      <j1 rule="hyper" parents="1757 2350"/>
    </justification>
  </clause>

  <clause id="2429">
    <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(319,a,1646,a(flip),b,2428,a),flip(a)].">
      <j1 rule="hyper" parents="319 1646 2428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2430">
    <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(800,a,2368,a)].">
      <j1 rule="hyper" parents="800 2368"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u \ 1,u))
    ]]></literal>
    <literal><![CDATA[
      K(L(u,y,x) \ 1,u) = z
    ]]></literal>
    <justification jstring="[para(2377(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2377 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2374,a,1111,a(flip))].">
      <j1 rule="hyper" parents="2374 1111"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      R(T(x \ 1,((x \ 1) \ 1) * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,2421,a)].">
      <j1 rule="hyper" parents="64 27 2421"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(1921(a,1),2436(a,1,1))].">
      <j1 rule="para" parents="1921 2436"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1006,a(flip),b,2437,a)].">
      <j1 rule="hyper" parents="64 1006 2437"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(110(a,2),2438(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="110 2438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2364(a,1),1396(a,1,1))].">
      <j1 rule="para" parents="2364 1396"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = x * (T(x,y) \ K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2397(a,1),2395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2397 2395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,1642,a(flip),b,2441,a),flip(a)].">
      <j1 rule="hyper" parents="319 1642 2441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = 1 / (1 / T(x,(1 / x) * y))
    ]]></literal>
    <justification jstring="[para(1903(a,1),2316(a,1,2))].">
      <j1 rule="para" parents="1903 2316"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      ((x \ 1) * x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1851,a(flip),b,2440,a)].">
      <j1 rule="hyper" parents="64 1851 2440"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(628,a,2444,a)].">
      <j1 rule="hyper" parents="628 2444"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2365(a,1),2430(a,1,1,2))].">
      <j1 rule="para" parents="2365 2430"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1676,a,2447,a)].">
      <j1 rule="hyper" parents="1676 2447"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1693(a,1),2429(a,1,1))].">
      <j1 rule="para" parents="1693 2429"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(991(a,1),2450(a,1,2))].">
      <j1 rule="para" parents="991 2450"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2446,a(flip),b,2451,a)].">
      <j1 rule="hyper" parents="64 2446 2451"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,1867,a(flip),b,2452,a),flip(a)].">
      <j1 rule="hyper" parents="319 1867 2452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2440,a,b,2453,a(flip))].">
      <j1 rule="hyper" parents="36 2440 2453"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,224,a(flip),b,2454,a)].">
      <j1 rule="hyper" parents="319 224 2454"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(224(a,1),2455(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="224 2455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2456,a)].">
      <j1 rule="hyper" parents="134 2456"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,2456,a(flip),b,2161,a),flip(a)].">
      <j1 rule="hyper" parents="126 2456 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,2458,a(flip),b,2170,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 2458 2170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a,b,2459,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,2459,a(flip),b,2060,a),flip(a)].">
      <j1 rule="hyper" parents="128 2459 2060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),2459(a,1,2,1))].">
      <j1 rule="para" parents="10 2459"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(1607,a,2460,a(flip))].">
      <j1 rule="hyper" parents="1607 2460"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(88(a,1),2460(a,1,2,1))].">
      <j1 rule="para" parents="88 2460"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      (((x * y) \ x) * y) / ((x * y) \ x) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(279,a,2463,a)].">
      <j1 rule="hyper" parents="279 2463"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,1630,a(flip),b,2461,a),flip(a)].">
      <j1 rule="hyper" parents="319 1630 2461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2467(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),2467(a,1,2,1))].">
      <j1 rule="para" parents="12 2467"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2467(a,2),1696(a,1,1))].">
      <j1 rule="para" parents="2467 1696"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2467(a,2),2323(a,1,1))].">
      <j1 rule="para" parents="2467 2323"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,684,a,b,2469,a)].">
      <j1 rule="hyper" parents="64 684 2469"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(81(a,1),2462(a,1,2))].">
      <j1 rule="para" parents="81 2462"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2462(a,2),1803(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2462 1803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      (x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2462(a,2),2385(a,1,1,2))].">
      <j1 rule="para" parents="2462 2385"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2471(a,1),2228(a,1,1))].">
      <j1 rule="para" parents="2471 2228"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2457(a,1),302(a,1,1))].">
      <j1 rule="para" parents="2457 302"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1641,a,2468,a)].">
      <j1 rule="hyper" parents="1641 2468"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2468(a,2,2))].">
      <j1 rule="para" parents="9 2468"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      (x * K(x \ y,y \ x)) / x = K(x \ y,1 / (y / x))
    ]]></literal>
    <justification jstring="[para(2468(a,1),2216(a,1,1,2))].">
      <j1 rule="para" parents="2468 2216"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(2468(a,1),2324(a,1,2))].">
      <j1 rule="para" parents="2468 2324"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) / x != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(2483(a,1),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2483 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      L(x,(y * x) \ y,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1552,a(flip),b,2465,a)].">
      <j1 rule="hyper" parents="64 1552 2465"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),2485(a,1,2,1))].">
      <j1 rule="para" parents="10 2485"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      x * K(x \ y,(x \ y) \ 1) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2487(a,1),1868(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2487 1868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,447,a(flip),b,2476,a)].">
      <j1 rule="hyper" parents="64 447 2476"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),2464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(404,a,2490,a),flip(a)].">
      <j1 rule="hyper" parents="404 2490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2098,a(flip),b,2491,a),flip(a)].">
      <j1 rule="hyper" parents="64 2098 2491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2492(a,1),200(a,1,2,2))].">
      <j1 rule="para" parents="2492 200"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / y = K(y \ x,1 / (x / y))
    ]]></literal>
    <justification jstring="[para(2488(a,1),2216(a,1,1))].">
      <j1 rule="para" parents="2488 2216"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2468(a,1),2488(a,1,2))].">
      <j1 rule="para" parents="2468 2488"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[para(2472(a,1),2497(a,1,2))].">
      <j1 rule="para" parents="2472 2497"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      K(((x * y) / x) \ y,1 / (y / ((x * y) / x))) = (y * (1 / (1 / K(x,(x / (y \ 1)) / x)))) / ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(1462(a,2),2496(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1462 2496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ ((x * (y * z)) / L(z,y,x))))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(197(a,1),2498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="197 2498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2478(a,2),409(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2478 409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      K(x \ y,1 / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(2482(a,1),2484(a,1))].">
      <j1 rule="para" parents="2482 2484"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(266(a,1),2479(a,2,1))].">
      <j1 rule="para" parents="266 2479"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2481,a(flip),b,2501,a)].">
      <j1 rule="hyper" parents="64 2481 2501"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1802,a(flip),b,2475,a),flip(a)].">
      <j1 rule="hyper" parents="64 1802 2475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2507">
    <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),2506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),2507(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2508(a,2,2))].">
      <j1 rule="para" parents="9 2508"/>
    </justification>
  </clause>

  <clause id="2511">
    <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(2509(a,1),2246(a,1))].">
      <j1 rule="para" parents="2509 2246"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ (K(x \ 1,x) * (y * (z * u))) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2369(a,1),2389(a,1,2))].">
      <j1 rule="para" parents="2369 2389"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * ((1 / x) * z)) / ((x \ 1) * z)) = R(y,K(x \ 1,x),(1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1674,a(flip),b,2392,a)].">
      <j1 rule="hyper" parents="64 1674 2392"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u \ 1,u)) = L(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(801,a,2512,a)].">
      <j1 rule="hyper" parents="801 2512"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1676,a,2514,a),flip(a)].">
      <j1 rule="hyper" parents="1676 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2517">
    <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(2367,a,2366,a),flip(a)].">
      <j1 rule="hyper" parents="2367 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,1667,a(flip),b,2517,a),flip(a)].">
      <j1 rule="hyper" parents="319 1667 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2519">
    <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(2517(a,2),1675(a,1)),flip(b)].">
      <j1 rule="para" parents="2517 1675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(41,a,926,a(flip),b,2518,a(flip))].">
      <j1 rule="hyper" parents="41 926 2518"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      x \ (y * K(x \ 1,x)) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1336(a,1),2521(a,1,1))].">
      <j1 rule="para" parents="1336 2521"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(39,a,1707,a(flip),b,2523,a),flip(a)].">
      <j1 rule="hyper" parents="39 1707 2523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(39,a,1707,a,b,2523,a(flip))].">
      <j1 rule="hyper" parents="39 1707 2523"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(2348,a,2524,a)].">
      <j1 rule="hyper" parents="2348 2524"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,2362,a,b,2524,a),flip(a)].">
      <j1 rule="hyper" parents="36 2362 2524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,2339,a(flip),b,2524,a),flip(a)].">
      <j1 rule="hyper" parents="36 2339 2524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(127,a,2524,a(flip),b,2339,a)].">
      <j1 rule="hyper" parents="127 2524 2339"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2524(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2524 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      R((K(x,x \ 1) * y) / z,z,K(x \ 1,x)) = y / (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2524(a,1),106(a,2,1))].">
      <j1 rule="para" parents="2524 106"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1715(a,1),2524(a,1,1))].">
      <j1 rule="para" parents="1715 2524"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2139(a,1),2524(a,1,1))].">
      <j1 rule="para" parents="2139 2524"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(2524(a,1),2341(a,2)),flip(b)].">
      <j1 rule="para" parents="2524 2341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),2521(a,1,2))].">
      <j1 rule="para" parents="2524 2521"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2525(a,1),1712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2525 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,1783,a(flip),b,2526,a),flip(a)].">
      <j1 rule="hyper" parents="35 1783 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(35,a,1672,a(flip),b,2526,a),flip(a)].">
      <j1 rule="hyper" parents="35 1672 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1715(a,1),2526(a,1,2))].">
      <j1 rule="para" parents="1715 2526"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2526(a,1),1673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2526 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[para(2325(a,1),2526(a,1,2))].">
      <j1 rule="para" parents="2325 2526"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2528(a,1),1712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2528 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2528(a,1),2149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2528 2149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2529(a,1),2205(a,1,2,1))].">
      <j1 rule="para" parents="2529 2205"/>
    </justification>
  </clause>

  <clause id="2547">
    <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(2529(a,1),2261(a,1,2,1))].">
      <j1 rule="para" parents="2529 2261"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2542(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2542 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(2542(a,1),1673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2542 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      (x \ y) \ (K(x,x \ 1) * z) = (((x \ 1) \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2527(a,1),1670(a,1,1))].">
      <j1 rule="para" parents="2527 1670"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,2532,a(flip),b,2361,a),flip(a)].">
      <j1 rule="hyper" parents="127 2532 2361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2532(a,1),2515(a,1,3))].">
      <j1 rule="para" parents="2532 2515"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1693(a,2),2537(a,1,2,2))].">
      <j1 rule="para" parents="1693 2537"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2442(a,1),2537(a,1,2))].">
      <j1 rule="para" parents="2442 2537"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(1258,a,2545,a),flip(a)].">
      <j1 rule="hyper" parents="1258 2545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1602(a,1),2549(a,2,2))].">
      <j1 rule="para" parents="1602 2549"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * (x * ((1 / y) * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ 1) * z,K(y,y \ 1),x) = u
    ]]></literal>
    <justification jstring="[para(2549(a,1),1710(a,1))].">
      <j1 rule="para" parents="2549 1710"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) \ ((T(x,y) \ 1) \ z) = T(x,y) \ ((1 / T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(2311(a,2),2551(a,1,1))].">
      <j1 rule="para" parents="2311 2551"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1602(a,1),2538(a,1,2,1))].">
      <j1 rule="para" parents="1602 2538"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2435(a,1),2554(a,1,2))].">
      <j1 rule="para" parents="2435 2554"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(127,a,2107,a(flip),b,2561,a(flip))].">
      <j1 rule="hyper" parents="127 2107 2561"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1989,a(flip),b,2562,a)].">
      <j1 rule="hyper" parents="64 1989 2562"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      T(1 / x,y) \ (1 / x) = x \ (T(1 / x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(81(a,1),2562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="81 2562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(111(a,1),2563(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 2563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(1 / x,y) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(942(a,1),2563(a,1,1))].">
      <j1 rule="para" parents="942 2563"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(111(a,1),2565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 2565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2567(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = x \ (T(1 / x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,2564,a(flip),b,2566,a),flip(a)].">
      <j1 rule="hyper" parents="319 2564 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      (x \ y) \ (T(1 / (x \ y),z) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1180(a,1),2569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1180 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      R(K(x,x \ 1) * (y / z),z,K(x \ 1,x)) = y / (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1671(a,1),2531(a,1,1))].">
      <j1 rule="para" parents="1671 2531"/>
    </justification>
  </clause>

  <clause id="2573">
    <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),2547(a,1,2,1,2))].">
      <j1 rule="para" parents="12 2547"/>
    </justification>
  </clause>

  <clause id="2574">
    <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(2325(a,1),2573(a,1,2,1))].">
      <j1 rule="para" parents="2325 2573"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * (x \ z)) / y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      L((x \ 1) * z,K(x,x \ 1),y) = u
    ]]></literal>
    <justification jstring="[para(2029(a,2),2558(a,1))].">
      <j1 rule="para" parents="2029 2558"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T((1 / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2156(a,1),2236(a,2,2,1,1))].">
      <j1 rule="para" parents="2156 2236"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (z * R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,436,a(flip),b,1479,a),flip(a)].">
      <j1 rule="hyper" parents="319 436 1479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(243(a,1),2578(a,2,2))].">
      <j1 rule="para" parents="243 2578"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) \ (y / (x * z))),x \ 1,x) = T(y / ((x \ 1) * z),(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(78(a,1),1687(a,1,1,2,2,2,1))].">
      <j1 rule="para" parents="78 1687"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),(y \ 1) * (y \ 1)) = y * ((y \ 1) \ (x / (y * z)))
    ]]></literal>
    <justification jstring="[hyper(588,a,2580,a),flip(a)].">
      <j1 rule="hyper" parents="588 2580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = (x \ 1) * R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1550(a,1),1980(a,2,1))].">
      <j1 rule="para" parents="1550 1980"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,1070,a(flip),b,2583,a),flip(a)].">
      <j1 rule="hyper" parents="319 1070 2583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      T(x \ R(x,y,z),x \ L(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1070(a,1),2584(a,1,1))].">
      <j1 rule="para" parents="1070 2584"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ R(x,u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,2586,a)].">
      <j1 rule="hyper" parents="55 2586"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2427(a,1),1998(a,1,1))].">
      <j1 rule="para" parents="2427 1998"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      L(((x * (1 / x)) \ 1) * y,x * (1 / x),x) = T(x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1659(a,1),2146(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1659 2146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      K(((x * y) / x) \ y,1 / (y / ((x * y) / x))) = (y * K(x,(x / (y \ 1)) / x)) / ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2495(a,1),2499(a,2,1,2))].">
      <j1 rule="para" parents="2495 2499"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      K(((x * y) / x) \ y,1 / (y / ((x * y) / x))) = ((x * y) / x) / ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(1464(a,1),2590(a,2,1))].">
      <j1 rule="para" parents="1464 2590"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      K(((x * y) / x) \ y,1 / (y / ((x * y) / x))) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,75,a(flip),b,2591,a),flip(a)].">
      <j1 rule="hyper" parents="319 75 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      K(((x * y) / x) \ y,y \ ((x * y) / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(2503,a,2592,a)].">
      <j1 rule="hyper" parents="2503 2592"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      1 / (((x * y) / x) \ y) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,2593,a(flip),b,2480,a),flip(a)].">
      <j1 rule="hyper" parents="127 2593 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      ((((x * y) / x) \ y) \ 1) \ 1 = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(199,a,2595,a)].">
      <j1 rule="hyper" parents="199 2595"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      (x \ ((y * x) / y)) \ 1 = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[para(2571(a,1),2596(a,1,1))].">
      <j1 rule="para" parents="2571 2596"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) \ y = (y \ (y * (x * T(x \ 1,y)))) \ 1
    ]]></literal>
    <justification jstring="[para(1922(a,1),2597(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1922 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) \ y = (x * T(x \ 1,y)) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2598(a,2,1))].">
      <j1 rule="para" parents="9 2598"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) \ y = x \ (T(1 / x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,2569,a(flip),b,2599,a),flip(a)].">
      <j1 rule="hyper" parents="319 2569 2599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) \ x = y \ (T(1 / y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(1922(a,1),2600(a,1,1))].">
      <j1 rule="para" parents="1922 2600"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) \ 1 = x \ (y \ (T(1 / y,x) \ 1))
    ]]></literal>
    <justification jstring="[para(2602(a,1),2195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2602 2195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      x \ (((x * y) \ x) \ (T(1 / ((x * y) \ x),x) \ 1)) = (x * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(959(a,2),2603(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="959 2603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      x \ (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = (x * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(2570(a,1),2604(a,1,2))].">
      <j1 rule="para" parents="2570 2604"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      x \ (((x * y) \ (x * T(y,x))) \ 1) = (x * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2605(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="9 2605"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      x \ (((x * y) \ (y * x)) \ 1) = (x * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(109(a,1),2606(a,1,2,1,2))].">
      <j1 rule="para" parents="109 2606"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ (K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(16(a,2),2607(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 2607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <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(94(a,1),1178(a,1,2,1,1))].">
      <j1 rule="para" parents="94 1178"/>
    </justification>
  </clause>

  <clause id="2610">
    <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(1159,a,2609,a),flip(a)].">
      <j1 rule="hyper" parents="1159 2609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2611">
    <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(983(a,1),2610(a,2,2))].">
      <j1 rule="para" parents="983 2610"/>
    </justification>
  </clause>

  <clause id="2612">
    <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(488,a,2611,a),flip(a)].">
      <j1 rule="hyper" parents="488 2611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <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(64,a,1067,a(flip),b,2612,a),flip(a)].">
      <j1 rule="hyper" parents="64 1067 2612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2614">
    <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(1555(a,1),2613(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1555 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2615">
    <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(2227,a,2614,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2227 2614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,263,a(flip),b,2615,a),flip(a)].">
      <j1 rule="hyper" parents="36 263 2615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(81(a,1),2616(a,1,1))].">
      <j1 rule="para" parents="81 2616"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(991(a,1),2617(a,1,2))].">
      <j1 rule="para" parents="991 2617"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,2618,a)].">
      <j1 rule="hyper" parents="144 2618"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,2280,a,b,2619,a)].">
      <j1 rule="hyper" parents="36 2280 2619"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1420(a,1),2620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1420 2620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2622">
    <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(319,a,2069,a(flip),b,2071,a),flip(a)].">
      <j1 rule="hyper" parents="319 2069 2071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      R(T(x,x \ 1) * T(T(x \ 1,x),x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1337(a,1),2234(a,1,1,2,1))].">
      <j1 rule="para" parents="1337 2234"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(T(x,x \ 1) * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(1508(a,1),2623(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1508 2623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2626">
    <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(94(a,1),1415(a,1,2,1,2,1))].">
      <j1 rule="para" parents="94 1415"/>
    </justification>
  </clause>

  <clause id="2627">
    <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(64,a,1144,a(flip),b,2626,a),flip(a)].">
      <j1 rule="hyper" parents="64 1144 2626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2628">
    <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(1004(a,1),2627(a,2,2))].">
      <j1 rule="para" parents="1004 2627"/>
    </justification>
  </clause>

  <clause id="2629">
    <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(488,a,2628,a),flip(a)].">
      <j1 rule="hyper" parents="488 2628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2630">
    <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),2629(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2631">
    <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(319,a,1628,a,b,2630,a),flip(a)].">
      <j1 rule="hyper" parents="319 1628 2630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2632">
    <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(1469(a,1),2631(a,1,1))].">
      <j1 rule="para" parents="1469 2631"/>
    </justification>
  </clause>

  <clause id="2633">
    <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),1434(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1434"/>
    </justification>
  </clause>

  <clause id="2634">
    <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(980(a,1),2633(a,1,2))].">
      <j1 rule="para" parents="980 2633"/>
    </justification>
  </clause>

  <clause id="2635">
    <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(866(a,1),2634(a,1,2,2))].">
      <j1 rule="para" parents="866 2634"/>
    </justification>
  </clause>

  <clause id="2636">
    <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(489,a,2635,a),flip(a)].">
      <j1 rule="hyper" parents="489 2635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,x,1 / x) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(744(a,1),2636(a,2,1,2))].">
      <j1 rule="para" parents="744 2636"/>
    </justification>
  </clause>

  <clause id="2638">
    <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(1424(a,1),2636(a,1,2))].">
      <j1 rule="para" parents="1424 2636"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1174(a,1),2637(a,1,2))].">
      <j1 rule="para" parents="1174 2637"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(208(a,1),2639(a,2,1,2))].">
      <j1 rule="para" parents="208 2639"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1628(a,2),2640(a,2,1))].">
      <j1 rule="para" parents="1628 2640"/>
    </justification>
  </clause>

  <clause id="2642">
    <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),2638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 2638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <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(2242(a,1),2642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2242 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <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(319,a,2632,a(flip),b,2643,a),flip(a)].">
      <j1 rule="hyper" parents="319 2632 2643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1628,a(flip),b,2644,a),flip(a)].">
      <j1 rule="hyper" parents="35 1628 2644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2621,a,b,2645,a)].">
      <j1 rule="hyper" parents="64 2621 2645"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(206,a,2645,a(flip),b,2621,a),flip(a)].">
      <j1 rule="hyper" parents="206 2645 2621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      1 / L((x \ 1) \ 1,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(200(a,1),2646(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="200 2646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),2647(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 2647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      L(1 / (1 / (x \ (y \ z))),x,y) = 1 / (1 / ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(302(a,1),2647(a,2,2,2))].">
      <j1 rule="para" parents="302 2647"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2647(a,1),251(a,1,1))].">
      <j1 rule="para" parents="2647 251"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(199,a,2648,a),flip(a)].">
      <j1 rule="hyper" parents="199 2648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[hyper(206,a,373,a(flip),b,2648,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 373 2648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(371(a,1),2649(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="371 2649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2649(a,1),2647(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2649 2647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,2293,a,b,2655,a)].">
      <j1 rule="hyper" parents="64 2293 2655"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1610,a,b,2657,a)].">
      <j1 rule="hyper" parents="35 1610 2657"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,683,a(flip),b,2658,a),flip(a)].">
      <j1 rule="hyper" parents="319 683 2658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2658(a,1),2533(a,1,2))].">
      <j1 rule="para" parents="2658 2533"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),2651(a,2,1))].">
      <j1 rule="para" parents="81 2651"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2661(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2661 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2478,a,b,2659,a)].">
      <j1 rule="hyper" parents="64 2478 2659"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2659(a,1),1190(a,1,2))].">
      <j1 rule="para" parents="2659 1190"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(2663(a,1),2505(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2663 2505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2470,a(flip),b,2665,a),flip(a)].">
      <j1 rule="hyper" parents="64 2470 2665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      K(x \ (x / y),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),2666(a,1,1,1))].">
      <j1 rule="para" parents="12 2666"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      K(x \ (x / y),y) = (y \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,263,a(flip),b,2668,a),flip(a)].">
      <j1 rule="hyper" parents="319 263 2668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2467(a,1),2664(a,1,2))].">
      <j1 rule="para" parents="2467 2664"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2459(a,1),2670(a,2,2))].">
      <j1 rule="para" parents="2459 2670"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2327,a,2671,a)].">
      <j1 rule="hyper" parents="2327 2671"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(569,a,2671,a)].">
      <j1 rule="hyper" parents="569 2671"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(324,a,2671,a),flip(a)].">
      <j1 rule="hyper" parents="324 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,2352,a(flip),b,2671,a),flip(a)].">
      <j1 rule="hyper" parents="64 2352 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1706,a,2673,a)].">
      <j1 rule="hyper" parents="1706 2673"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,313,a,b,2673,a),flip(a)].">
      <j1 rule="hyper" parents="319 313 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2355,a,b,2673,a)].">
      <j1 rule="hyper" parents="64 2355 2673"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[hyper(64,a,2539,a(flip),b,2673,a),flip(a)].">
      <j1 rule="hyper" parents="64 2539 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,2525,a,b,2673,a)].">
      <j1 rule="hyper" parents="35 2525 2673"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      (x / T(y,z)) * T((y \ 1) \ 1,z) = x * K(T(y,z),T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2311(a,2),2675(a,1,2))].">
      <j1 rule="para" parents="2311 2675"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2151(a,1),2678(a,1,1))].">
      <j1 rule="para" parents="2151 2678"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2527(a,1),2678(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2527 2678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      K(x \ 1,x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2529,a,b,2679,a)].">
      <j1 rule="hyper" parents="64 2529 2679"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(35,a,2528,a,b,2679,a)].">
      <j1 rule="hyper" parents="35 2528 2679"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2679(a,1),1712(a,1,2))].">
      <j1 rule="para" parents="2679 1712"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,2376,a(flip),b,2680,a),flip(a)].">
      <j1 rule="hyper" parents="128 2376 2680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * (K(y,y \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1647(a,2),2680(a,2,2))].">
      <j1 rule="para" parents="1647 2680"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,2681,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 2681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2681(a,1),1729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2681 1729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(263(a,1),2687(a,1,1))].">
      <j1 rule="para" parents="263 2687"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      K(x \ 1,x) * R(y * T(x,x \ 1),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2687(a,1),2260(a,1,2,1))].">
      <j1 rule="para" parents="2687 2260"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      x * K(y \ 1,y) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * T(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2688(a,1),2341(a,1)),flip(a)].">
      <j1 rule="para" parents="2688 2341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2342,a,2694,a)].">
      <j1 rule="hyper" parents="2342 2694"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2359,a(flip),b,2694,a)].">
      <j1 rule="hyper" parents="64 2359 2694"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1395,a(flip),b,2700,a(flip))].">
      <j1 rule="hyper" parents="130 1395 2700"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2474(a,1),2701(a,1,2))].">
      <j1 rule="para" parents="2474 2701"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,z / y) = R(x,(y / z) \ 1,y / z)
    ]]></literal>
    <justification jstring="[para(2055(a,2),2702(a,1,2))].">
      <j1 rule="para" parents="2055 2702"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(2193,a,2676,a),flip(a)].">
      <j1 rule="hyper" parents="2193 2676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,2023,a,b,2692,a)].">
      <j1 rule="hyper" parents="35 2023 2692"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,2323,a,b,2707,a)].">
      <j1 rule="hyper" parents="319 2323 2707"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1)
    ]]></literal>
    <justification jstring="[para(2305(a,1),2708(a,1,1))].">
      <j1 rule="para" parents="2305 2708"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      R(x,K(y,y \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,2693,a)].">
      <j1 rule="hyper" parents="529 2693"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      L(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,2693,a)].">
      <j1 rule="hyper" parents="488 2693"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      R(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[para(1693(a,1),2711(a,1,2))].">
      <j1 rule="para" parents="1693 2711"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      L(1 / (1 / x),K(x,x \ 1),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(2712(a,1),2647(a,2,2,2))].">
      <j1 rule="para" parents="2712 2647"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2713(a,1),1613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2713 1613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,2715,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 2715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2369,a(flip),b,2715,a)].">
      <j1 rule="hyper" parents="64 2369 2715"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,1313,a(flip),b,2715,a),flip(a)].">
      <j1 rule="hyper" parents="36 1313 2715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2532(a,1),2715(a,1,1))].">
      <j1 rule="para" parents="2532 2715"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2533(a,1),2715(a,1,1))].">
      <j1 rule="para" parents="2533 2715"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2530,a,2716,a)].">
      <j1 rule="hyper" parents="2530 2716"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2348,a,2716,a)].">
      <j1 rule="hyper" parents="2348 2716"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      L(x,y,z / (1 / u)) = L(x,y,z / (u \ 1))
    ]]></literal>
    <justification jstring="[para(2716(a,1),2515(a,1,3))].">
      <j1 rule="para" parents="2716 2515"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(2548,a,2717,a)].">
      <j1 rule="hyper" parents="2548 2717"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2534,a,2717,a)].">
      <j1 rule="hyper" parents="2534 2717"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1395,a,b,2718,a)].">
      <j1 rule="hyper" parents="36 1395 2718"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(607,a,2728,a)].">
      <j1 rule="hyper" parents="607 2728"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(323,a,2728,a),flip(a)].">
      <j1 rule="hyper" parents="323 2728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,2728,a)].">
      <j1 rule="hyper" parents="144 2728"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,2715,a(flip),b,2728,a),flip(a)].">
      <j1 rule="hyper" parents="130 2715 2728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2728(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2728 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2728(a,1),111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2728 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2728(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2728 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),2729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = K(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(130,a,2721,a(flip),b,1671,a)].">
      <j1 rule="hyper" parents="130 2721 1671"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(324,a,2724,a),flip(a)].">
      <j1 rule="hyper" parents="324 2724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,2151,a(flip),b,2737,a)].">
      <j1 rule="hyper" parents="128 2151 2737"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(36,a,1633,a(flip),b,2738,a),flip(a)].">
      <j1 rule="hyper" parents="36 1633 2738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      T(R(x,y,1 / y),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(27(a,1),2740(a,1,1))].">
      <j1 rule="para" parents="27 2740"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2138,a(flip),b,2714,a)].">
      <j1 rule="hyper" parents="64 2138 2714"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(131,a,2742,a(flip),b,2549,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 2742 2549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(2742(a,1),322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2742 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(2548,a,2744,a)].">
      <j1 rule="hyper" parents="2548 2744"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ (y * x)) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,2555,a,b,2744,a)].">
      <j1 rule="hyper" parents="64 2555 2744"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,2498,a(flip),b,2745,a)].">
      <j1 rule="hyper" parents="64 2498 2745"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,2745,a(flip),b,2738,a)].">
      <j1 rule="hyper" parents="128 2745 2738"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(127,a,2745,a(flip),b,2498,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 2745 2498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(134,a,2704,a),flip(a)].">
      <j1 rule="hyper" parents="134 2704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(305(a,1),2720(a,1,1)),flip(a)].">
      <j1 rule="para" parents="305 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(111(a,2),2739(a,1,1))].">
      <j1 rule="para" parents="111 2739"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(22(a,2),2747(a,1,2))].">
      <j1 rule="para" parents="22 2747"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(385,a,2754,a),flip(a)].">
      <j1 rule="hyper" parents="385 2754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),2755(a,1,2,2))].">
      <j1 rule="para" parents="78 2755"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),2755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="200 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      (1 / x) * T(y,x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,2757,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2757 22"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,2758,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2758 22"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z)) = T(x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(2058(a,2),2758(a,1,2))].">
      <j1 rule="para" parents="2058 2758"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      T(x,T(y \ (z \ y),z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(2407(a,2),2758(a,1,2))].">
      <j1 rule="para" parents="2407 2758"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,313,a,b,2761,a),flip(a)].">
      <j1 rule="hyper" parents="319 313 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(635,a,2764,a)].">
      <j1 rule="hyper" parents="635 2764"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R((x \ 1) * T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2765(a,1),2624(a,2,1))].">
      <j1 rule="para" parents="2765 2624"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(78(a,1),2748(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="78 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(2748(a,1),2375(a,1,1))].">
      <j1 rule="para" parents="2748 2375"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(78(a,1),2750(a,2,2,2,2))].">
      <j1 rule="para" parents="78 2750"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(199,a,2767,a)].">
      <j1 rule="hyper" parents="199 2767"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2767(a,2,2,2,2))].">
      <j1 rule="para" parents="9 2767"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(78(a,1),2768(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 2768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(22(a,2),2772(a,1,1,2,2,2))].">
      <j1 rule="para" parents="22 2772"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(2653(a,2),2773(a,1,2))].">
      <j1 rule="para" parents="2653 2773"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(78(a,1),2776(a,2,2,2))].">
      <j1 rule="para" parents="78 2776"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(2777(a,2),683(a,1,1,2))].">
      <j1 rule="para" parents="2777 683"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2222,a,b,2779,a)].">
      <j1 rule="hyper" parents="64 2222 2779"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(81(a,1),2780(a,1,2))].">
      <j1 rule="para" parents="81 2780"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(199,a,2774,a),flip(a)].">
      <j1 rule="hyper" parents="199 2774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2783">
    <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(1242(a,1),2732(a,2,1))].">
      <j1 rule="para" parents="1242 2732"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,16,a,b,2695,a),flip(a)].">
      <j1 rule="hyper" parents="319 16 2695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      K(T(x,y),T(T(x,y),z) \ 1) = K(T(x,y),1 / T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2297,a,b,2710,a),flip(a)].">
      <j1 rule="hyper" parents="64 2297 2710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2313(a,1),2775(a,1,1,2))].">
      <j1 rule="para" parents="2313 2775"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2707,a(flip),b,2786,a)].">
      <j1 rule="hyper" parents="64 2707 2786"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(270(a,1),2789(a,2,2))].">
      <j1 rule="para" parents="270 2789"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      K(T(x,y),1 / x) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2305,a(flip),b,2790,a)].">
      <j1 rule="hyper" parents="64 2305 2790"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(109(a,1),2787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 2787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(199,a,2792,a)].">
      <j1 rule="hyper" parents="199 2792"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(78(a,1),2793(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 2793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(199,a,2794,a)].">
      <j1 rule="hyper" parents="199 2794"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1588(a,1),2795(a,1,1,1,1))].">
      <j1 rule="para" parents="1588 2795"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ z))) = x * (y * (1 / (1 / (y \ (x \ z)))))
    ]]></literal>
    <justification jstring="[hyper(131,a,2650,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 2650 18"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(948(a,1),2781(a,1,1))].">
      <j1 rule="para" parents="948 2781"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,831,a(flip),b,2798,a),flip(a)].">
      <j1 rule="hyper" parents="64 831 2798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2799(a,2),231(a,1,1))].">
      <j1 rule="para" parents="2799 231"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2472(a,1),2660(a,1,2))].">
      <j1 rule="para" parents="2472 2660"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2305(a,1),2674(a,1,2))].">
      <j1 rule="para" parents="2305 2674"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,2315,a(flip),b,2802,a),flip(a)].">
      <j1 rule="hyper" parents="319 2315 2802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2791(a,1),2803(a,1,2))].">
      <j1 rule="para" parents="2791 2803"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      K(T(x,y),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,2353,a,b,2804,a),flip(a)].">
      <j1 rule="hyper" parents="35 2353 2804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2790,a,b,2805,a)].">
      <j1 rule="hyper" parents="64 2790 2805"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,2806,a(flip),b,1628,a(flip))].">
      <j1 rule="hyper" parents="127 2806 1628"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2326,a(flip),b,2810,a)].">
      <j1 rule="hyper" parents="64 2326 2810"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(130,a,2810,a(flip),b,2326,a(flip))].">
      <j1 rule="hyper" parents="130 2810 2326"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) \ 1 = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2811,a,b,156,a)].">
      <j1 rule="hyper" parents="129 2811 156"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1284,a,2812,a)].">
      <j1 rule="hyper" parents="1284 2812"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(244,a,2812,a,b,1018,a)].">
      <j1 rule="hyper" parents="244 2812 1018"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(130,a,2812,a(flip),b,1274,a(flip))].">
      <j1 rule="hyper" parents="130 2812 1274"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2812(a,1),1284(a,1))].">
      <j1 rule="para" parents="2812 1284"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(199,a,2814,a)].">
      <j1 rule="hyper" parents="199 2814"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,2169,a,b,2816,a)].">
      <j1 rule="hyper" parents="64 2169 2816"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2819(a,1),2168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2819 2168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,2815,a(flip),b,2373,a)].">
      <j1 rule="hyper" parents="130 2815 2373"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(310,a,2821,a),flip(a)].">
      <j1 rule="hyper" parents="310 2821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(279,a,2823,a)].">
      <j1 rule="hyper" parents="279 2823"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,2823,a)].">
      <j1 rule="hyper" parents="55 2823"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2823,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 2823 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      L(K(x,y),z,u) * y = y * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2823(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2823 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,2825,a)].">
      <j1 rule="hyper" parents="149 2825"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      K(x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,2825,a)].">
      <j1 rule="hyper" parents="56 2825"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,27,a,b,2825,a(flip))].">
      <j1 rule="hyper" parents="43 27 2825"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,2825,a(flip))].">
      <j1 rule="hyper" parents="42 25 2825"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2825(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2825 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2825(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2825 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2825(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2825 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2825(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2825 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2825(a,1),389(a,1,2,1))].">
      <j1 rule="para" parents="2825 389"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(2825(a,1),509(a,1,1,2))].">
      <j1 rule="para" parents="2825 509"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(2825(a,1),442(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2825 442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1106(a,1),2825(a,1,2))].">
      <j1 rule="para" parents="1106 2825"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2825(a,1),2219(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2825 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,2828,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2828 22"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,2839,a)].">
      <j1 rule="hyper" parents="55 2839"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2830(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2830 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      K(x,L(y,z,u)) * y = y * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,2831,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2831 22"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2199,a,b,2824,a)].">
      <j1 rule="hyper" parents="64 2199 2824"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1154,a,b,2824,a)].">
      <j1 rule="hyper" parents="64 1154 2824"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2824(a,1),336(a,1,1))].">
      <j1 rule="para" parents="2824 336"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      (x * (y * K(z,y))) * a(x,K(z,y),y) = (x * K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(2826(a,1),85(a,1,1,2))].">
      <j1 rule="para" parents="2826 85"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(y,z),u) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(2832(a,1),389(a,1,2,1))].">
      <j1 rule="para" parents="2832 389"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,264,a,b,2845,a)].">
      <j1 rule="hyper" parents="64 264 2845"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,2845,a(flip),b,1894,a),flip(a)].">
      <j1 rule="hyper" parents="127 2845 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,2845,a(flip),b,264,a)].">
      <j1 rule="hyper" parents="127 2845 264"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(2842(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2842 291"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,2850,a(flip),b,193,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 2850 193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      ((x * (y \ 1)) * K(z,y)) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(206,a,2851,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="206 2851 194"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(358,a,2822,a)].">
      <j1 rule="hyper" parents="358 2822"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,263,a(flip),b,2822,a),flip(a)].">
      <j1 rule="hyper" parents="319 263 2822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2856(a,1),2317(a,1,2))].">
      <j1 rule="para" parents="2856 2317"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(2856(a,1),2545(a,1,2,1))].">
      <j1 rule="para" parents="2856 2545"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(245,a,2827,a)].">
      <j1 rule="hyper" parents="245 2827"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,2834,a)].">
      <j1 rule="hyper" parents="245 2834"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      R(x,y,z) * u != K(w,x) * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      K(w,x) = u
    ]]></literal>
    <justification jstring="[para(2835(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2835 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2211,a,b,2858,a)].">
      <j1 rule="hyper" parents="36 2211 2858"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2864,a),flip(a)].">
      <j1 rule="hyper" parents="134 2864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(2864(a,1),82(a,1,1,2))].">
      <j1 rule="para" parents="2864 82"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1151,a,2866,a)].">
      <j1 rule="hyper" parents="1151 2866"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(956,a,2866,a),flip(a)].">
      <j1 rule="hyper" parents="956 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(953,a,2866,a)].">
      <j1 rule="hyper" parents="953 2866"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,270,a,b,2866,a)].">
      <j1 rule="hyper" parents="37 270 2866"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(2866(a,1),106(a,1,1))].">
      <j1 rule="para" parents="2866 106"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(2866(a,1),540(a,1,1))].">
      <j1 rule="para" parents="2866 540"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2866(a,1),2204(a,1,1,2))].">
      <j1 rule="para" parents="2866 2204"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1106(a,2),2871(a,1,2))].">
      <j1 rule="para" parents="1106 2871"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1416,a,b,2867,a)].">
      <j1 rule="hyper" parents="64 1416 2867"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1445,a,b,2867,a),flip(a)].">
      <j1 rule="hyper" parents="36 1445 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,2867,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 2867 197"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(2867(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="2867 531"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(244,a,2868,a,b,937,a)].">
      <j1 rule="hyper" parents="244 2868 937"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,81,a(flip),b,2883,a),flip(a)].">
      <j1 rule="hyper" parents="319 81 2883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2883(a,1),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2883 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2883(a,1),384(a,2,1))].">
      <j1 rule="para" parents="2883 384"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2883(a,1),1110(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2883 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1115,a,2878,a)].">
      <j1 rule="hyper" parents="1115 2878"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2884(a,1),1606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2884 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2889(a,1),1456(a,1,1))].">
      <j1 rule="para" parents="2889 1456"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,2888,a)].">
      <j1 rule="hyper" parents="145 2888"/>
    </justification>
  </clause>

  <clause id="2892">
    <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(1677(a,1),2891(a,1,1,1,1))].">
      <j1 rule="para" parents="1677 2891"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(225(a,1),2879(a,1,2))].">
      <j1 rule="para" parents="225 2879"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2869(a,1),753(a,1,1))].">
      <j1 rule="para" parents="2869 753"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2869(a,1),2563(a,1,1))].">
      <j1 rule="para" parents="2869 2563"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2576,a,b,2870,a)].">
      <j1 rule="hyper" parents="64 2576 2870"/>
    </justification>
  </clause>

  <clause id="2897">
    <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(2870(a,1),1805(a,2,1))].">
      <j1 rule="para" parents="2870 1805"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2885(a,1),2887(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2885 2887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,348,a(flip),b,2899,a),flip(a)].">
      <j1 rule="hyper" parents="319 348 2899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,x),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(2900(a,1),986(a,1,1,2))].">
      <j1 rule="para" parents="2900 986"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(2880(a,1),2871(a,1,2))].">
      <j1 rule="para" parents="2880 2871"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(232(a,1),2904(a,1,2,2))].">
      <j1 rule="para" parents="232 2904"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,2905,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 2905 22"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(2906(a,1),1576(a,1,2,1))].">
      <j1 rule="para" parents="2906 1576"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(2906(a,1),1952(a,1,1,2,1))].">
      <j1 rule="para" parents="2906 1952"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,88,a(flip),b,2840,a),flip(a)].">
      <j1 rule="hyper" parents="35 88 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ x = z
    ]]></literal>
    <justification jstring="[para(2909(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2909 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(691,a,2890,a)].">
      <j1 rule="hyper" parents="691 2890"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      (x * T(1 / x,y)) \ (((x \ 1) \ 1) * (T(x \ 1,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2890(a,1),675(a,1,1))].">
      <j1 rule="para" parents="2890 675"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1109(a,2),2895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1109 2895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1180(a,1),2895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1180 2895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2313(a,1),2859(a,2,1))].">
      <j1 rule="para" parents="2313 2859"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2894,a,2780,a),flip(a)].">
      <j1 rule="hyper" parents="2894 2780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2780(a,1),2894(a,1))].">
      <j1 rule="para" parents="2780 2894"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,684,a(flip),b,2917,a),flip(a)].">
      <j1 rule="hyper" parents="319 684 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),2917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = K(T(x \ 1,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(2309(a,1),2917(a,1,1))].">
      <j1 rule="para" parents="2309 2917"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2919(a,1),2800(a,1,1))].">
      <j1 rule="para" parents="2919 2800"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2511,a,2922,a)].">
      <j1 rule="hyper" parents="2511 2922"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,2922,a)].">
      <j1 rule="hyper" parents="55 2922"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2922(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2922 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      T(x,K(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,2924,a)].">
      <j1 rule="hyper" parents="149 2924"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2924(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2924 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2924(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2924 291"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2924(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2924 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2924(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2924 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      T(x / y,K(y \ x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(111(a,1),2926(a,1,2,1))].">
      <j1 rule="para" parents="111 2926"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,2),2920(a,1,1))].">
      <j1 rule="para" parents="110 2920"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(2795(a,1),2920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2795 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,2927,a)].">
      <j1 rule="hyper" parents="55 2927"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2934(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2934 291"/>
    </justification>
  </clause>

  <clause id="2936">
    <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(2934(a,1),575(a,1,2))].">
      <j1 rule="para" parents="2934 575"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,2925,a,b,88,a),flip(a)].">
      <j1 rule="hyper" parents="126 2925 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,2929,a)].">
      <j1 rule="hyper" parents="245 2929"/>
    </justification>
  </clause>

  <clause id="2939">
    <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(2938(a,1),291(a,1,2))].">
      <j1 rule="para" parents="2938 291"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,2930,a)].">
      <j1 rule="hyper" parents="245 2930"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = (x * (T(y,x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(2906(a,1),2907(a,2,1))].">
      <j1 rule="para" parents="2906 2907"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / (1 / x),y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,2916,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      (T(x,y) \ z) * K(x,x \ 1) = T(1 / (1 / x),y) \ z
    ]]></literal>
    <justification jstring="[hyper(2548,a,2942,a)].">
      <j1 rule="hyper" parents="2548 2942"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / (1 / (x \ 1)),y) \ z
    ]]></literal>
    <justification jstring="[para(1640(a,1),2943(a,1,2))].">
      <j1 rule="para" parents="1640 2943"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(2866(a,1),2876(a,2,2,1,2))].">
      <j1 rule="para" parents="2866 2876"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2906,a(flip),b,2908,a),flip(a)].">
      <j1 rule="hyper" parents="319 2906 2908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ z = u
    ]]></literal>
    <justification jstring="[para(2945(a,2),44(a,1))].">
      <j1 rule="para" parents="2945 44"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(443(a,1),2874(a,2,1))].">
      <j1 rule="para" parents="443 2874"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,x),z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2870(a,1),2896(a,1,1))].">
      <j1 rule="para" parents="2870 2896"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T((T(x,z) \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(271(a,1),2683(a,1,1)),flip(a)].">
      <j1 rule="para" parents="271 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1640(a,1),2801(a,1,2))].">
      <j1 rule="para" parents="1640 2801"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / x,y) \ z
    ]]></literal>
    <justification jstring="[para(78(a,1),2944(a,2,1,1,2))].">
      <j1 rule="para" parents="78 2944"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      K(x,x \ 1) * (T(1 / x,y) \ z) = T(x \ 1,y) \ z
    ]]></literal>
    <justification jstring="[hyper(2530,a,2952,a)].">
      <j1 rule="hyper" parents="2530 2952"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      T(x \ 1,y) \ (T(1 / x,y) * z) = K(x,x \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(586,a,2953,a),flip(a)].">
      <j1 rule="hyper" parents="586 2953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      T(x \ 1,y) * ((x \ 1) \ (K(x,x \ 1) * z)) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1714,a,b,2954,a)].">
      <j1 rule="hyper" parents="131 1714 2954"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      T(1 / x,y) * ((1 / x) \ z) = T(x \ 1,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1715,a(flip),b,2954,a),flip(a)].">
      <j1 rule="hyper" parents="131 1715 2954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[hyper(131,a,2956,a(flip),b,1010,a)].">
      <j1 rule="hyper" parents="131 2956 1010"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      R(K(x \ 1,x) * (y * T(x,x \ 1)),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,1783,a,b,2698,a)].">
      <j1 rule="hyper" parents="64 1783 2698"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ (x * z)))) = x * (y * (1 / (1 / (y \ z))))
    ]]></literal>
    <justification jstring="[para(9(a,1),2797(a,2,2,2,2,2,2))].">
      <j1 rule="para" parents="9 2797"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2688(a,1),2958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2688 2958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),2960(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      x * (R(y * x,z,u) / x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(2960(a,1),77(a,1,2,1))].">
      <j1 rule="para" parents="2960 77"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,177,a(flip),b,2961,a),flip(a)].">
      <j1 rule="hyper" parents="43 177 2961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(177(a,1),2961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="177 2961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(538(a,1),2961(a,2,1,2))].">
      <j1 rule="para" parents="538 2961"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2730(a,1),2961(a,2,1,2))].">
      <j1 rule="para" parents="2730 2961"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(142,a,2963,a)].">
      <j1 rule="hyper" parents="142 2963"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(346,a,2964,a)].">
      <j1 rule="hyper" parents="346 2964"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,2964,a)].">
      <j1 rule="hyper" parents="142 2964"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1483,a,b,2964,a)].">
      <j1 rule="hyper" parents="36 1483 2964"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1481,a,b,2967,a)].">
      <j1 rule="hyper" parents="64 1481 2967"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(2969(a,1),546(a,1,1))].">
      <j1 rule="para" parents="2969 546"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2970(a,1),2363(a,1,1))].">
      <j1 rule="para" parents="2970 2363"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2962(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2975">
    <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(2974(a,2),2622(a,1,1))].">
      <j1 rule="para" parents="2974 2622"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1072,a,b,2973,a)].">
      <j1 rule="hyper" parents="35 1072 2973"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,2965,a(flip),b,266,a)].">
      <j1 rule="hyper" parents="128 2965 266"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,2966,a(flip),b,2731,a),flip(a)].">
      <j1 rule="hyper" parents="128 2966 2731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,1244,a(flip),b,2979,a)].">
      <j1 rule="hyper" parents="64 1244 2979"/>
    </justification>
  </clause>

  <clause id="2981">
    <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(319,a,419,a,b,2752,a)].">
      <j1 rule="hyper" parents="319 419 2752"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2770(a,1),2951(a,2,1))].">
      <j1 rule="para" parents="2770 2951"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      T(x \ 1,y) * ((((x \ 1) \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2550(a,1),2955(a,1,2))].">
      <j1 rule="para" parents="2550 2955"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(110(a,2),2983(a,1,2,1))].">
      <j1 rule="para" parents="110 2983"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(228(a,1),2766(a,2,1))].">
      <j1 rule="para" parents="228 2766"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,362,a(flip),b,2985,a),flip(a)].">
      <j1 rule="hyper" parents="319 362 2985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1
    ]]></literal>
    <justification jstring="[hyper(131,a,2986,a(flip),b,89,a),flip(a)].">
      <j1 rule="hyper" parents="131 2986 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a(flip),b,2989,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(2990(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2990 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T(T((x \ 1) \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(2311(a,2),2950(a,2,2,1))].">
      <j1 rule="para" parents="2311 2950"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,241,a(flip),b,2992,a),flip(a)].">
      <j1 rule="hyper" parents="319 241 2992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(x,z),T(x,z) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2806(a,1),2993(a,1,2))].">
      <j1 rule="para" parents="2806 2993"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,x \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2806(a,1),2994(a,1,2))].">
      <j1 rule="para" parents="2806 2994"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      (1 / x) * (T(((1 / x) \ 1) \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(2995(a,1),2553(a,1,2))].">
      <j1 rule="para" parents="2995 2553"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),2997(a,1,2,1,1,1))].">
      <j1 rule="para" parents="81 2997"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / x,y) * z) = T(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,2544,a,b,2999,a)].">
      <j1 rule="hyper" parents="35 2544 2999"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      (T(1 / x,y) * z) / (T(1 / x,y) * ((x \ 1) \ z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,2957,a(flip),b,2999,a(flip))].">
      <j1 rule="hyper" parents="128 2957 2999"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x \ 1,y) * z) = x * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(3000(a,1),1724(a,1,2))].">
      <j1 rule="para" parents="3000 1724"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(2949(a,1),2903(a,1,1))].">
      <j1 rule="para" parents="2949 2903"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,x) * z
    ]]></literal>
    <justification jstring="[para(2900(a,1),3004(a,2,1))].">
      <j1 rule="para" parents="2900 3004"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      (x \ T(x,y)) * (z * K(x \ 1,x)) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(2344,a,3005,a)].">
      <j1 rule="hyper" parents="2344 3005"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1732(a,1),2897(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1732 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2933(a,1),3009(a,2,2))].">
      <j1 rule="para" parents="2933 3009"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,305,a(flip),b,3010,a)].">
      <j1 rule="hyper" parents="319 305 3010"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      (x * T(1 / x,y)) \ (x * (T(1 / x,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3002(a,1),2912(a,1,2))].">
      <j1 rule="para" parents="3002 2912"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      L(x,T(y \ 1,z),(y \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(1 / y,z),y) = u
    ]]></literal>
    <justification jstring="[para(3012(a,1),489(a,1))].">
      <j1 rule="para" parents="3012 489"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      L(x,T(1 / y,z),y) = L(x,T(y \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(3013,a,1589,a)].">
      <j1 rule="hyper" parents="3013 1589"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      L(T(1 / x,y) \ z,T(x \ 1,y),x) = (x * T(1 / x,y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,96,a(flip),b,3014,a),flip(a)].">
      <j1 rule="hyper" parents="64 96 3014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(2982(a,1),2783(a,1,1))].">
      <j1 rule="para" parents="2982 2783"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(935(a,1),3016(a,2,1,2))].">
      <j1 rule="para" parents="935 3016"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2966,a(flip),b,3017,a)].">
      <j1 rule="hyper" parents="64 2966 3017"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),3018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,3019,a),flip(a)].">
      <j1 rule="hyper" parents="142 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,3019,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(2853,a,3020,a)].">
      <j1 rule="hyper" parents="2853 3020"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,3020,a)].">
      <j1 rule="hyper" parents="134 3020"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,232,a(flip),b,3020,a)].">
      <j1 rule="hyper" parents="127 232 3020"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(127,a,155,a(flip),b,3020,a),flip(a)].">
      <j1 rule="hyper" parents="127 155 3020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3020(a,1),2191(a,1,1))].">
      <j1 rule="para" parents="3020 2191"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,3022,a)].">
      <j1 rule="hyper" parents="142 3022"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      T((x \ T(x,y)) * y,x) = y
    ]]></literal>
    <justification jstring="[para(3022(a,2),231(a,1,1))].">
      <j1 rule="para" parents="3022 231"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(3022(a,1),194(a,1,2,1))].">
      <j1 rule="para" parents="3022 194"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2880,a,b,3023,a(flip))].">
      <j1 rule="hyper" parents="39 2880 3023"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3023(a,1),505(a,1,1))].">
      <j1 rule="para" parents="3023 505"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      T(x,y) \ x = T(y,T(x,y)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,3030,a(flip),b,1446,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3030 1446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(2419(a,1),3030(a,1,2))].">
      <j1 rule="para" parents="2419 3030"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      x * (T(y,x) \ y) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,3024,a,b,xx)].">
      <j1 rule="hyper" parents="131 3024"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(3024(a,2),2873(a,1,1))].">
      <j1 rule="para" parents="3024 2873"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(3027(a,1),517(a,1,1,1))].">
      <j1 rule="para" parents="3027 517"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      T(x,T(y,x)) / x = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(2817,a,3032,a),flip(a)].">
      <j1 rule="hyper" parents="2817 3032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2762,a(flip),b,3033,a)].">
      <j1 rule="hyper" parents="64 2762 3033"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1232,a,3038,a)].">
      <j1 rule="hyper" parents="1232 3038"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2893,a(flip),b,3038,a)].">
      <j1 rule="hyper" parents="64 2893 3038"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(127,a,3038,a(flip),b,1231,a)].">
      <j1 rule="hyper" parents="127 3038 1231"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2072,a,3040,a)].">
      <j1 rule="hyper" parents="2072 3040"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2070,a,3040,a)].">
      <j1 rule="hyper" parents="2070 3040"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1463,a,b,3040,a)].">
      <j1 rule="hyper" parents="64 1463 3040"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3040,a(flip),b,2068,a)].">
      <j1 rule="hyper" parents="128 3040 2068"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(127,a,3040,a(flip),b,2068,a)].">
      <j1 rule="hyper" parents="127 3040 2068"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,3040,a(flip),b,1463,a),flip(a)].">
      <j1 rule="hyper" parents="127 3040 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3040(a,1),1414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3040 1414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      (x \ y) * (x \ ((x \ y) \ y)) = y / x
    ]]></literal>
    <justification jstring="[para(110(a,1),3021(a,1,2,2))].">
      <j1 rule="para" parents="110 3021"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(127,a,2758,a(flip),b,3039,a)].">
      <j1 rule="hyper" parents="127 2758 3039"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3039(a,1,2,2,1))].">
      <j1 rule="para" parents="9 3039"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),3041(a,2,2,1))].">
      <j1 rule="para" parents="81 3041"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,2758,a(flip),b,3042,a)].">
      <j1 rule="hyper" parents="128 2758 3042"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(270(a,1),3046(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="270 3046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(78(a,1),3047(a,2,2,1))].">
      <j1 rule="para" parents="78 3047"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),3047(a,1,1,2))].">
      <j1 rule="para" parents="81 3047"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(3047(a,2),224(a,2,1))].">
      <j1 rule="para" parents="3047 224"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,3051,a)].">
      <j1 rule="hyper" parents="134 3051"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(232(a,1),3031(a,2,2)),flip(a)].">
      <j1 rule="para" parents="232 3031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(111(a,1),3025(a,1,2))].">
      <j1 rule="para" parents="111 3025"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2012,a,b,3050,a)].">
      <j1 rule="hyper" parents="64 2012 3050"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2629,a(flip),b,3050,a)].">
      <j1 rule="hyper" parents="64 2629 3050"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(3050(a,1),2079(a,1,1))].">
      <j1 rule="para" parents="3050 2079"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(3050(a,1),2115(a,2,2,1))].">
      <j1 rule="para" parents="3050 2115"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(3050(a,1),2081(a,2,2,1))].">
      <j1 rule="para" parents="3050 2081"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,964,a(flip),b,3054,a)].">
      <j1 rule="hyper" parents="64 964 3054"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(35,a,934,a,b,3053,a)].">
      <j1 rule="hyper" parents="35 934 3053"/>
    </justification>
  </clause>

  <clause id="3073">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(3057(a,2),44(a,1))].">
      <j1 rule="para" parents="3057 44"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3049,a(flip),b,3067,a),flip(a)].">
      <j1 rule="hyper" parents="319 3049 3067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3070(a,1),458(a,1,2))].">
      <j1 rule="para" parents="3070 458"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,2686,a(flip),b,3072,a),flip(a)].">
      <j1 rule="hyper" parents="64 2686 3072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3077">
    <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(2886(a,1),3074(a,2,2,2,1))].">
      <j1 rule="para" parents="2886 3074"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(223(a,2),3076(a,1,2))].">
      <j1 rule="para" parents="223 3076"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,3078,a(flip),b,823,a),flip(a)].">
      <j1 rule="hyper" parents="128 3078 823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3080">
    <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(3035(a,1),881(a,1,1))].">
      <j1 rule="para" parents="3035 881"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3050(a,1),3066(a,1,1))].">
      <j1 rule="para" parents="3050 3066"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      (x \ T(x,y \ 1)) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(3049(a,1),3068(a,1,1))].">
      <j1 rule="para" parents="3049 3068"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,3026,a(flip),b,3079,a)].">
      <j1 rule="hyper" parents="64 3026 3079"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,1822,a(flip),b,3084,a)].">
      <j1 rule="hyper" parents="64 1822 3084"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3085(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3086(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3088">
    <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),3080(a,2,1))].">
      <j1 rule="para" parents="16 3080"/>
    </justification>
  </clause>

  <clause id="3089">
    <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(2975(a,1),290(a,1))].">
      <j1 rule="para" parents="2975 290"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(3089,a,3069,a)].">
      <j1 rule="hyper" parents="3089 3069"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3042(a,1),3090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3042 3090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(2758(a,1),3091(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2758 3091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2758(a,1),3092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2758 3092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(586,a,3094,a),flip(a)].">
      <j1 rule="hyper" parents="586 3094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(128,a,154,a(flip),b,3094,a(flip))].">
      <j1 rule="hyper" parents="128 154 3094"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(740,a,3095,a)].">
      <j1 rule="hyper" parents="740 3095"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1013,a,b,3095,a),flip(a)].">
      <j1 rule="hyper" parents="35 1013 3095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,1009,a(flip),b,3095,a),flip(a)].">
      <j1 rule="hyper" parents="35 1009 3095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(3022(a,1),3095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3022 3095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3024(a,2),3095(a,1,2,1))].">
      <j1 rule="para" parents="3024 3095"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1030,a,3103,a)].">
      <j1 rule="hyper" parents="1030 3103"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1020,a,3103,a),flip(a)].">
      <j1 rule="hyper" parents="1020 3103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      x \ (T(x,y) * y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(571,a,3103,a)].">
      <j1 rule="hyper" parents="571 3103"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1380,a,b,3103,a)].">
      <j1 rule="hyper" parents="36 1380 3103"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3103(a,2,2,1))].">
      <j1 rule="para" parents="10 3103"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      T(x / y,y) * y = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),3103(a,2,2,1))].">
      <j1 rule="para" parents="12 3103"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1385,a(flip),b,3109,a)].">
      <j1 rule="hyper" parents="64 1385 3109"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1229,a(flip),b,3109,a)].">
      <j1 rule="hyper" parents="64 1229 3109"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(130,a,3109,a(flip),b,1306,a(flip))].">
      <j1 rule="hyper" parents="130 3109 1306"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(127,a,3109,a(flip),b,1224,a)].">
      <j1 rule="hyper" parents="127 3109 1224"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(78(a,1),3109(a,1,2,2))].">
      <j1 rule="para" parents="78 3109"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),3109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="200 3109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      x \ T(y,x \ y) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(127,a,3116,a(flip),b,1220,a)].">
      <j1 rule="hyper" parents="127 3116 1220"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(T(x,y \ x) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(3116(a,1),1214(a,1,1,1))].">
      <j1 rule="para" parents="3116 1214"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      T(x \ T(y,x \ y),y) = x \ y
    ]]></literal>
    <justification jstring="[para(3116(a,1),1217(a,1,1,2))].">
      <j1 rule="para" parents="3116 1217"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,2),3117(a,1,2))].">
      <j1 rule="para" parents="110 3117"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3121(a,1,2,2))].">
      <j1 rule="para" parents="9 3121"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(244,a,1290,a,b,3106,a)].">
      <j1 rule="hyper" parents="244 1290 3106"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      T(x,T(x \ y,y)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(244,a,1293,a(flip),b,3106,a)].">
      <j1 rule="hyper" parents="244 1293 3106"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(244,a,1280,a(flip),b,3106,a)].">
      <j1 rule="hyper" parents="244 1280 3106"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(134,a,3106,a)].">
      <j1 rule="hyper" parents="134 3106"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      T(T(x,y) * (x \ y),x) = y
    ]]></literal>
    <justification jstring="[para(3106(a,2),231(a,1,1))].">
      <j1 rule="para" parents="3106 231"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * ((x \ y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3106(a,1),489(a,1,1))].">
      <j1 rule="para" parents="3106 489"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),2846(a,1,1,1))].">
      <j1 rule="para" parents="3106 2846"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(3123(a,1),250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3123 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3127(a,1,1,2))].">
      <j1 rule="para" parents="9 3127"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(3112(a,1),1310(a,1,1))].">
      <j1 rule="para" parents="3112 1310"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(244,a,3113,a,b,1031,a)].">
      <j1 rule="hyper" parents="244 3113 1031"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      T(T(x * y,z),T(x,y)) = T(T(x * y,x),z)
    ]]></literal>
    <justification jstring="[para(3122(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3122 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      T(x,T(x \ y,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a,b,3124,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 3124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,22,a,b,3125,a),flip(a)].">
      <j1 rule="hyper" parents="319 22 3125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      T(T(x,y),x) * L(T(T(x,y),x) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[para(3126(a,1),1994(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3126 1994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,3130,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3130 22"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3130(a,1),291(a,1,2))].">
      <j1 rule="para" parents="3130 291"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(756,a,3096,a)].">
      <j1 rule="hyper" parents="756 3096"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,154,a(flip),b,3100,a)].">
      <j1 rule="hyper" parents="128 154 3100"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(127,a,154,a(flip),b,3100,a)].">
      <j1 rule="hyper" parents="127 154 3100"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3082,a(flip),b,3100,a),flip(a)].">
      <j1 rule="hyper" parents="64 3082 3100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      T(x,y) * (x \ (z * K(x \ 1,x))) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,3007,a(flip),b,3100,a),flip(a)].">
      <j1 rule="hyper" parents="64 3007 3100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,3101,a)].">
      <j1 rule="hyper" parents="127 10 3101"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      L(x,y,y \ T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,2881,a,b,3101,a(flip))].">
      <j1 rule="hyper" parents="35 2881 3101"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(3101(a,1),330(a,1,2))].">
      <j1 rule="para" parents="3101 330"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      L(x,y,T(z,y) \ z) = x
    ]]></literal>
    <justification jstring="[para(3024(a,2),3147(a,1,3))].">
      <j1 rule="para" parents="3024 3147"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      L(x,y,K(z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[para(2914(a,1),3149(a,1,3))].">
      <j1 rule="para" parents="2914 3149"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1741,a,3150,a)].">
      <j1 rule="hyper" parents="1741 3150"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1143,a,3151,a),flip(a)].">
      <j1 rule="hyper" parents="1143 3151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,3151,a)].">
      <j1 rule="hyper" parents="54 3151"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      L(x,y,T(z,y) / z) = x
    ]]></literal>
    <justification jstring="[para(1105(a,1),3151(a,1,3))].">
      <j1 rule="para" parents="1105 3151"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      L(x,T(y,z),y / T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(3037(a,1),3155(a,1,3))].">
      <j1 rule="para" parents="3037 3155"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(691,a,3110,a)].">
      <j1 rule="hyper" parents="691 3110"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(127,a,3041,a,b,3110,a)].">
      <j1 rule="hyper" parents="127 3041 3110"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3100,a,b,3110,a)].">
      <j1 rule="hyper" parents="64 3100 3110"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2882,a,3142,a)].">
      <j1 rule="hyper" parents="2882 3142"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3142(a,1),3088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3142 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2948,a(flip),b,3160,a)].">
      <j1 rule="hyper" parents="64 2948 3160"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,1031,a(flip),b,3146,a),flip(a)].">
      <j1 rule="hyper" parents="319 1031 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(3146(a,2),1036(a,1))].">
      <j1 rule="para" parents="3146 1036"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,2818,a,b,3164,a)].">
      <j1 rule="hyper" parents="40 2818 3164"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2869(a,1),3164(a,1,1))].">
      <j1 rule="para" parents="2869 3164"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3034(a,2),3166(a,1,1))].">
      <j1 rule="para" parents="3034 3166"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3166(a,2),3097(a,1,2))].">
      <j1 rule="para" parents="3166 3097"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(231(a,1),3169(a,1,2,1,2))].">
      <j1 rule="para" parents="231 3169"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(529,a,3152,a)].">
      <j1 rule="hyper" parents="529 3152"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(2826(a,1),3152(a,1,1))].">
      <j1 rule="para" parents="2826 3152"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(207,a,3168,a)].">
      <j1 rule="hyper" parents="207 3168"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ 1 = x \ (y \ T(y,x))
    ]]></literal>
    <justification jstring="[para(3168(a,1),2941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3168 2941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(3168(a,1),2946(a,1,1,2))].">
      <j1 rule="para" parents="3168 2946"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (x * K(y,x)) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,74,a(flip),b,3172,a)].">
      <j1 rule="hyper" parents="127 74 3172"/>
    </justification>
  </clause>

  <clause id="3177">
    <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(960(a,1),3173(a,1,2,2))].">
      <j1 rule="para" parents="960 3173"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3027(a,1),3129(a,1,1))].">
      <j1 rule="para" parents="3027 3129"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3113,a(flip),b,3132,a),flip(a)].">
      <j1 rule="hyper" parents="319 3113 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(3181(a,1),911(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3181 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(35,a,3114,a(flip),b,3104,a),flip(a)].">
      <j1 rule="hyper" parents="35 3114 3104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(244,a,3183,a,b,88,a),flip(a)].">
      <j1 rule="hyper" parents="244 3183 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(142,a,3183,a)].">
      <j1 rule="hyper" parents="142 3183"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),3185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(3185(a,1),392(a,1))].">
      <j1 rule="para" parents="3185 392"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),3111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      T(x \ T(x * y,y),x * y) = y
    ]]></literal>
    <justification jstring="[para(3134(a,1),231(a,1,1))].">
      <j1 rule="para" parents="3134 231"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(3134(a,1),765(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3134 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      T(x \ T(y,x \ y),x) = R(x \ y,x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3191(a,1,1,2,1))].">
      <j1 rule="para" parents="10 3191"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,444,a,b,3182,a)].">
      <j1 rule="hyper" parents="36 444 3182"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(111(a,1),3187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 3187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3061,a(flip),b,3194,a),flip(a)].">
      <j1 rule="hyper" parents="319 3061 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3065,a(flip),b,3195,a),flip(a)].">
      <j1 rule="hyper" parents="64 3065 3195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = L(R(y,x * y,y),x * y,y)
    ]]></literal>
    <justification jstring="[para(3134(a,1),3193(a,1,1))].">
      <j1 rule="para" parents="3134 3193"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),3148(a,1,2))].">
      <j1 rule="para" parents="10 3148"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3062,a,b,3161,a),flip(a)].">
      <j1 rule="hyper" parents="319 3062 3161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3200">
    <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(3161(a,1),366(a,1)),flip(b)].">
      <j1 rule="para" parents="3161 366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3199,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 3199 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,3202,a)].">
      <j1 rule="hyper" parents="488 3202"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3203(a,1),51(a,2))].">
      <j1 rule="para" parents="3203 51"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      L(x,1 / y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(2917(a,1),3203(a,1,3))].">
      <j1 rule="para" parents="2917 3203"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1098,a,3163,a),flip(a)].">
      <j1 rule="hyper" parents="1098 3163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(2947,a,3175,a)].">
      <j1 rule="hyper" parents="2947 3175"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3020(a,1),3210(a,1,1))].">
      <j1 rule="para" parents="3020 3210"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(3021(a,1),3210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3021 3210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3213">
    <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(3211(a,1),1061(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3211 1061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3211(a,1),1206(a,1,2,2,1))].">
      <j1 rule="para" parents="3211 1206"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[para(3211(a,1),2891(a,1,1))].">
      <j1 rule="para" parents="3211 2891"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3063,a(flip),b,3212,a),flip(a)].">
      <j1 rule="hyper" parents="319 3063 3212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(673,a,3196,a)].">
      <j1 rule="hyper" parents="673 3196"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(206,a,3217,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="206 3217 110"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,3217,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="131 3217 110"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3217(a,1,2,2))].">
      <j1 rule="para" parents="9 3217"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(81(a,1),3217(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 3217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3217(a,1),3216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3217 3216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3221(a,1),3054(a,1,2))].">
      <j1 rule="para" parents="3221 3054"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2758(a,1),3218(a,1,2))].">
      <j1 rule="para" parents="2758 3218"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,22,a,b,3219,a),flip(a)].">
      <j1 rule="hyper" parents="319 22 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(81(a,1),3219(a,1,2,2))].">
      <j1 rule="para" parents="81 3219"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),3224(a,2,2))].">
      <j1 rule="para" parents="11 3224"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      ((x / y) * ((x * (y / x)) / T(x,x \ y))) * ((x / y) \ 1) = R(1 / (x / y),x / y,(x / y) \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(3224(a,1),1521(a,1,1,2,1))].">
      <j1 rule="para" parents="3224 1521"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(404,a,3220,a),flip(a)].">
      <j1 rule="hyper" parents="404 3220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,3053,a,b,3230,a)].">
      <j1 rule="hyper" parents="64 3053 3230"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2758,a(flip),b,3230,a)].">
      <j1 rule="hyper" parents="64 2758 3230"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,3230,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3230 22"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(81(a,1),3230(a,1,2))].">
      <j1 rule="para" parents="81 3230"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),3228(a,1,2,2))].">
      <j1 rule="para" parents="22 3228"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1823,a(flip),b,3232,a),flip(a)].">
      <j1 rule="hyper" parents="64 1823 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3179(a,1),3200(a,1))].">
      <j1 rule="para" parents="3179 3200"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3161(a,2),3200(a,1))].">
      <j1 rule="para" parents="3161 3200"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3217(a,1),3158(a,1,1))].">
      <j1 rule="para" parents="3217 3158"/>
    </justification>
  </clause>

  <clause id="3240">
    <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(1594(a,1),3239(a,2,2))].">
      <j1 rule="para" parents="1594 3239"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3025,a(flip),b,3207,a)].">
      <j1 rule="hyper" parents="64 3025 3207"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(3207(a,1),3164(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3207 3164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3223,a(flip),b,3241,a)].">
      <j1 rule="hyper" parents="64 3223 3241"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,935,a(flip),b,3243,a),flip(a)].">
      <j1 rule="hyper" parents="319 935 3243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      (T(x,y \ 1) \ x) \ (y * (T(y \ 1,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(y \ 1,x),y) = u
    ]]></literal>
    <justification jstring="[para(3243(a,2),489(a,1,1))].">
      <j1 rule="para" parents="3243 489"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2758(a,1),3244(a,1,1))].">
      <j1 rule="para" parents="2758 3244"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      x \ ((y * x) / y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,3023,a,b,3246,a)].">
      <j1 rule="hyper" parents="319 3023 3246"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      T(x,y) \ x = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,2866,a,b,3246,a),flip(a)].">
      <j1 rule="hyper" parents="319 2866 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3025,a(flip),b,3246,a),flip(a)].">
      <j1 rule="hyper" parents="319 3025 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,3246,a,b,3163,a)].">
      <j1 rule="hyper" parents="130 3246 3163"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,3166,a,b,3246,a)].">
      <j1 rule="hyper" parents="40 3166 3246"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      (x \ T(x,y)) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(130,a,3246,a(flip),b,2814,a)].">
      <j1 rule="hyper" parents="130 3246 2814"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      x \ (y \ T(y,x)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,3246,a(flip),b,1018,a)].">
      <j1 rule="hyper" parents="127 3246 1018"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(3246(a,2),3095(a,1,2,1))].">
      <j1 rule="para" parents="3246 3095"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(3246(a,2),3100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3246 3100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(3246(a,1),3184(a,2,1))].">
      <j1 rule="para" parents="3246 3184"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1042,a,3252,a)].">
      <j1 rule="hyper" parents="1042 3252"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(455,a,3252,a)].">
      <j1 rule="hyper" parents="455 3252"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(405,a,3252,a)].">
      <j1 rule="hyper" parents="405 3252"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      x * T(y,T(x,y)) = y * x
    ]]></literal>
    <justification jstring="[hyper(131,a,3252,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3252 22"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3181,a,b,3252,a)].">
      <j1 rule="hyper" parents="64 3181 3252"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3113,a,b,3252,a)].">
      <j1 rule="hyper" parents="64 3113 3252"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1295,a,b,3252,a)].">
      <j1 rule="hyper" parents="64 1295 3252"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(417,a,3252,a(flip),b,3113,a)].">
      <j1 rule="hyper" parents="417 3252 3113"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,3252,a(flip),b,1295,a),flip(a)].">
      <j1 rule="hyper" parents="206 3252 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(206,a,3252,a(flip),b,240,a)].">
      <j1 rule="hyper" parents="206 3252 240"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,3252,a(flip),b,240,a)].">
      <j1 rule="hyper" parents="131 3252 240"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,3252,a(flip),b,1031,a)].">
      <j1 rule="hyper" parents="128 3252 1031"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,3252,a(flip),b,1031,a),flip(a)].">
      <j1 rule="hyper" parents="127 3252 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(3252(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3252 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      T(L(x,y,z),T(u,x)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3252(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3252 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),3252(a,1,2))].">
      <j1 rule="para" parents="25 3252"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),3252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3252(a,1),241(a,1,2,1))].">
      <j1 rule="para" parents="3252 241"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3252(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="3252 242"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3252(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="3252 243"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3252(a,1),389(a,1,2,1))].">
      <j1 rule="para" parents="3252 389"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(3252(a,1),3114(a,1,1))].">
      <j1 rule="para" parents="3252 3114"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(3252(a,1),3235(a,1,2))].">
      <j1 rule="para" parents="3252 3235"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      x / (y \ T(x,y)) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3253,a(flip),b,3100,a(flip))].">
      <j1 rule="hyper" parents="128 3253 3100"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      T(x,x \ y) \ y = T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(1036,a,3258,a)].">
      <j1 rule="hyper" parents="1036 3258"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(206,a,27,a,b,3260,a)].">
      <j1 rule="hyper" parents="206 27 3260"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(22(a,1),3260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 3260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (x * y) / T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3260(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3260 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,3182,a,b,3261,a(flip))].">
      <j1 rule="hyper" parents="36 3182 3261"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1228,a,3290,a)].">
      <j1 rule="hyper" parents="1228 3290"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(515,a,3290,a)].">
      <j1 rule="hyper" parents="515 3290"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29,a,b,3290,a)].">
      <j1 rule="hyper" parents="64 29 3290"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      x * R(T(R(y,x,y),y * x),y,x) = y \ ((y * y) * x)
    ]]></literal>
    <justification jstring="[para(3290(a,1),1062(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3290 1062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      L(T(x,y),y,T(x,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(43,a,1301,a,b,3293,a),flip(a)].">
      <j1 rule="hyper" parents="43 1301 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(43,a,904,a,b,3293,a),flip(a)].">
      <j1 rule="hyper" parents="43 904 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      R(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(3293(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="3293 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[para(3293(a,1),516(a,1,1,1))].">
      <j1 rule="para" parents="3293 516"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      T(x,y) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(1309,a,3263,a),flip(a)].">
      <j1 rule="hyper" parents="1309 3263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      (x / y) / T(y,x / y) = (y \ x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,111,a(flip),b,3263,a),flip(a)].">
      <j1 rule="hyper" parents="128 111 3263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ y,z,x / T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(3263(a,1),610(a,1,2))].">
      <j1 rule="para" parents="3263 610"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3264(a,1),193(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3264 193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      (x / T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) / y) * z = u
    ]]></literal>
    <justification jstring="[para(3264(a,1),570(a,1,1,2))].">
      <j1 rule="para" parents="3264 570"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,3266,a(flip),b,1250,a),flip(a)].">
      <j1 rule="hyper" parents="131 3266 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[hyper(130,a,3267,a(flip),b,1294,a),flip(a)].">
      <j1 rule="hyper" parents="130 3267 1294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,3268,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="131 3268 194"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      (x * y) * L(z,T(y,x),T(x,y)) = T(x,y) * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3268,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 3268 197"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * T(y,z)) * T(z,y)) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[para(3268(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3268 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(3268(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3268 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(3268(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="3268 531"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      (T(x,y) \ y) * z = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3269(a,1),202(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3269 202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      T((x \ y) * x,x) = (T(x,y) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(130,a,3270,a,b,1248,a),flip(a)].">
      <j1 rule="hyper" parents="130 3270 1248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3270(a,2),89(a,1,2,1))].">
      <j1 rule="para" parents="3270 89"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      (T(x,y) * ((x \ T(y,x)) * z)) \ (y * z) = a(T(x,y),T(x,y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3270(a,1),86(a,1,1,2,1))].">
      <j1 rule="para" parents="3270 86"/>
    </justification>
  </clause>

  <clause id="3315">
    <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(3270(a,1),1834(a,1,2,1))].">
      <j1 rule="para" parents="3270 1834"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a(flip),b,3274,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      (x * (y / x)) / T(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(206,a,3274,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="206 3274 22"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3274(a,1),860(a,2,2))].">
      <j1 rule="para" parents="3274 860"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,3291,a(flip),b,1226,a)].">
      <j1 rule="hyper" parents="131 3291 1226"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3252(a,1),3291(a,1,3))].">
      <j1 rule="para" parents="3252 3291"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),3317(a,1,2))].">
      <j1 rule="para" parents="78 3317"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(3317(a,1),860(a,2,2))].">
      <j1 rule="para" parents="3317 860"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(785,a,3262,a),flip(a)].">
      <j1 rule="hyper" parents="785 3262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(784,a,3262,a)].">
      <j1 rule="hyper" parents="784 3262"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a(flip),b,3262,a)].">
      <j1 rule="hyper" parents="64 27 3262"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3262(a,1,1,2))].">
      <j1 rule="para" parents="10 3262"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(130,a,3326,a(flip),b,3284,a)].">
      <j1 rule="hyper" parents="130 3326 3284"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),3326(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 3326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,611,a,b,3327,a)].">
      <j1 rule="hyper" parents="319 611 3327"/>
    </justification>
  </clause>

  <clause id="3333">
    <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(64,a,27,a,b,3327,a)].">
      <j1 rule="hyper" parents="64 27 3327"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(3327(a,2),618(a,1,2))].">
      <j1 rule="para" parents="3327 618"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3327(a,1),3137(a,1,2))].">
      <j1 rule="para" parents="3327 3137"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      T(T(x,y),(x \ z) * x) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(3331(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3331 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(3331(a,1),291(a,1,2))].">
      <j1 rule="para" parents="3331 291"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      T((x \ y) * T(x,y),x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(3331(a,1),1277(a,1,1,2))].">
      <j1 rule="para" parents="3331 1277"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(3331(a,1),3263(a,1,1,2))].">
      <j1 rule="para" parents="3331 3263"/>
    </justification>
  </clause>

  <clause id="3340">
    <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(3335(a,1),391(a,1,2,1))].">
      <j1 rule="para" parents="3335 391"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3292(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),3292(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(3292(a,1),96(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3292 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(R(z,y,z),y,x) = u
    ]]></literal>
    <justification jstring="[para(3322(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="3322 489"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(3322(a,1),1494(a,1,1))].">
      <j1 rule="para" parents="3322 1494"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,x,x \ 1) = L(T((x \ 1) * x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(3322(a,1),2612(a,2,1))].">
      <j1 rule="para" parents="3322 2612"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2028,a,b,3332,a)].">
      <j1 rule="hyper" parents="64 2028 3332"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      T(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(3332(a,1),726(a,1))].">
      <j1 rule="para" parents="3332 726"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(39,a,3216,a(flip),b,3247,a),flip(a)].">
      <j1 rule="hyper" parents="39 3216 3247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3254(a,1),302(a,1,1))].">
      <j1 rule="para" parents="3254 302"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3074,a(flip),b,3257,a)].">
      <j1 rule="hyper" parents="319 3074 3257"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3259(a,1),698(a,1,1))].">
      <j1 rule="para" parents="3259 698"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,23,a,b,3271,a),flip(a)].">
      <j1 rule="hyper" parents="319 23 3271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      T(T(x,y),L(T(z,x),u,w)) = T(T(x,L(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(25(a,2),3271(a,1,2))].">
      <j1 rule="para" parents="25 3271"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(342,a,3281,a)].">
      <j1 rule="hyper" parents="342 3281"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(207,a,3281,a)].">
      <j1 rule="hyper" parents="207 3281"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(225(a,2),3281(a,1,1))].">
      <j1 rule="para" parents="225 3281"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      T(x,x \ T(x * y,y)) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3191,a(flip),b,3285,a),flip(a)].">
      <j1 rule="hyper" parents="319 3191 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      T((x / y) \ x,x / y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(318(a,1),3285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="318 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3217(a,1),3285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3217 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3324(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3324 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(3324(a,1),747(a,1,1))].">
      <j1 rule="para" parents="3324 747"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,3354,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3354 22"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(111(a,1),3354(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(3354(a,2),410(a,1))].">
      <j1 rule="para" parents="3354 410"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,225,a,b,3357,a),flip(a)].">
      <j1 rule="hyper" parents="319 225 3357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,y),z)
    ]]></literal>
    <justification jstring="[para(3296(a,1),25(a,2,1))].">
      <j1 rule="para" parents="3296 25"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1539,a,3298,a)].">
      <j1 rule="hyper" parents="1539 3298"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(3298(a,1),231(a,1,1))].">
      <j1 rule="para" parents="3298 231"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3298(a,2),899(a,1))].">
      <j1 rule="para" parents="3298 899"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3369(a,1),278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3369 278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,3372,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3372 22"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(3370(a,1),3252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3370 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,110,a(flip),b,3329,a),flip(a)].">
      <j1 rule="hyper" parents="319 110 3329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(681,a,3367,a)].">
      <j1 rule="hyper" parents="681 3367"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(634(a,1),3374(a,1,2))].">
      <j1 rule="para" parents="634 3374"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      R(T(T(x,y),z),x \ y,x) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3375(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3375 27"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      R(x,x \ y,x) * y = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(3375(a,1),243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3375 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(3188,a,3249,a)].">
      <j1 rule="hyper" parents="3188 3249"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      T(T(x,y) / y,z) = T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(244,a,3302,a,b,109,a)].">
      <j1 rule="hyper" parents="244 3302 109"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(244,a,3311,a,b,109,a)].">
      <j1 rule="hyper" parents="244 3311 109"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      (x * (x * (T(x,y) \ y))) / T((x \ y) * x,x) = T(x,T(x,y) \ y)
    ]]></literal>
    <justification jstring="[para(3312(a,2),3299(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3312 3299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(417,a,313,a(flip),b,3320,a)].">
      <j1 rule="hyper" parents="417 313 3320"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,3320,a(flip),b,710,a)].">
      <j1 rule="hyper" parents="127 3320 710"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,3349,a)].">
      <j1 rule="hyper" parents="144 3349"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(3349(a,1),231(a,1,1))].">
      <j1 rule="para" parents="3349 231"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(3349(a,1),633(a,1,1))].">
      <j1 rule="para" parents="3349 633"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(81(a,1),3387(a,1,2))].">
      <j1 rule="para" parents="81 3387"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(279,a,3390,a)].">
      <j1 rule="hyper" parents="279 3390"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y)
    ]]></literal>
    <justification jstring="[para(3390(a,1),758(a,1,1))].">
      <j1 rule="para" parents="3390 758"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,3389,a,b,95,a)].">
      <j1 rule="hyper" parents="131 3389 95"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(3389(a,2),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3389 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      (x * y) / a(T(x,x \ z) / z,(x \ z) * x,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(3356(a,2),708(a,1,2,1))].">
      <j1 rule="para" parents="3356 708"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(3217(a,1),3356(a,1,1))].">
      <j1 rule="para" parents="3217 3356"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),3376(a,1,3)),flip(a)].">
      <j1 rule="para" parents="111 3376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      ((x \ y) * x) * (y / x) = y * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(130,a,3386,a(flip),b,1315,a)].">
      <j1 rule="hyper" parents="130 3386 1315"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * ((y / x) \ y)
    ]]></literal>
    <justification jstring="[para(81(a,1),3399(a,1,1,1))].">
      <j1 rule="para" parents="81 3399"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(3116(a,1),3342(a,2,2))].">
      <j1 rule="para" parents="3116 3342"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      R(x,x \ y,x) * y = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,3325,a,b,3379,a),flip(a)].">
      <j1 rule="hyper" parents="319 3325 3379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,525,a,b,3402,a)].">
      <j1 rule="hyper" parents="36 525 3402"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3403(a,2,2))].">
      <j1 rule="para" parents="9 3403"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),3404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 3404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3323,a,b,3405,a)].">
      <j1 rule="hyper" parents="64 3323 3405"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(3406(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3406 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,1184,a(flip),b,3251,a)].">
      <j1 rule="hyper" parents="319 1184 3251"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(127,a,3268,a(flip),b,3275,a)].">
      <j1 rule="hyper" parents="127 3268 3275"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (y * L(x,z,u)) = T(T(y,L(x,z,u)),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),3410(a,1,1))].">
      <j1 rule="para" parents="25 3410"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      L(T(x,y),T(z,x),z / T(z,x)) * z = (z / T(z,x)) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,3364,a(flip),b,746,a),flip(a)].">
      <j1 rule="hyper" parents="131 3364 746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3331,a(flip),b,3377,a),flip(a)].">
      <j1 rule="hyper" parents="319 3331 3377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3413(a,1),1299(a,1,1))].">
      <j1 rule="para" parents="3413 1299"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3304,a(flip),b,3384,a),flip(a)].">
      <j1 rule="hyper" parents="64 3304 3384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      R(1 / x,x,x \ y) \ (y / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3398(a,1),381(a,1,1))].">
      <j1 rule="para" parents="3398 381"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      R(T(T(x,y),(x \ z) * x),x \ z,x) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(3336(a,2),3378(a,1,1))].">
      <j1 rule="para" parents="3336 3378"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(3416(a,1),596(a,1,2))].">
      <j1 rule="para" parents="3416 596"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3167,a(flip),b,3242,a),flip(a)].">
      <j1 rule="hyper" parents="319 3167 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(3352,a,3419,a),flip(a)].">
      <j1 rule="hyper" parents="3352 3419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3352,a,3420,a),flip(a)].">
      <j1 rule="hyper" parents="3352 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(3420(a,1),3352(a,1))].">
      <j1 rule="para" parents="3420 3352"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3421(a,1,2,1))].">
      <j1 rule="para" parents="9 3421"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),3421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 3421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      T(x / (y / (z * y)),z \ 1) = (y / (z * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,3423,a),flip(a)].">
      <j1 rule="hyper" parents="393 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3423,a),flip(a)].">
      <j1 rule="hyper" parents="334 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      (x / (y * x)) * T(z,y \ 1) = z * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(131,a,3423,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3423 22"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),3424(a,2,2))].">
      <j1 rule="para" parents="78 3424"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(81(a,1),3422(a,1,2,1))].">
      <j1 rule="para" parents="81 3422"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(611(a,1),3276(a,1,2))].">
      <j1 rule="para" parents="611 3276"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3373,a(flip),b,3433,a),flip(a)].">
      <j1 rule="hyper" parents="319 3373 3433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(3327(a,2),3434(a,1,2))].">
      <j1 rule="para" parents="3327 3434"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      (x * (R(x,y,z) * T(u,x))) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(3277(a,1),234(a,1,1,2))].">
      <j1 rule="para" parents="3277 234"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3262(a,1),3277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3262 3277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1250(a,1),3330(a,1,2))].">
      <j1 rule="para" parents="1250 3330"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3266(a,1),3438(a,1,2))].">
      <j1 rule="para" parents="3266 3438"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3440(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="3440 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1247,a(flip),b,3339,a),flip(a)].">
      <j1 rule="hyper" parents="36 1247 3339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,3442,a)].">
      <j1 rule="hyper" parents="144 3442"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      L(x,K(y,z \ 1),y) = x
    ]]></literal>
    <justification jstring="[para(3351(a,1),3097(a,1,2))].">
      <j1 rule="para" parents="3351 3097"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      R(x,K(x,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(3351(a,1),3141(a,1,2))].">
      <j1 rule="para" parents="3351 3141"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),3444(a,1,2,2))].">
      <j1 rule="para" parents="81 3444"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      L(x,K(y,z),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(1743,a,3446,a)].">
      <j1 rule="hyper" parents="1743 3446"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      L(x,K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3446(a,1),51(a,2))].">
      <j1 rule="para" parents="3446 51"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),3445(a,1,2,2))].">
      <j1 rule="para" parents="81 3445"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3449(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3449 27"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(3449(a,1),432(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3449 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(x,w)) * v5 = R(T(x,y),z,u) * (K(x,w) * v5)
    ]]></literal>
    <justification jstring="[para(3450(a,1),430(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3450 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      (T(x,y \ 1) / (y \ x)) \ x = (x \ (y \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,3397,a,b,156,a)].">
      <j1 rule="hyper" parents="129 3397 156"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(587,a,3400,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="587 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      (x * y) * ((y * x) / ((y * x) / x)) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),3455(a,1,1,2))].">
      <j1 rule="para" parents="11 3455"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(2758(a,1),3454(a,1,1,1))].">
      <j1 rule="para" parents="2758 3454"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      (x * y) * ((y * x) / y) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),3456(a,1,2,2))].">
      <j1 rule="para" parents="11 3456"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      x * (((y \ x) * y) / (y \ x)) = ((y \ x) * y) * y
    ]]></literal>
    <justification jstring="[hyper(568,a,3458,a)].">
      <j1 rule="hyper" parents="568 3458"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(3349(a,1),3459(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3349 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(3270(a,1),3460(a,1,1,1))].">
      <j1 rule="para" parents="3270 3460"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      (x * R(x * K(y,x),z,u)) / R(x * K(y,x),z,u) = T(x,R(x * K(y,x),z,u))
    ]]></literal>
    <justification jstring="[para(1929(a,1),3286(a,1,2,1))].">
      <j1 rule="para" parents="1929 3286"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3345,a(flip),b,3437,a),flip(a)].">
      <j1 rule="hyper" parents="319 3345 3437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) = L(R(x,y,x),y,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(3463(a,1),3343(a,1,2))].">
      <j1 rule="para" parents="3463 3343"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),3226(a,1,1,2))].">
      <j1 rule="para" parents="22 3226"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      x * R(T(R(y,x,y),y * x),y,x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,452,a(flip),b,3294,a),flip(a)].">
      <j1 rule="hyper" parents="319 452 3294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      x * R(T(y,x),y,x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(3328(a,1),3466(a,1,2,1))].">
      <j1 rule="para" parents="3328 3466"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      R(x,x,y) * y = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(391,a,3467,a)].">
      <j1 rule="hyper" parents="391 3467"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,1191,a(flip),b,3408,a),flip(a)].">
      <j1 rule="hyper" parents="64 1191 3408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,3451,a)].">
      <j1 rule="hyper" parents="488 3451"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2929(a,1),3451(a,1,1))].">
      <j1 rule="para" parents="2929 3451"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(3470(a,1),51(a,2))].">
      <j1 rule="para" parents="3470 51"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = R(R(x,u,x),y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(3407(a,1),3306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3407 3306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,696,a(flip),b,3393,a),flip(a)].">
      <j1 rule="hyper" parents="319 696 3393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x
    ]]></literal>
    <justification jstring="[para(3392(a,2),3474(a,1,2))].">
      <j1 rule="para" parents="3392 3474"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      ((x \ y) * x) * T((x \ y) \ y,z) = (T(x,z) * (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,3417,a(flip),b,654,a)].">
      <j1 rule="hyper" parents="131 3417 654"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * (T(x,y \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[para(3100(a,1),3144(a,2,2))].">
      <j1 rule="para" parents="3100 3144"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      T(x,y) * (T(x,x \ 1) \ z) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(2523(a,1),3145(a,1,2))].">
      <j1 rule="para" parents="2523 3145"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      (((x \ 1) \ 1) * T(x \ 1,y)) * z = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2984,a(flip),b,3478,a),flip(a)].">
      <j1 rule="hyper" parents="64 2984 3478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y * x) * T(y,x) = z
    ]]></literal>
    <justification jstring="[para(3305(a,2),3278(a,1))].">
      <j1 rule="para" parents="3305 3278"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(3443(a,1),3461(a,1,1))].">
      <j1 rule="para" parents="3443 3461"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(3337,a,3481,a),flip(a)].">
      <j1 rule="hyper" parents="3337 3481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3394,a,b,3482,a),flip(a)].">
      <j1 rule="hyper" parents="35 3394 3482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(199,a,3483,a)].">
      <j1 rule="hyper" parents="199 3483"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(78(a,1),3484(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 3484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(3389(a,1),3484(a,1,1))].">
      <j1 rule="para" parents="3389 3484"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      L(x,x \ y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(206,a,3266,a,b,3486,a),flip(a)].">
      <j1 rule="hyper" parents="206 3266 3486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      ((x \ y) * x) * T(T(x,x \ y),z) = (T(x,z) * (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(110(a,2),3476(a,1,2,1))].">
      <j1 rule="para" parents="110 3476"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      (x * y) * T(T(y,y \ (y * x)),z) = (T(y,z) * (y \ (y * x))) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3488(a,1,1,1))].">
      <j1 rule="para" parents="9 3488"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,430,a(flip),b,3473,a),flip(a)].">
      <j1 rule="hyper" parents="319 430 3473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1132(a,1),3490(a,1,1))].">
      <j1 rule="para" parents="1132 3490"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3345,a(flip),b,3491,a),flip(a)].">
      <j1 rule="hyper" parents="64 3345 3491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(127,a,3437,a,b,3491,a(flip))].">
      <j1 rule="hyper" parents="127 3437 3491"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(3492(a,1),332(a,1,2))].">
      <j1 rule="para" parents="3492 332"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(3344,a,3493,a)].">
      <j1 rule="hyper" parents="3344 3493"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(319,a,3290,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="319 3290 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      T(x,x \ T(x * y,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3496(a,1),3136(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3496 3136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      T(x,y) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(3498(a,1),3359(a,1,1))].">
      <j1 rule="para" parents="3498 3359"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),3499(a,1,1))].">
      <j1 rule="para" parents="22 3499"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      (x * T(y,x)) / T((x \ y) * x,x) = T(x,T(x,y) \ y)
    ]]></literal>
    <justification jstring="[para(3258(a,1),3383(a,1,1,2))].">
      <j1 rule="para" parents="3258 3383"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      (x * y) / T((y \ x) * y,y) = T(y,T(y,x) \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),3501(a,1,1))].">
      <j1 rule="para" parents="109 3501"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (y * L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(y,L(x,z,u)),L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(3411(a,2),410(a,1))].">
      <j1 rule="para" parents="3411 410"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      T(1 / x,y) * ((x \ 1) \ z) = (x * T(1 / x,y)) * z
    ]]></literal>
    <justification jstring="[para(2911(a,1),3479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2911 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      (T(1 / x,y) * z) / ((x * T(1 / x,y)) * z) = x \ 1
    ]]></literal>
    <justification jstring="[para(3504(a,1),3001(a,1,2))].">
      <j1 rule="para" parents="3504 3001"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      T(1 / x,y) * ((x * T(1 / x,y)) \ z) = (x \ 1) * z
    ]]></literal>
    <justification jstring="[para(3505(a,1),321(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3505 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      (x \ 1) \ T(1 / x,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,178,a(flip),b,3506,a(flip))].">
      <j1 rule="hyper" parents="127 178 3506"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      (T(x,y) * (x \ (x * z))) * x = (z * x) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3489(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      (x * y) * T(T(y,x),z) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3508(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      (x * y) * T(T(y,z),x) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[para(23(a,1),3509(a,1,2))].">
      <j1 rule="para" parents="23 3509"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      R(T(T(x,y),z * x),z,x) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(895,a,3510,a)].">
      <j1 rule="hyper" parents="895 3510"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(3464(a,1),3494(a,1))].">
      <j1 rule="para" parents="3464 3494"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),3475(a,2,1,2))].">
      <j1 rule="para" parents="81 3475"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      T(x,y) * L(T(T(x,y),x) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[para(186(a,1),3138(a,1,1))].">
      <j1 rule="para" parents="186 3138"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x,y) * L(T(x,y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(186(a,1),3515(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="186 3515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,1995,a(flip),b,3516,a),flip(a)].">
      <j1 rule="hyper" parents="319 1995 3516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3518">
    <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),3517(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3519">
    <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),3518(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      L(T((x \ 1) * x,x \ 1),y,z) = a(1 / L(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1055,a,3346,a),flip(a)].">
      <j1 rule="hyper" parents="1055 3346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      a(1 / L(x,y,z),x,x \ 1) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(2347(a,1),3520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2347 3520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) / R(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,3521,a(flip),b,1051,a)].">
      <j1 rule="hyper" parents="128 3521 1051"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) / R(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2349(a,1),3522(a,1,1))].">
      <j1 rule="para" parents="2349 3522"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3211(a,1),3214(a,2,2))].">
      <j1 rule="para" parents="3211 3214"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,3170,a(flip),b,3525,a),flip(a)].">
      <j1 rule="hyper" parents="127 3170 3525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,3526,a)].">
      <j1 rule="hyper" parents="145 3526"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3256,a,b,3527,a),flip(a)].">
      <j1 rule="hyper" parents="319 3256 3527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,3036,a,b,3527,a)].">
      <j1 rule="hyper" parents="64 3036 3527"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(127,a,3106,a(flip),b,3528,a),flip(a)].">
      <j1 rule="hyper" parents="127 3106 3528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1201,a,b,3528,a)].">
      <j1 rule="hyper" parents="64 1201 3528"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,3462,a),flip(a)].">
      <j1 rule="hyper" parents="257 3462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      (R(x,y,z) * (u * x)) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(1120(a,1),3436(a,1,1))].">
      <j1 rule="para" parents="1120 3436"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      (R(x,y,z) * (u * x)) \ ((R(x,y,z) * u) * x) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(1142(a,1),3534(a,1,2))].">
      <j1 rule="para" parents="1142 3534"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(713,a,3535,a),flip(a)].">
      <j1 rule="hyper" parents="713 3535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3537">
    <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(2172(a,1),3213(a,1,1))].">
      <j1 rule="para" parents="2172 3213"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(109(a,1),3537(a,1,1,1,2))].">
      <j1 rule="para" parents="109 3537"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3211(a,1),3538(a,1,2))].">
      <j1 rule="para" parents="3211 3538"/>
    </justification>
  </clause>

  <clause id="3540">
    <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),2892(a,1,1,1))].">
      <j1 rule="para" parents="11 2892"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,3215,a,b,3540,a),flip(a)].">
      <j1 rule="hyper" parents="36 3215 3540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(1774,a,3541,a)].">
      <j1 rule="hyper" parents="1774 3541"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(1920(a,1),3544(a,2,1))].">
      <j1 rule="para" parents="1920 3544"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3087,a(flip),b,3545,a),flip(a)].">
      <j1 rule="hyper" parents="64 3087 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,3185,a(flip),b,3546,a),flip(a)].">
      <j1 rule="hyper" parents="40 3185 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1820(a,1),3547(a,1,2))].">
      <j1 rule="para" parents="1820 3547"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3352,a,3548,a)].">
      <j1 rule="hyper" parents="3352 3548"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1920,a,b,3549,a)].">
      <j1 rule="hyper" parents="64 1920 3549"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(3549(a,1),3011(a,2,1,2))].">
      <j1 rule="para" parents="3549 3011"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3549(a,1),3351(a,1,2,2,1))].">
      <j1 rule="para" parents="3549 3351"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(206,a,3550,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="206 3550 110"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = 1 / (1 / T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(3550(a,1),2443(a,2,2,2))].">
      <j1 rule="para" parents="3550 2443"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(78(a,1),3553(a,1,2,2,1))].">
      <j1 rule="para" parents="78 3553"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(199,a,3555,a),flip(a)].">
      <j1 rule="hyper" parents="199 3555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(12(a,1),3556(a,1,2))].">
      <j1 rule="para" parents="12 3556"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,3552,a),flip(a)].">
      <j1 rule="hyper" parents="145 3552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3073,a,3558,a)].">
      <j1 rule="hyper" parents="3073 3558"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = T(1 / (1 / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2313,a(flip),b,3554,a),flip(a)].">
      <j1 rule="hyper" parents="319 2313 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3159,a(flip),b,3551,a),flip(a)].">
      <j1 rule="hyper" parents="319 3159 3551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(2923(a,1),3177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2923 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(2910,a,3562,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2910 3562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      x \ ((((x * y) \ x) \ 1) \ T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(3563(a,1),3174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3563 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      x \ (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(2869(a,1),3564(a,1,2))].">
      <j1 rule="para" parents="2869 3564"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      (K(x,y) \ y) \ 1 = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(959(a,2),3565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="959 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      1 / (x \ K(y,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(207,a,3566,a)].">
      <j1 rule="hyper" parents="207 3566"/>
    </justification>
  </clause>

  <clause id="3568">
    <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(81(a,1),2981(a,1,1,3))].">
      <j1 rule="para" parents="81 2981"/>
    </justification>
  </clause>

  <clause id="3569">
    <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(2729(a,1),3568(a,1,1))].">
      <j1 rule="para" parents="2729 3568"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2966(a,1),3569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2966 3569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),3570(a,2,1,1,2))].">
      <j1 rule="para" parents="7 3570"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(81(a,1),3571(a,2,2))].">
      <j1 rule="para" parents="81 3571"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = ((x / y) * (y / x)) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(3318(a,1),3229(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3318 3229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(319,a,1518,a(flip),b,3573,a),flip(a)].">
      <j1 rule="hyper" parents="319 1518 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      R(1 / (x / y),x / y,x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(3224(a,1),3574(a,1,3))].">
      <j1 rule="para" parents="3224 3574"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * R(1 / (y / x),y / x,y * (x / y)) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(3575(a,1),2963(a,1,1,1))].">
      <j1 rule="para" parents="3575 2963"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(3575(a,1),3576(a,1,2))].">
      <j1 rule="para" parents="3575 3576"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      T(x / y,(x / y) \ (1 / (y / x))) = x / y
    ]]></literal>
    <justification jstring="[hyper(346,a,3577,a)].">
      <j1 rule="hyper" parents="346 3577"/>
    </justification>
  </clause>

  <clause id="3579">
    <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(81(a,1),3240(a,1,1,2))].">
      <j1 rule="para" parents="81 3240"/>
    </justification>
  </clause>

  <clause id="3580">
    <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),3579(a,1,1))].">
      <j1 rule="para" parents="25 3579"/>
    </justification>
  </clause>

  <clause id="3581">
    <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(1592(a,1),3580(a,1,1))].">
      <j1 rule="para" parents="1592 3580"/>
    </justification>
  </clause>

  <clause id="3582">
    <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(81(a,1),3581(a,1,2,2,2))].">
      <j1 rule="para" parents="81 3581"/>
    </justification>
  </clause>

  <clause id="3583">
    <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),3582(a,1,2,2))].">
      <j1 rule="para" parents="25 3582"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1592(a,1),3583(a,1,2,2))].">
      <j1 rule="para" parents="1592 3583"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3584(a,1,2))].">
      <j1 rule="para" parents="9 3584"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R(R(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),1439(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1439"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (((x * y) * R((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * R(R(x,y,w) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(1457(a,1),3587(a,1,1))].">
      <j1 rule="para" parents="1457 3587"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      (((x * R(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1477(a,1),3588(a,1,1,1))].">
      <j1 rule="para" parents="1477 3588"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      R(x,y,z) * R(R(x,y,z) \ 1,u,w) = R(x * R(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(531,a,3589,a),flip(a)].">
      <j1 rule="hyper" parents="531 3589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      R(x * R(x \ 1,R(x,y,z),x \ 1),y,z) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1074,a(flip),b,3590,a),flip(a)].">
      <j1 rule="hyper" parents="64 1074 3590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x * T(x \ 1,R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(1510(a,1),3591(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1510 3591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,2235,a(flip),b,3592,a),flip(a)].">
      <j1 rule="hyper" parents="36 2235 3592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2991,a,3593,a)].">
      <j1 rule="hyper" parents="2991 3593"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,3594,a(flip),b,2182,a)].">
      <j1 rule="hyper" parents="127 3594 2182"/>
    </justification>
  </clause>

  <clause id="3599">
    <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(105(a,1),1442(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 1442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3600">
    <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(319,a,835,a(flip),b,3599,a),flip(a)].">
      <j1 rule="hyper" parents="319 835 3599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3601">
    <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(319,a,2065,a(flip),b,3600,a),flip(a)].">
      <j1 rule="hyper" parents="319 2065 3600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3602">
    <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(835(a,1),3601(a,1,1))].">
      <j1 rule="para" parents="835 3601"/>
    </justification>
  </clause>

  <clause id="3603">
    <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(2076(a,1),3602(a,2,1))].">
      <j1 rule="para" parents="2076 3602"/>
    </justification>
  </clause>

  <clause id="3604">
    <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(36,a,105,a,b,3603,a),flip(a)].">
      <j1 rule="hyper" parents="36 105 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1461,a,b,3604,a),flip(a)].">
      <j1 rule="hyper" parents="64 1461 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(3050(a,1),3605(a,1,1))].">
      <j1 rule="para" parents="3050 3605"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3049,a(flip),b,3606,a),flip(a)].">
      <j1 rule="hyper" parents="319 3049 3606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3608">
    <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(319,a,3077,a,b,3607,a)].">
      <j1 rule="hyper" parents="319 3077 3607"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(2758(a,1),3608(a,2,1,2))].">
      <j1 rule="para" parents="2758 3608"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(3424(a,1),3609(a,1,1,2))].">
      <j1 rule="para" parents="3424 3609"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),3610(a,1,1,2,2))].">
      <j1 rule="para" parents="11 3610"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3611(a,2),366(a,1)),flip(b)].">
      <j1 rule="para" parents="3611 366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3612,a,3611,a),flip(a)].">
      <j1 rule="hyper" parents="3612 3611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(3613(a,1),3029(a,1,1))].">
      <j1 rule="para" parents="3613 3029"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(3613(a,1),3529(a,1,1))].">
      <j1 rule="para" parents="3613 3529"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(3198,a,3615,a),flip(a)].">
      <j1 rule="hyper" parents="3198 3615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(3148,a,3615,a),flip(a)].">
      <j1 rule="hyper" parents="3148 3615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3256,a,b,3616,a)].">
      <j1 rule="hyper" parents="64 3256 3616"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,3469,a(flip),b,3616,a),flip(a)].">
      <j1 rule="hyper" parents="64 3469 3616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3251,a(flip),b,3616,a)].">
      <j1 rule="hyper" parents="64 3251 3616"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      (T(x,y) \ x) \ z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,3617,a)].">
      <j1 rule="hyper" parents="127 10 3617"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(64,a,3256,a,b,3617,a)].">
      <j1 rule="hyper" parents="64 3256 3617"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,3617,a(flip),b,3527,a),flip(a)].">
      <j1 rule="hyper" parents="127 3617 3527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      T(x,y) \ (y * z) = x \ (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,3617,a(flip),b,3256,a)].">
      <j1 rule="hyper" parents="127 3617 3256"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(3617(a,1),3255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3617 3255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,1017,a(flip),b,3619,a)].">
      <j1 rule="hyper" parents="127 1017 3619"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * (T(y \ 1,x) * z))) = L(z,T(y \ 1,x),y)
    ]]></literal>
    <justification jstring="[hyper(3245,a,3622,a),flip(a)].">
      <j1 rule="hyper" parents="3245 3622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,3623,a(flip),b,3531,a)].">
      <j1 rule="hyper" parents="131 3623 3531"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(481(a,1),3623(a,1,2))].">
      <j1 rule="para" parents="481 3623"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,3626,a(flip),b,3307,a)].">
      <j1 rule="hyper" parents="127 3626 3307"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(3626(a,1),3309(a,1,1))].">
      <j1 rule="para" parents="3626 3309"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,(y * x) / y) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(617(a,1),3627(a,1,1))].">
      <j1 rule="para" parents="617 3627"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(83(a,1),3614(a,1,2))].">
      <j1 rule="para" parents="83 3614"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(110(a,1),3634(a,1,1,2))].">
      <j1 rule="para" parents="110 3634"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(207,a,3636,a)].">
      <j1 rule="hyper" parents="207 3636"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      (x * (1 / x)) \ 1 = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2142(a,1),3636(a,1,1))].">
      <j1 rule="para" parents="2142 3636"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3195,a,b,3637,a)].">
      <j1 rule="hyper" parents="319 3195 3637"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(965,a,3621,a)].">
      <j1 rule="hyper" parents="965 3621"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      x * (T(x,y / (z \ 1)) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ T(z * y,x) = u
    ]]></literal>
    <justification jstring="[para(3621(a,1),965(a,1))].">
      <j1 rule="para" parents="3621 965"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(3128,a,3624,a),flip(a)].">
      <j1 rule="hyper" parents="3128 3624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3629(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(767(a,1),3629(a,1,2))].">
      <j1 rule="para" parents="767 3629"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(3629(a,1),87(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3629 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3631(a,1),489(a,1))].">
      <j1 rule="para" parents="3631 489"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      L(x,T(y,y \ z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(3221(a,1),3646(a,1,2))].">
      <j1 rule="para" parents="3221 3646"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(713,a,3632,a),flip(a)].">
      <j1 rule="hyper" parents="713 3632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3632(a,1),713(a,1))].">
      <j1 rule="para" parents="3632 713"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      a(T(x,T(y,x)),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3536,a(flip),b,3648,a),flip(a)].">
      <j1 rule="hyper" parents="319 3536 3648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      a(T(x * (y / x),x),T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * (y / x),x,z) = u
    ]]></literal>
    <justification jstring="[para(3326(a,1),3649(a,1,2))].">
      <j1 rule="para" parents="3326 3649"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      (x * L(y,z \ T(x,z),z)) \ (x * y) = a(T(z,x),T(z,x) \ x,y)
    ]]></literal>
    <justification jstring="[para(3630(a,1),3314(a,1,1))].">
      <j1 rule="para" parents="3630 3314"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,234,a(flip),b,3645,a),flip(a)].">
      <j1 rule="hyper" parents="319 234 3645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(3252(a,1),3650(a,1,1))].">
      <j1 rule="para" parents="3252 3650"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      x * (T(y,x \ 1) * (y \ (T(x \ 1,y) * z))) = L(z,T(x \ 1,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3477,a(flip),b,3628,a)].">
      <j1 rule="hyper" parents="64 3477 3628"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(3623(a,1),3655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3623 3655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(3656(a,2),606(a,1))].">
      <j1 rule="para" parents="3656 606"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      L(T(1 / x,y) \ z,x \ 1,x) = (x * T(1 / x,y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3657,a,3015,a)].">
      <j1 rule="hyper" parents="3657 3015"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * ((x * T(1 / x,y)) \ (x * z))
    ]]></literal>
    <justification jstring="[para(3659(a,1),2588(a,2,2))].">
      <j1 rule="para" parents="3659 2588"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * z) / y)),y) = (x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3506,a(flip),b,3660,a),flip(a)].">
      <j1 rule="hyper" parents="319 3506 3660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * (x * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(2575,a,3661,a)].">
      <j1 rule="hyper" parents="2575 3661"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,153,a(flip),b,3662,a),flip(a)].">
      <j1 rule="hyper" parents="319 153 3662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      (x * ((1 / y) * z)) / ((y \ 1) * z) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3664(a,1),1709(a,1,2))].">
      <j1 rule="para" parents="3664 1709"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      R(x,K(y \ 1,y),(1 / y) * z) = K(y \ 1,y) * (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3666(a,1),2513(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3666 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      R(x,K(y \ 1,y),(1 / y) * z) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,2542,a(flip),b,3667,a),flip(a)].">
      <j1 rule="hyper" parents="319 2542 3667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),3669(a,1,3))].">
      <j1 rule="para" parents="10 3669"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3673,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 3673 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2369,a(flip),b,3676,a)].">
      <j1 rule="hyper" parents="64 2369 3676"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      a(x,K(y \ 1,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,3676,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="126 3676 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(2534,a,3682,a)].">
      <j1 rule="hyper" parents="2534 3682"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(600,a,3682,a)].">
      <j1 rule="hyper" parents="600 3682"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,2343,a(flip),b,3682,a),flip(a)].">
      <j1 rule="hyper" parents="319 2343 3682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2526(a,1),3685(a,1,2,2))].">
      <j1 rule="para" parents="2526 3685"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2540(a,1),3685(a,1,2,2))].">
      <j1 rule="para" parents="2540 3685"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2717(a,1),3685(a,1,2,2))].">
      <j1 rule="para" parents="2717 3685"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2722(a,1),3685(a,1,2,2))].">
      <j1 rule="para" parents="2722 3685"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2339,a(flip),b,3686,a),flip(a)].">
      <j1 rule="hyper" parents="319 2339 3686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2541,a,b,3686,a)].">
      <j1 rule="hyper" parents="64 2541 3686"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) * y) \ z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,1732,a(flip),b,3686,a),flip(a)].">
      <j1 rule="hyper" parents="64 1732 3686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(2358(a,1),3686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2358 3686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(3700(a,1),2539(a,1,2,1))].">
      <j1 rule="para" parents="3700 2539"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(2342,a,3689,a)].">
      <j1 rule="hyper" parents="2342 3689"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3689(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3689 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(3689(a,1),1672(a,1,1))].">
      <j1 rule="para" parents="3689 1672"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(3689(a,1),1673(a,1,1))].">
      <j1 rule="para" parents="3689 1673"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      (x * ((K(y,y \ 1) * z) * u)) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(3693(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3693 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2541,a,b,3697,a)].">
      <j1 rule="hyper" parents="64 2541 3697"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1602(a,1),3697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1602 3697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3682(a,1),3697(a,1,2))].">
      <j1 rule="para" parents="3682 3697"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2431,a,3704,a)].">
      <j1 rule="hyper" parents="2431 3704"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,3704,a)].">
      <j1 rule="hyper" parents="529 3704"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,3704,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="126 3704 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3704(a,1),2536(a,1,1))].">
      <j1 rule="para" parents="3704 2536"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2519,a,3719,a),flip(a)].">
      <j1 rule="hyper" parents="2519 3719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2572,a(flip),b,3719,a)].">
      <j1 rule="hyper" parents="64 2572 3719"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3719(a,1),52(a,2))].">
      <j1 rule="para" parents="3719 52"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),3719(a,1,3,1))].">
      <j1 rule="para" parents="81 3719"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) = x
    ]]></literal>
    <justification jstring="[para(263(a,1),3719(a,1,3))].">
      <j1 rule="para" parents="263 3719"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1639(a,1),3719(a,1,3))].">
      <j1 rule="para" parents="1639 3719"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1694(a,2),3719(a,1,3))].">
      <j1 rule="para" parents="1694 3719"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1639(a,1),3720(a,1,3))].">
      <j1 rule="para" parents="1639 3720"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      a(x,y,K(1 / z,z)) = 1
    ]]></literal>
    <justification jstring="[para(1694(a,2),3720(a,1,3))].">
      <j1 rule="para" parents="1694 3720"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3726(a,1),52(a,2))].">
      <j1 rule="para" parents="3726 52"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      R(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(265(a,1),3726(a,1,3))].">
      <j1 rule="para" parents="265 3726"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      x * K(y,1 / y) != z * (u * K(y,1 / y))
    ]]></literal>
    <literal><![CDATA[
      z * u = x
    ]]></literal>
    <justification jstring="[para(3726(a,1),530(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3726 530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3727(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="3727 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(130,a,3728,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 3728 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3728(a,1),402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3728 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3728(a,1),519(a,1,1))].">
      <j1 rule="para" parents="3728 519"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,3729,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 3729 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3729(a,1),552(a,1,1))].">
      <j1 rule="para" parents="3729 552"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(53,a,3730,a)].">
      <j1 rule="hyper" parents="53 3730"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(53,a,3731,a)].">
      <j1 rule="hyper" parents="53 3731"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      (x * (y * (1 / y))) / z = x / (z / (y * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,540,a(flip),b,3733,a)].">
      <j1 rule="hyper" parents="64 540 3733"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1639(a,1),3723(a,1,2,2))].">
      <j1 rule="para" parents="1639 3723"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2339(a,2),3723(a,1,2))].">
      <j1 rule="para" parents="2339 3723"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2362(a,1),3723(a,1,2))].">
      <j1 rule="para" parents="2362 3723"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2363(a,1),3723(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2363 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),3723(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2524 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2532(a,1),3723(a,1,2))].">
      <j1 rule="para" parents="2532 3723"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2533(a,1),3723(a,1,2))].">
      <j1 rule="para" parents="2533 3723"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2716(a,1),3723(a,1,2))].">
      <j1 rule="para" parents="2716 3723"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2718(a,1),3723(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2718 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3716(a,1),3723(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3716 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      T(x,((1 / y) * z) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(2352(a,1),3745(a,1,2))].">
      <j1 rule="para" parents="2352 3745"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3698(a,2),3746(a,1,2))].">
      <j1 rule="para" parents="3698 3746"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2428(a,1),3749(a,1,2))].">
      <j1 rule="para" parents="2428 3749"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,3718,a(flip),b,1175,a)].">
      <j1 rule="hyper" parents="131 3718 1175"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,699,a(flip),b,3747,a),flip(a)].">
      <j1 rule="hyper" parents="64 699 3747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2058(a,2),3747(a,1,2,1))].">
      <j1 rule="para" parents="2058 3747"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,y \ 1)) = T(x,y \ K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(2854(a,1),3748(a,2,2))].">
      <j1 rule="para" parents="2854 3748"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3752(a,1),3620(a,1,2,1))].">
      <j1 rule="para" parents="3752 3620"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      T(x / y,(x / y) \ ((y / x) \ 1)) = x / y
    ]]></literal>
    <justification jstring="[hyper(64,a,3578,a(flip),b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="64 3578 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,3763,a)].">
      <j1 rule="hyper" parents="56 3763"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3737(a,1),2680(a,1,1))].">
      <j1 rule="para" parents="3737 2680"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ u) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(1704(a,1),3758(a,1,2,1))].">
      <j1 rule="para" parents="1704 3758"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(2527(a,1),3758(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2527 3758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      ((x / y) \ ((y / x) \ 1)) * (x / y) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,3767,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="131 3767 110"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3693(a,1),3715(a,1,1))].">
      <j1 rule="para" parents="3693 3715"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(2339(a,2),3724(a,1,2))].">
      <j1 rule="para" parents="2339 3724"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      T(x,y * (z * K(u,u \ 1))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3736(a,1),3745(a,1,2))].">
      <j1 rule="para" parents="3736 3745"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2354(a,1),3777(a,1,2,2))].">
      <j1 rule="para" parents="2354 3777"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2143(a,1),3738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2143 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2325(a,2),3738(a,1,2))].">
      <j1 rule="para" parents="2325 3738"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3780(a,1),2355(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3780 2355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      (x * (y * (1 / y))) / z = x / ((y * (1 / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2335(a,1),3743(a,2,2))].">
      <j1 rule="para" parents="2335 3743"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      T(x,((y \ 1) * y) \ z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(172(a,1),3770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="172 3770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = (x / z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,2325,a(flip),b,3776,a),flip(a)].">
      <j1 rule="hyper" parents="319 2325 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3693(a,1),3781(a,1,2))].">
      <j1 rule="para" parents="3693 3781"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * (x / z) = u
    ]]></literal>
    <justification jstring="[para(3785(a,2),2327(a,1))].">
      <j1 rule="para" parents="3785 2327"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2150,a(flip),b,3703,a)].">
      <j1 rule="hyper" parents="64 2150 3703"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3788(a,1),3572(a,1,1))].">
      <j1 rule="para" parents="3788 3572"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(3789(a,1),44(a,1))].">
      <j1 rule="para" parents="3789 44"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2699,a,3760,a)].">
      <j1 rule="hyper" parents="2699 3760"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * x) * (1 / x) = (L(x,y,z) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3760(a,1),2715(a,1,1))].">
      <j1 rule="para" parents="3760 2715"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(2706(a,1),3765(a,1,2))].">
      <j1 rule="para" parents="2706 3765"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(3641,a,3766,a)].">
      <j1 rule="hyper" parents="3641 3766"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,3766,a(flip),b,3640,a),flip(a)].">
      <j1 rule="hyper" parents="131 3766 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3640,a,b,3766,a(flip))].">
      <j1 rule="hyper" parents="130 3640 3766"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3794(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),3794(a,1,2,1,2))].">
      <j1 rule="para" parents="78 3794"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),3794(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 3794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(3103(a,2),3794(a,1,2,1))].">
      <j1 rule="para" parents="3103 3794"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,3795,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 3795 22"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3795(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(108(a,1),3795(a,2,2,1))].">
      <j1 rule="para" parents="108 3795"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(111(a,1),3795(a,2,2,1))].">
      <j1 rule="para" parents="111 3795"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2924(a,1),3795(a,2,2,1))].">
      <j1 rule="para" parents="2924 3795"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(3274(a,1),3795(a,2,2,1))].">
      <j1 rule="para" parents="3274 3795"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(3804(a,2),3639(a,1,1))].">
      <j1 rule="para" parents="3804 3639"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2546,a,b,3796,a)].">
      <j1 rule="hyper" parents="64 2546 3796"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3796(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 3796"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(77(a,1),3796(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 3796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(968,a,3797,a),flip(a)].">
      <j1 rule="hyper" parents="968 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,885,a,b,3797,a)].">
      <j1 rule="hyper" parents="319 885 3797"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(3797(a,1),111(a,1,1))].">
      <j1 rule="para" parents="3797 111"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(3797(a,2),388(a,1,2))].">
      <j1 rule="para" parents="3797 388"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(3797(a,1),2980(a,1,2))].">
      <j1 rule="para" parents="3797 2980"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(3799(a,1),111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3799 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      T(x,y) / T(x,z) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2816(a,1),3799(a,1,1,1))].">
      <j1 rule="para" parents="2816 3799"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2963(a,1),3799(a,1,1,1))].">
      <j1 rule="para" parents="2963 3799"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(3803(a,1),3326(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3803 3326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,3808,a)].">
      <j1 rule="hyper" parents="55 3808"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3827(a,1,2,2))].">
      <j1 rule="para" parents="11 3827"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(3812(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3812 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      T((x \ L(y,z,u)) * x,w) = (x \ L(T(y,w),z,u)) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),3813(a,2,1,2))].">
      <j1 rule="para" parents="25 3813"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(108(a,1),3813(a,2,1,2))].">
      <j1 rule="para" parents="108 3813"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(111(a,1),3813(a,2,1,2))].">
      <j1 rule="para" parents="111 3813"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      T((x \ y) * x,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(3813(a,2),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3813 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(3813(a,2),90(a,1,1))].">
      <j1 rule="para" parents="3813 90"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3813(a,2),3539(a,1,1,1,2))].">
      <j1 rule="para" parents="3813 3539"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(111(a,1),3802(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 3802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(3076(a,1),3810(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3076 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(279,a,3832,a)].">
      <j1 rule="hyper" parents="279 3832"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,3832,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 3832 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3841">
    <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),3829(a,1,1,1))].">
      <j1 rule="para" parents="10 3829"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,1210,a(flip),b,3798,a),flip(a)].">
      <j1 rule="hyper" parents="319 1210 3798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3795,a,b,3809,a),flip(a)].">
      <j1 rule="hyper" parents="319 3795 3809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(2534,a,3811,a),flip(a)].">
      <j1 rule="hyper" parents="2534 3811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(3815(a,2),3833(a,1))].">
      <j1 rule="para" parents="3815 3833"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(3089,a,3837,a),flip(a)].">
      <j1 rule="hyper" parents="3089 3837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x))
    ]]></literal>
    <justification jstring="[para(224(a,2),3837(a,2,2,2,1))].">
      <j1 rule="para" parents="224 3837"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3839(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 3839"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(69(a,1),3839(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="69 3839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2978,a,b,3840,a)].">
      <j1 rule="hyper" parents="64 2978 3840"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1238,a,b,3840,a)].">
      <j1 rule="hyper" parents="64 1238 3840"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      (x \ y) * ((z \ ((x \ y) \ y)) * z) = ((z \ x) * z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),3840(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 3840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(225(a,2),3840(a,1,1,1,2))].">
      <j1 rule="para" parents="225 3840"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(3432,a,3843,a)].">
      <j1 rule="hyper" parents="3432 3843"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2325(a,1),3844(a,1,1))].">
      <j1 rule="para" parents="2325 3844"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3371,a,3850,a),flip(a)].">
      <j1 rule="hyper" parents="3371 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * (y \ 1) = (x \ y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2725,a(flip),b,3782,a),flip(a)].">
      <j1 rule="hyper" parents="64 2725 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(3782(a,1),1712(a,1,2))].">
      <j1 rule="para" parents="3782 1712"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3782(a,1),1716(a,1,1))].">
      <j1 rule="para" parents="3782 1716"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(1406,a,3821,a)].">
      <j1 rule="hyper" parents="1406 3821"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(3734,a,2356,a(flip))].">
      <j1 rule="hyper" parents="3734 2356"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(1668,a,3863,a)].">
      <j1 rule="hyper" parents="1668 3863"/>
    </justification>
  </clause>

  <clause id="3865">
    <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(128,a,3707,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="128 3707 105"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(2390,a,3708,a)].">
      <j1 rule="hyper" parents="2390 3708"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,16,a,b,3866,a),flip(a)].">
      <j1 rule="hyper" parents="319 16 3866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1639(a,1),3867(a,1,1,2))].">
      <j1 rule="para" parents="1639 3867"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2339(a,2),3867(a,1,1))].">
      <j1 rule="para" parents="2339 3867"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2362(a,1),3867(a,1,1))].">
      <j1 rule="para" parents="2362 3867"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2363(a,1),3867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2363 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),3867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2524 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(2532(a,1),3867(a,1,1))].">
      <j1 rule="para" parents="2532 3867"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2533(a,1),3867(a,1,1))].">
      <j1 rule="para" parents="2533 3867"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2682(a,1),3867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2682 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2716(a,1),3867(a,1,1))].">
      <j1 rule="para" parents="2716 3867"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2718(a,1),3867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2718 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3715(a,2),3867(a,1,1))].">
      <j1 rule="para" parents="3715 3867"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2746(a,1),3868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2746 3868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(3738(a,2),3868(a,1,1))].">
      <j1 rule="para" parents="3738 3868"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3781(a,2),3868(a,1,1))].">
      <j1 rule="para" parents="3781 3868"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2784,a(flip),b,3869,a),flip(a)].">
      <j1 rule="hyper" parents="64 2784 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3699(a,1),3869(a,1,1))].">
      <j1 rule="para" parents="3699 3869"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(81(a,1),3883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,2),3883(a,1,2))].">
      <j1 rule="para" parents="110 3883"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(205(a,1),3883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="205 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1619(a,2),3883(a,1,2))].">
      <j1 rule="para" parents="1619 3883"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2055(a,2),3883(a,1,2))].">
      <j1 rule="para" parents="2055 3883"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(2312(a,1),3883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2312 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2489(a,2),3883(a,1,2))].">
      <j1 rule="para" parents="2489 3883"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(3886(a,1),2194(a,2,1))].">
      <j1 rule="para" parents="3886 2194"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(3886(a,2),2854(a,2,2))].">
      <j1 rule="para" parents="3886 2854"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,674,a,b,3887,a),flip(a)].">
      <j1 rule="hyper" parents="64 674 3887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / y) = K(x,(y / z) / y)
    ]]></literal>
    <justification jstring="[para(2768(a,2),3888(a,1,2))].">
      <j1 rule="para" parents="2768 3888"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,u),w,v5)) = K(x,L(L(y \ 1,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2656(a,1),3888(a,1,2))].">
      <j1 rule="para" parents="2656 3888"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      K(R(1 / x,y,z),u) = K(R(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2560(a,1),3872(a,1,1))].">
      <j1 rule="para" parents="2560 3872"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      K(x * ((1 / y) \ z),u) = K(x * ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3694(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3694 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2406(a,2),3875(a,1,1,2))].">
      <j1 rule="para" parents="2406 3875"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2527(a,1),3879(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2527 3879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(2351(a,1),3881(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2351 3881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(2724(a,1),3881(a,1,1,2))].">
      <j1 rule="para" parents="2724 3881"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(2560(a,1),3882(a,1,1,2))].">
      <j1 rule="para" parents="2560 3882"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(1588(a,1),3884(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1588 3884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3897(a,2),676(a,1))].">
      <j1 rule="para" parents="3897 676"/>
    </justification>
  </clause>

  <clause id="3913">
    <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),3717(a,2,1))].">
      <j1 rule="para" parents="18 3717"/>
    </justification>
  </clause>

  <clause id="3914">
    <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(2391,a,3722,a),flip(a)].">
      <j1 rule="hyper" parents="2391 3722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(713,a,3786,a),flip(a)].">
      <j1 rule="hyper" parents="713 3786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3854,a(flip),b,3860,a)].">
      <j1 rule="hyper" parents="64 3854 3860"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * y) = T((y \ x) * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(244,a,3916,a,b,1712,a),flip(a)].">
      <j1 rule="hyper" parents="244 3916 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,3789,a(flip),b,3916,a),flip(a)].">
      <j1 rule="hyper" parents="64 3789 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,3840,a(flip),b,3862,a)].">
      <j1 rule="hyper" parents="64 3840 3862"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(3561(a,1),3838(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3561 3838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(3831(a,1),3920(a,1,1))].">
      <j1 rule="para" parents="3831 3920"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3380,a(flip),b,3921,a),flip(a)].">
      <j1 rule="hyper" parents="319 3380 3921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3918,a,b,3922,a)].">
      <j1 rule="hyper" parents="64 3918 3922"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(1 / u,u))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3739(a,1),3740(a,1,2))].">
      <j1 rule="para" parents="3739 3740"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(3923(a,1),3861(a,2,2))].">
      <j1 rule="para" parents="3923 3861"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3706,a(flip),b,3913,a)].">
      <j1 rule="hyper" parents="64 3706 3913"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2339(a,2),3926(a,1,1))].">
      <j1 rule="para" parents="2339 3926"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,2339,a,b,3927,a),flip(a)].">
      <j1 rule="hyper" parents="319 2339 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      (x \ 1) \ L(K(x \ 1,x) * ((1 / x) * y),z,u) = x * T(L(x \ y,z,u),(x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(3927(a,2),2250(a,1,2))].">
      <j1 rule="para" parents="3927 2250"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2542(a,1),3928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2542 3928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2548,a,3930,a),flip(a)].">
      <j1 rule="hyper" parents="2548 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2534,a,3930,a),flip(a)].">
      <j1 rule="hyper" parents="2534 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2574,a(flip),b,3930,a)].">
      <j1 rule="hyper" parents="64 2574 3930"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      x \ L(x * (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,3930,a(flip),b,2574,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3930 2574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),3933(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 3933"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3933(a,1),77(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3933 77"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(77(a,1),3933(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 3933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,177,a(flip),b,3938,a),flip(a)].">
      <j1 rule="hyper" parents="42 177 3938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(131,a,3938,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 3938 18"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(177(a,1),3938(a,1,1)),flip(a)].">
      <j1 rule="para" parents="177 3938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(503(a,1),3938(a,2,1,2))].">
      <j1 rule="para" parents="503 3938"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(504(a,1),3938(a,2,1,2))].">
      <j1 rule="para" parents="504 3938"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1534,a,3939,a)].">
      <j1 rule="hyper" parents="1534 3939"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(346,a,3939,a)].">
      <j1 rule="hyper" parents="346 3939"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3939,a)].">
      <j1 rule="hyper" parents="134 3939"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3939(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3939 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      L(x,y,z) * (x / L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[para(3939(a,1),77(a,1,2,1))].">
      <j1 rule="para" parents="3939 77"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1964(a,1),3939(a,1,1))].">
      <j1 rule="para" parents="1964 3939"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(346,a,3941,a)].">
      <j1 rule="hyper" parents="346 3941"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,3941,a)].">
      <j1 rule="hyper" parents="142 3941"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(3941(a,1),2174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3941 2174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3950(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3950 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1964(a,1),3946(a,1,1))].">
      <j1 rule="para" parents="1964 3946"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      (((L(x,y,z) \ 1) * x) \ x) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(127,a,3948,a(flip),b,3561,a)].">
      <j1 rule="hyper" parents="127 3948 3561"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1421,a,b,3951,a)].">
      <j1 rule="hyper" parents="64 1421 3951"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(244,a,3944,a,b,1169,a)].">
      <j1 rule="hyper" parents="244 3944 1169"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      (1 / L(x,y,y \ 1)) \ a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(127,a,1964,a(flip),b,3944,a)].">
      <j1 rule="hyper" parents="127 1964 3944"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(244,a,3956,a,b,1065,a)].">
      <j1 rule="hyper" parents="244 3956 1065"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3959(a,1),3891(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3959 3891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,3945,a(flip))].">
      <j1 rule="hyper" parents="42 25 3945"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1700,a(flip),b,3952,a)].">
      <j1 rule="hyper" parents="64 1700 3952"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(110(a,2),3964(a,1,2,1))].">
      <j1 rule="para" parents="110 3964"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1649(a,1),3931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1649 3931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3931(a,2),3738(a,1,2))].">
      <j1 rule="para" parents="3931 3738"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3966(a,1),2557(a,1,1))].">
      <j1 rule="para" parents="3966 2557"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2145(a,1),3932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2145 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      T(x,L(T(y,y \ 1),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3969(a,1),3749(a,1,2))].">
      <j1 rule="para" parents="3969 3749"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(127,a,3953,a(flip),b,1013,a)].">
      <j1 rule="hyper" parents="127 3953 1013"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(302(a,1),3940(a,1,2,1,2))].">
      <j1 rule="para" parents="302 3940"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(127,a,3942,a(flip),b,262,a),flip(a)].">
      <j1 rule="hyper" parents="127 3942 262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3919,a(flip),b,3973,a)].">
      <j1 rule="hyper" parents="64 3919 3973"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,3973,a(flip),b,3919,a(flip))].">
      <j1 rule="hyper" parents="130 3973 3919"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,3925,a(flip),b,3943,a),flip(a)].">
      <j1 rule="hyper" parents="64 3925 3943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(170(a,1),3976(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="170 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,305,a,b,3977,a),flip(a)].">
      <j1 rule="hyper" parents="35 305 3977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3978,a),flip(a)].">
      <j1 rule="hyper" parents="145 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,683,a(flip),b,3978,a),flip(a)].">
      <j1 rule="hyper" parents="131 683 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3923,a,b,3978,a)].">
      <j1 rule="hyper" parents="64 3923 3978"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(130,a,3978,a(flip),b,3922,a)].">
      <j1 rule="hyper" parents="130 3978 3922"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(130,a,3978,a(flip),b,3380,a)].">
      <j1 rule="hyper" parents="130 3978 3380"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      (x * K(x \ y,x)) \ y = y / x
    ]]></literal>
    <justification jstring="[hyper(199,a,3979,a)].">
      <j1 rule="hyper" parents="199 3979"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      (x * K(x \ y,x)) * (y / x) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,3979,a)].">
      <j1 rule="hyper" parents="144 3979"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(3979(a,1),3389(a,1,1))].">
      <j1 rule="para" parents="3979 3389"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      (T(x,y) \ z) / ((T(x,y) \ z) / T(y,x)) = T(y,x) * K(y \ (x \ z),T(y,x))
    ]]></literal>
    <justification jstring="[para(3627(a,1),3979(a,2,2,1))].">
      <j1 rule="para" parents="3627 3979"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(459,a,3984,a)].">
      <j1 rule="hyper" parents="459 3984"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(3984(a,1),1824(a,2,2))].">
      <j1 rule="para" parents="3984 1824"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      K(x \ y,x) * ((y \ 1) \ 1) = K(y,y \ 1) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(3984(a,1),2673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3984 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),3993(a,1,2,1))].">
      <j1 rule="para" parents="9 3993"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(406,a,3996,a)].">
      <j1 rule="hyper" parents="406 3996"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(206,a,3996,a(flip),b,309,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 3996 309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,3996,a(flip),b,309,a(flip))].">
      <j1 rule="hyper" parents="131 3996 309"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      K(x,x \ y) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3997(a,1,2))].">
      <j1 rule="para" parents="10 3997"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,3185,a(flip),b,3998,a),flip(a)].">
      <j1 rule="hyper" parents="319 3185 3998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      x / ((y \ x) * y) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,156,a(flip),b,3998,a)].">
      <j1 rule="hyper" parents="319 156 3998"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,3998,a,b,3185,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 3998 3185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,3998,a,b,3185,a(flip))].">
      <j1 rule="hyper" parents="131 3998 3185"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3247,a,b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 3247 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,3211,a,b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 3211 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,2814,a,b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 2814 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,2812,a,b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 2812 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,1018,a,b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 1018 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,158,a,b,4001,a)].">
      <j1 rule="hyper" parents="319 158 4001"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,3248,a(flip),b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 3248 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3246,a(flip),b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 3246 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3243,a(flip),b,4001,a)].">
      <j1 rule="hyper" parents="319 3243 4001"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3166,a(flip),b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="319 3166 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      T(x,y) / K(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(206,a,4001,a,b,3246,a(flip))].">
      <j1 rule="hyper" parents="206 4001 3246"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4001,a,b,3247,a),flip(a)].">
      <j1 rule="hyper" parents="131 4001 3247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,4001,a,b,2562,a)].">
      <j1 rule="hyper" parents="131 4001 2562"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4001,a,b,3249,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 4001 3249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4001,a,b,3246,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 4001 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,4001,a,b,312,a(flip))].">
      <j1 rule="hyper" parents="131 4001 312"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(130,a,4001,a,b,2814,a)].">
      <j1 rule="hyper" parents="130 4001 2814"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(130,a,4001,a,b,3248,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 4001 3248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4001,a,b,2812,a)].">
      <j1 rule="hyper" parents="128 4001 2812"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,4001,a,b,1018,a),flip(a)].">
      <j1 rule="hyper" parents="127 4001 1018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      x \ K(x \ 1,y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4001,a,b,3243,a(flip))].">
      <j1 rule="hyper" parents="127 4001 3243"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4001(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),4001(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(111(a,1),4001(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      T(x,y) = (x * x) / (x * K(y,x))
    ]]></literal>
    <justification jstring="[para(4001(a,2),1015(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4001 1015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(4001(a,2),2818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4001 2818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(4001(a,2),2813(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4001 2813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(4001(a,2),3215(a,1,1))].">
      <j1 rule="para" parents="4001 3215"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      T(x,x * y) \ x = K(y * x,x)
    ]]></literal>
    <justification jstring="[para(3327(a,1),4001(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3327 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4001(a,2),3255(a,1,2,1))].">
      <j1 rule="para" parents="4001 3255"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4001(a,2),3256(a,2,1))].">
      <j1 rule="para" parents="4001 3256"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4001(a,2),3251(a,1,1))].">
      <j1 rule="para" parents="4001 3251"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4001(a,2),3527(a,2,1))].">
      <j1 rule="para" parents="4001 3527"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4001(a,2),3616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4001 3616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4001(a,2),3617(a,1,1))].">
      <j1 rule="para" parents="4001 3617"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      T(x \ T(y,x),z) * K(z,T(x,y) \ y) = T(x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(130,a,3382,a(flip),b,4003,a(flip))].">
      <j1 rule="hyper" parents="130 3382 4003"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      ((x \ y) \ y) * K(y / x,x) = x
    ]]></literal>
    <justification jstring="[hyper(130,a,3317,a(flip),b,4003,a(flip))].">
      <j1 rule="hyper" parents="130 3317 4003"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[hyper(130,a,111,a(flip),b,4003,a(flip))].">
      <j1 rule="hyper" parents="130 111 4003"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      T(x,y) != x / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4003(a,2),46(a,1))].">
      <j1 rule="para" parents="4003 46"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4003(a,2),333(a,1,1))].">
      <j1 rule="para" parents="4003 333"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(4004(a,1),3626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4004 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      x / T(x,y \ ((z \ 1) \ u)) = K(y \ ((1 / z) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3906,a,b,4007,a),flip(a)].">
      <j1 rule="hyper" parents="64 3906 4007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      K(x,y) != y / z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4007(a,2),46(a,1))].">
      <j1 rule="para" parents="4007 46"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4007(a,2),333(a,1,1))].">
      <j1 rule="para" parents="4007 333"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      L(T(x,y),T(z,x),z / T(z,x)) * z = K(x,z) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(4007(a,2),3412(a,2,1))].">
      <j1 rule="para" parents="4007 3412"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,949,a,b,4011,a),flip(a)].">
      <j1 rule="hyper" parents="319 949 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T((1 / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,948,a,b,4011,a),flip(a)].">
      <j1 rule="hyper" parents="319 948 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,4011,a,b,3032,a)].">
      <j1 rule="hyper" parents="131 4011 3032"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,4011,a,b,949,a)].">
      <j1 rule="hyper" parents="128 4011 949"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      T(x,y) = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4011,a,b,949,a),flip(a)].">
      <j1 rule="hyper" parents="127 4011 949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      R(T(x,y),z,u) / R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(27(a,2),4011(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4011(a,2),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4011 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      K(x,y) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(4011(a,2),2302(a,1,1))].">
      <j1 rule="para" parents="4011 2302"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(417,a,4012,a,b,937,a)].">
      <j1 rule="hyper" parents="417 4012 937"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3163,a,b,4012,a)].">
      <j1 rule="hyper" parents="319 3163 4012"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3142,a,b,4012,a)].">
      <j1 rule="hyper" parents="319 3142 4012"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3081,a,b,4012,a)].">
      <j1 rule="hyper" parents="319 3081 4012"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3074,a,b,4012,a)].">
      <j1 rule="hyper" parents="319 3074 4012"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3050,a,b,4012,a)].">
      <j1 rule="hyper" parents="319 3050 4012"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,3027,a,b,4012,a),flip(a)].">
      <j1 rule="hyper" parents="319 3027 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3026,a,b,4012,a),flip(a)].">
      <j1 rule="hyper" parents="319 3026 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,937,a,b,4012,a),flip(a)].">
      <j1 rule="hyper" parents="319 937 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z),y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,160,a,b,4012,a)].">
      <j1 rule="hyper" parents="319 160 4012"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,942,a(flip),b,4012,a)].">
      <j1 rule="hyper" parents="319 942 4012"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,4012,a,b,3142,a)].">
      <j1 rule="hyper" parents="130 4012 3142"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,4012,a,b,3027,a),flip(a)].">
      <j1 rule="hyper" parents="130 4012 3027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,4012,a,b,3026,a)].">
      <j1 rule="hyper" parents="127 4012 3026"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3886,a,b,4012,a),flip(a)].">
      <j1 rule="hyper" parents="64 3886 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      K(x \ (x * y),z) = y \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,683,a,b,4012,a)].">
      <j1 rule="hyper" parents="64 683 4012"/>
    </justification>
  </clause>

  <clause id="4086">
    <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),4012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4087">
    <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),4012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4012(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4012 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      (x * x) \ T(x,y) = (1 / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4012(a,2),450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4012 450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1453(a,1),4012(a,2,2))].">
      <j1 rule="para" parents="1453 4012"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      (x \ 1) / K(x,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4012(a,2),1983(a,1,2))].">
      <j1 rule="para" parents="4012 1983"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      T(x,y) \ x = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4012(a,2),2563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4012 2563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4012(a,2),3019(a,1,1,2))].">
      <j1 rule="para" parents="4012 3019"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(4012(a,2),3028(a,1,1,1))].">
      <j1 rule="para" parents="4012 3028"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4012(a,2),3021(a,1,2))].">
      <j1 rule="para" parents="4012 3021"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      x \ T(x,y \ x) = K(x,x / y)
    ]]></literal>
    <justification jstring="[para(3116(a,1),4012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3116 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4012(a,2),3143(a,1,1))].">
      <j1 rule="para" parents="4012 3143"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4012(a,2),3146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4012 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4012(a,2),3165(a,1,1))].">
      <j1 rule="para" parents="4012 3165"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      x \ T(x,x * y) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(3327(a,1),4012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3327 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4015(a,1),135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4015 135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4015(a,1),333(a,1,1))].">
      <j1 rule="para" parents="4015 333"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      R(x / y,y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) / (y * K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(4015(a,1),601(a,1,1,1))].">
      <j1 rule="para" parents="4015 601"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(206,a,4019,a,b,194,a)].">
      <j1 rule="hyper" parents="206 4019 194"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4019,a,b,301,a),flip(a)].">
      <j1 rule="hyper" parents="131 4019 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      x * K(x,y * (z \ 1)) = T(x,y * (1 / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,3753,a,b,4019,a),flip(a)].">
      <j1 rule="hyper" parents="64 3753 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ 1) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3431,a,b,4019,a)].">
      <j1 rule="hyper" parents="64 3431 4019"/>
    </justification>
  </clause>

  <clause id="4114">
    <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(4019(a,2),529(a,2,2))].">
      <j1 rule="para" parents="4019 529"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(111(a,1),4021(a,1,2))].">
      <j1 rule="para" parents="111 4021"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4021(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4021 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = T(x,y) / R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,4022,a,b,1482,a),flip(a)].">
      <j1 rule="hyper" parents="128 4022 1482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(131,a,4022,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 4022 22"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4022(a,2),96(a,2,2))].">
      <j1 rule="para" parents="4022 96"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4022(a,2),2928(a,1))].">
      <j1 rule="para" parents="4022 2928"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      K(x,y / x) \ (y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(393,a,4030,a),flip(a)].">
      <j1 rule="hyper" parents="393 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3567,a,b,4030,a),flip(a)].">
      <j1 rule="hyper" parents="319 3567 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      K(x \ y,x) * R(T(x,x \ y),z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(4030(a,2),2257(a,1,2,1))].">
      <j1 rule="para" parents="4030 2257"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(253,a,4096,a),flip(a)].">
      <j1 rule="hyper" parents="253 4096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(2826(a,1),4096(a,1,1))].">
      <j1 rule="para" parents="2826 4096"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),T(x,y)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,1491,a,b,4130,a),flip(a)].">
      <j1 rule="hyper" parents="41 1491 4130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,4130,a(flip),b,4003,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 4130 4003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      ((x * x) \ y) * K(x * x,y) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4130,a(flip),b,702,a),flip(a)].">
      <j1 rule="hyper" parents="128 4130 702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4130(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4130 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      T(R(x * K(y,x),z,u),y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4130(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4130 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(4130(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4130(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      T((x * (y * K(z,y))) / x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4130(a,1),453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4130 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      (((x * x) \ (y * K(x * x,y))) * x) * x = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(4130(a,1),913(a,2,1))].">
      <j1 rule="para" parents="4130 913"/>
    </justification>
  </clause>

  <clause id="4142">
    <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(4130(a,1),1971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 1971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2854(a,1),4130(a,1,1))].">
      <j1 rule="para" parents="2854 4130"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4130(a,1),3252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4130 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4130(a,1),3273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 3273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(3895(a,1),4130(a,1,1))].">
      <j1 rule="para" parents="3895 4130"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4005(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4005(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4005 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(4005(a,2),153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4005 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      T(x \ y,z) \ T(y / x,z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(447(a,1),4005(a,2,2)),flip(a)].">
      <j1 rule="para" parents="447 4005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      K(x,y) = x * (((y * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,1202,a,b,4006,a),flip(a)].">
      <j1 rule="hyper" parents="319 1202 4006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,4006,a,b,1202,a),flip(a)].">
      <j1 rule="hyper" parents="127 4006 1202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      K(x,y) \ x = (y * x) / y
    ]]></literal>
    <justification jstring="[para(4006(a,2),2888(a,1,1))].">
      <j1 rule="para" parents="4006 2888"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      ((x * (1 / T(y,z))) * y) / K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(4008(a,2),531(a,1,2))].">
      <j1 rule="para" parents="4008 531"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4009(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4009 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(4009(a,2),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4009 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,4014,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 4014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      T(x,y) \ K(T(x,y),y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,4014,a,b,937,a)].">
      <j1 rule="hyper" parents="127 4014 937"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3237,a,4159,a),flip(a)].">
      <j1 rule="hyper" parents="3237 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      (x * y) * K(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,4159,a(flip),b,235,a)].">
      <j1 rule="hyper" parents="131 4159 235"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      T(x,y) * K(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4159,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 4159 4012"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      K(x,y) * T(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(130,a,4159,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 4159 4011"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),4159(a,1,1))].">
      <j1 rule="para" parents="22 4159"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(111(a,1),4159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      K((x * y) / x,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(110(a,1),4159(a,1,1))].">
      <j1 rule="para" parents="110 4159"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      K(R(x \ y,x,z),x) = K((y * z) / (x * z),x)
    ]]></literal>
    <justification jstring="[para(668(a,1),4159(a,1,1))].">
      <j1 rule="para" parents="668 4159"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(779(a,1),4159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="779 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4159(a,1),3237(a,1))].">
      <j1 rule="para" parents="4159 3237"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),4162(a,1,2))].">
      <j1 rule="para" parents="22 4162"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4162(a,1,2))].">
      <j1 rule="para" parents="25 4162"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),4162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(251(a,1),4162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="251 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(252(a,1),4162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="252 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4162(a,1),4030(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4162 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3480,a,4016,a),flip(a)].">
      <j1 rule="hyper" parents="3480 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,3896,a(flip),b,4016,a)].">
      <j1 rule="hyper" parents="319 3896 4016"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,3895,a(flip),b,4016,a)].">
      <j1 rule="hyper" parents="319 3895 4016"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,4016,a,b,2852,a),flip(a)].">
      <j1 rule="hyper" parents="131 4016 2852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(130,a,2854,a(flip),b,4016,a)].">
      <j1 rule="hyper" parents="130 2854 4016"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4016(a,1),295(a,1))].">
      <j1 rule="para" parents="4016 295"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4016(a,1),336(a,1,1))].">
      <j1 rule="para" parents="4016 336"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),4016(a,1,1))].">
      <j1 rule="para" parents="105 4016"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4016(a,1),106(a,1,1))].">
      <j1 rule="para" parents="4016 106"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(4016(a,2),520(a,1,2))].">
      <j1 rule="para" parents="4016 520"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4016(a,1),765(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4016 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4016(a,1),820(a,1,1))].">
      <j1 rule="para" parents="4016 820"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4016(a,1),824(a,1,1))].">
      <j1 rule="para" parents="4016 824"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(4016(a,1),822(a,1,1))].">
      <j1 rule="para" parents="4016 822"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(4016(a,1),1375(a,2,1,2))].">
      <j1 rule="para" parents="4016 1375"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      ((x * y) * R(y,z,u)) / (x * R(y,z,u)) = y * K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1480(a,1),4016(a,1,1))].">
      <j1 rule="para" parents="1480 4016"/>
    </justification>
  </clause>

  <clause id="4197">
    <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(1524(a,1),4016(a,1,1))].">
      <j1 rule="para" parents="1524 4016"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ ((x * K(y,x)) * (L(z,K(y,x),x) * u)) = L(u,L(z,K(y,x),x),(y * x) / y)
    ]]></literal>
    <justification jstring="[para(4016(a,2),483(a,2,3))].">
      <j1 rule="para" parents="4016 483"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      a(x * K(y,x),y,z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4016(a,1),3653(a,1,1))].">
      <j1 rule="para" parents="4016 3653"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4016(a,1),3858(a,1,1,2))].">
      <j1 rule="para" parents="4016 3858"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      (x * K(y,x)) \ x = K(x,y)
    ]]></literal>
    <justification jstring="[para(4016(a,1),4006(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4016 4006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      ((x \ y) \ y) \ 1 = x \ K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(680,a,4024,a)].">
      <j1 rule="hyper" parents="680 4024"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(4024(a,1),1999(a,1,2,1))].">
      <j1 rule="para" parents="4024 1999"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4024(a,1),2308(a,2,1))].">
      <j1 rule="para" parents="4024 2308"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,4032,a),flip(a)].">
      <j1 rule="hyper" parents="142 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),4032(a,1,2,1))].">
      <j1 rule="para" parents="10 4032"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),4032(a,1,2,1))].">
      <j1 rule="para" parents="85 4032"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[para(920(a,1),4075(a,2,1)),flip(a)].">
      <j1 rule="para" parents="920 4075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(356,a,4077,a(flip))].">
      <j1 rule="hyper" parents="356 4077"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(4077(a,2),489(a,1,2,2))].">
      <j1 rule="para" parents="4077 489"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4001,a,b,4094,a),flip(a)].">
      <j1 rule="hyper" parents="64 4001 4094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,4001,a,b,4094,a(flip))].">
      <j1 rule="hyper" parents="206 4001 4094"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,4001,a,b,4094,a(flip))].">
      <j1 rule="hyper" parents="131 4001 4094"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,2915,a(flip),b,4094,a(flip))].">
      <j1 rule="hyper" parents="40 2915 4094"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4213(a,1),72(a,1,2,2))].">
      <j1 rule="para" parents="4213 72"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4213(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4213 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4213(a,1),1584(a,1,3))].">
      <j1 rule="para" parents="4213 1584"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(4213(a,1),1741(a,1,3))].">
      <j1 rule="para" parents="4213 1741"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4213(a,1),1814(a,2,2,1))].">
      <j1 rule="para" parents="4213 1814"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      T(K(x,y),z) * R(T(K(x,y),z) \ 1,u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(4213(a,1),1978(a,2,1,2,1))].">
      <j1 rule="para" parents="4213 1978"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4213(a,1),2608(a,2,2))].">
      <j1 rule="para" parents="4213 2608"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4213(a,1),4077(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4213 4077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      K(x,y) != 1 / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4214(a,1),46(a,1))].">
      <j1 rule="para" parents="4214 46"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4214(a,1),135(a,1,1))].">
      <j1 rule="para" parents="4214 135"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4214(a,1),333(a,1,1))].">
      <j1 rule="para" parents="4214 333"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      ((x * y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(y * K(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(4095(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="4095 531"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y * K(x,y)) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4095(a,1),3281(a,1,1,2))].">
      <j1 rule="para" parents="4095 3281"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4016,a(flip),b,4155,a),flip(a)].">
      <j1 rule="hyper" parents="319 4016 4155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      x / (y / (y / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(206,a,3349,a(flip),b,4155,a)].">
      <j1 rule="hyper" parents="206 3349 4155"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      R(K(x,y) \ x,y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4155(a,2),106(a,1,1))].">
      <j1 rule="para" parents="4155 106"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,4167,a,b,89,a)].">
      <j1 rule="hyper" parents="131 4167 89"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      L(x,K(y \ z,y),z / y) = x
    ]]></literal>
    <justification jstring="[para(4167(a,1),3446(a,1,2))].">
      <j1 rule="para" parents="4167 3446"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,91,a,b,4175,a)].">
      <j1 rule="hyper" parents="64 91 4175"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3559,a(flip),b,4175,a),flip(a)].">
      <j1 rule="hyper" parents="64 3559 4175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4175,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="131 4175 91"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,4206,a,b,1376,a)].">
      <j1 rule="hyper" parents="128 4206 1376"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4232(a,1),3176(a,2,2))].">
      <j1 rule="para" parents="4232 3176"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      (K(x,y) \ x) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(4232(a,2),3176(a,1,1))].">
      <j1 rule="para" parents="4232 3176"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      x * K(T(y,x),x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4159(a,2),4232(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4159 4232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),4046(a,1,1))].">
      <j1 rule="para" parents="23 4046"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),4046(a,1,1))].">
      <j1 rule="para" parents="25 4046"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27(a,2),4046(a,1,1))].">
      <j1 rule="para" parents="27 4046"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(3243(a,1),4046(a,1))].">
      <j1 rule="para" parents="3243 4046"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(22(a,1),4172(a,1,2))].">
      <j1 rule="para" parents="22 4172"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),4172(a,1,2))].">
      <j1 rule="para" parents="25 4172"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      K(x,R(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27(a,2),4172(a,1,2))].">
      <j1 rule="para" parents="27 4172"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      K(x,R(T(y,x * z),x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(x * z) \ ((x * y) * z)) = u
    ]]></literal>
    <justification jstring="[para(1003(a,1),4172(a,1,2))].">
      <j1 rule="para" parents="1003 4172"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      K(x \ y,x) \ y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,3985,a)].">
      <j1 rule="hyper" parents="134 3985"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      (x \ K((x \ 1) \ y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2854(a,1),3989(a,1,1))].">
      <j1 rule="para" parents="2854 3989"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      (((x \ y) * x) \ y) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(90(a,2),4000(a,1,1))].">
      <j1 rule="para" parents="90 4000"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      (x * (y / x)) / y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3639,a,b,4002,a)].">
      <j1 rule="hyper" parents="64 3639 4002"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(887,a,4013,a)].">
      <j1 rule="hyper" parents="887 4013"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(448,a,4013,a)].">
      <j1 rule="hyper" parents="448 4013"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2232,a(flip),b,4013,a)].">
      <j1 rule="hyper" parents="64 2232 4013"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4013,a(flip),b,1180,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 4013 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4013,a(flip),b,1361,a(flip))].">
      <j1 rule="hyper" parents="130 4013 1361"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(127,a,4013,a(flip),b,875,a(flip))].">
      <j1 rule="hyper" parents="127 4013 875"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4013(a,1),733(a,2,2))].">
      <j1 rule="para" parents="4013 733"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      (x / y) * K(y \ 1,z) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[para(4013(a,1),888(a,1,2))].">
      <j1 rule="para" parents="4013 888"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4013(a,1),893(a,2,2))].">
      <j1 rule="para" parents="4013 893"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(4013(a,1),1096(a,1,1))].">
      <j1 rule="para" parents="4013 1096"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4013(a,1),1324(a,2,1))].">
      <j1 rule="para" parents="4013 1324"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(4013(a,1),1323(a,1))].">
      <j1 rule="para" parents="4013 1323"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4013(a,1),1454(a,2,2))].">
      <j1 rule="para" parents="4013 1454"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = K(x \ 1,y) \ x
    ]]></literal>
    <justification jstring="[para(4013(a,1),1990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4013 1990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4018(a,2),1356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4018 1356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4029(a,2),1682(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4029 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4046,a,4034,a),flip(a)].">
      <j1 rule="hyper" parents="4046 4034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      K(x * y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(4034(a,1),4046(a,1))].">
      <j1 rule="para" parents="4034 4046"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      K(x * (y / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),4281(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 4281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(600,a,4036,a)].">
      <j1 rule="hyper" parents="600 4036"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(599,a,4036,a),flip(a)].">
      <j1 rule="hyper" parents="599 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) = T(x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="417 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      T(x,y) * (K(x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(331,a,4036,a),flip(a)].">
      <j1 rule="hyper" parents="331 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4036,a)].">
      <j1 rule="hyper" parents="134 4036"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4077,a,b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="127 4077 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,3106,a(flip),b,4036,a)].">
      <j1 rule="hyper" parents="127 3106 4036"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,3528,a,b,4036,a)].">
      <j1 rule="hyper" parents="35 3528 4036"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1011,a,b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="35 1011 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,3434,a(flip),b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="35 3434 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4036(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4036 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4036(a,1),44(a,1))].">
      <j1 rule="para" parents="4036 44"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4036(a,1),330(a,1,2))].">
      <j1 rule="para" parents="4036 330"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(2099(a,1),4036(a,1,2))].">
      <j1 rule="para" parents="2099 4036"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      x * (T(K(x,y),z) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3279(a,2),4036(a,1,2))].">
      <j1 rule="para" parents="3279 4036"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(4159(a,1),4036(a,1,2,1))].">
      <j1 rule="para" parents="4159 4036"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(897,a,4037,a)].">
      <j1 rule="hyper" parents="897 4037"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(134,a,4037,a)].">
      <j1 rule="hyper" parents="134 4037"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      x \ (K(x,y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,4037,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 4037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4036,a,b,4037,a)].">
      <j1 rule="hyper" parents="64 4036 4037"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3953,a(flip),b,4037,a)].">
      <j1 rule="hyper" parents="64 3953 4037"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3623,a(flip),b,4037,a(flip))].">
      <j1 rule="hyper" parents="128 3623 4037"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,3623,a(flip),b,4037,a(flip))].">
      <j1 rule="hyper" parents="127 3623 4037"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,4037,a(flip),b,3619,a(flip))].">
      <j1 rule="hyper" parents="127 4037 3619"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4037(a,1),586(a,1))].">
      <j1 rule="para" parents="4037 586"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4012(a,2),4037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4012 4037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1043,a,4040,a)].">
      <j1 rule="hyper" parents="1043 4040"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1037,a,4040,a)].">
      <j1 rule="hyper" parents="1037 4040"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1036,a,4040,a),flip(a)].">
      <j1 rule="hyper" parents="1036 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      x * (y * (T(y,z) \ u)) = x * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,4040,a,b,9,a)].">
      <j1 rule="hyper" parents="131 4040 9"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,4040,a(flip),b,1016,a)].">
      <j1 rule="hyper" parents="206 4040 1016"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(131,a,4040,a(flip),b,1016,a)].">
      <j1 rule="hyper" parents="131 4040 1016"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,3766,a(flip),b,4040,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3766 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      x \ (y * (K(z,y \ x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(y \ x,z) \ u,y \ x,y) = w
    ]]></literal>
    <justification jstring="[para(4040(a,1),741(a,1,2,2))].">
      <j1 rule="para" parents="4040 741"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4040(a,1),1036(a,1))].">
      <j1 rule="para" parents="4040 1036"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(4040(a,1),1043(a,1))].">
      <j1 rule="para" parents="4040 1043"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3265(a,1),4040(a,1,2,1))].">
      <j1 rule="para" parents="3265 4040"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4012(a,2),4040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4012 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      ((x * y) * z) / (T(R(x,y,z),u) * (y * z)) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,105,a(flip),b,4041,a)].">
      <j1 rule="hyper" parents="128 105 4041"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      T(x \ y,z) * T(x,x \ y) = K(z,x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(127,a,228,a(flip),b,4041,a),flip(a)].">
      <j1 rule="hyper" parents="127 228 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4041(a,1),330(a,1,2))].">
      <j1 rule="para" parents="4041 330"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(206,a,4047,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="206 4047 194"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,4159,a(flip),b,4070,a)].">
      <j1 rule="hyper" parents="130 4159 4070"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(105(a,1),4070(a,1,2))].">
      <j1 rule="para" parents="105 4070"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(671(a,2),4070(a,1,2))].">
      <j1 rule="para" parents="671 4070"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1361,a(flip),b,4079,a)].">
      <j1 rule="hyper" parents="64 1361 4079"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,314,a(flip),b,4081,a),flip(a)].">
      <j1 rule="hyper" parents="319 314 4081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,109,a(flip),b,4081,a)].">
      <j1 rule="hyper" parents="127 109 4081"/>
    </justification>
  </clause>

  <clause id="4337">
    <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),4081(a,2,1))].">
      <j1 rule="para" parents="27 4081"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4081(a,1),331(a,1))].">
      <j1 rule="para" parents="4081 331"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(242(a,1),4081(a,1,2))].">
      <j1 rule="para" parents="242 4081"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(243(a,1),4081(a,1,2))].">
      <j1 rule="para" parents="243 4081"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(4081(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="4081 531"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3049,a,b,4084,a)].">
      <j1 rule="hyper" parents="64 3049 4084"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4084(a,1),4106(a,1))].">
      <j1 rule="para" parents="4084 4106"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4085(a,2),4106(a,1))].">
      <j1 rule="para" parents="4085 4106"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,4093,a)].">
      <j1 rule="hyper" parents="144 4093"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ 1,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(2920(a,2),4097(a,1,2))].">
      <j1 rule="para" parents="2920 4097"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(4097(a,1),3172(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4097 3172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(4097(a,1),3532(a,1,2,1))].">
      <j1 rule="para" parents="4097 3532"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4106,a,4098,a),flip(a)].">
      <j1 rule="hyper" parents="4106 4098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),4350(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 4350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      K(x,T(y,y \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,2),4351(a,1,2))].">
      <j1 rule="para" parents="110 4351"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      K(x * y,T(y,x)) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(3288(a,2),4351(a,1,2))].">
      <j1 rule="para" parents="3288 4351"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      K(x * y,T(x,y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4352(a,1,2,2))].">
      <j1 rule="para" parents="9 4352"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3621,a,b,4101,a),flip(a)].">
      <j1 rule="hyper" parents="64 3621 4101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4040,a(flip),b,4101,a),flip(a)].">
      <j1 rule="hyper" parents="64 4040 4101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(417,a,4101,a(flip),b,4040,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="417 4101 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(206,a,4040,a(flip),b,4101,a(flip))].">
      <j1 rule="hyper" parents="206 4040 4101"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      (x \ y) / (T(x,z) \ y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,1017,a(flip),b,4101,a(flip))].">
      <j1 rule="hyper" parents="206 1017 4101"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,3640,a,b,4101,a(flip))].">
      <j1 rule="hyper" parents="131 3640 4101"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,3621,a,b,4101,a(flip))].">
      <j1 rule="hyper" parents="131 3621 4101"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(131,a,4040,a(flip),b,4101,a(flip))].">
      <j1 rule="hyper" parents="131 4040 4101"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4101,a(flip),b,4040,a(flip))].">
      <j1 rule="hyper" parents="128 4101 4040"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      K(x,y) \ (K(y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(127,a,4101,a(flip),b,4040,a(flip))].">
      <j1 rule="hyper" parents="127 4101 4040"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(771,a,4356,a),flip(a)].">
      <j1 rule="hyper" parents="771 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(582,a,4356,a)].">
      <j1 rule="hyper" parents="582 4356"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,2838,a,b,4356,a),flip(a)].">
      <j1 rule="hyper" parents="319 2838 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * K(z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,2833,a,b,4356,a)].">
      <j1 rule="hyper" parents="206 2833 4356"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,2099,a,b,4356,a)].">
      <j1 rule="hyper" parents="131 2099 4356"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(130,a,4356,a,b,197,a)].">
      <j1 rule="hyper" parents="130 4356 197"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2448,a(flip),b,4356,a),flip(a)].">
      <j1 rule="hyper" parents="64 2448 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4356(a,1),140(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4356 140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(4356(a,1),145(a,1))].">
      <j1 rule="para" parents="4356 145"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(4356(a,1),260(a,1,2))].">
      <j1 rule="para" parents="4356 260"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(4356(a,1),261(a,1,2))].">
      <j1 rule="para" parents="4356 261"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(4356(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4356 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(4356(a,1),302(a,1,1,2))].">
      <j1 rule="para" parents="4356 302"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(4356(a,1),302(a,1,1))].">
      <j1 rule="para" parents="4356 302"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(4356(a,1),593(a,1,2))].">
      <j1 rule="para" parents="4356 593"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4356(a,1),354(a,1,1,3))].">
      <j1 rule="para" parents="4356 354"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u) = ((K(y,x) * z) * u) / (K(y,x) * (z * u))
    ]]></literal>
    <justification jstring="[para(4356(a,1),2972(a,1,1))].">
      <j1 rule="para" parents="4356 2972"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      x * (K(y,x) \ z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4356(a,2),4036(a,1,2))].">
      <j1 rule="para" parents="4356 4036"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4359(a,1),333(a,1,1))].">
      <j1 rule="para" parents="4359 333"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(4359(a,1),221(a,1)),flip(b)].">
      <j1 rule="para" parents="4359 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      x / (K(y,z) * ((x \ 1) \ 1)) = K(x \ 1,x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(4359(a,1),1734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4359 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,4363,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="131 4363 194"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      x * L(y,K(z,u) * x,K(u,z)) = K(u,z) * ((K(z,u) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(130,a,4363,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 4363 197"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4363(a,1),584(a,1))].">
      <j1 rule="para" parents="4363 584"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      L(T(x,x \ (K(y,z) * u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(4363(a,1),345(a,2,2))].">
      <j1 rule="para" parents="4363 345"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (K(u,z) * (K(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(4363(a,1),484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ u = z
    ]]></literal>
    <justification jstring="[para(4364(a,1),47(a,1))].">
      <j1 rule="para" parents="4364 47"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4364(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4364 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4106,a,4104,a),flip(a)].">
      <j1 rule="hyper" parents="4106 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(4104(a,1),4106(a,1))].">
      <j1 rule="para" parents="4104 4106"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(85(a,1),4394(a,2,2))].">
      <j1 rule="para" parents="85 4394"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(41,a,4130,a,b,4135,a)].">
      <j1 rule="hyper" parents="41 4130 4135"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,3328,a,b,4135,a),flip(a)].">
      <j1 rule="hyper" parents="41 3328 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,1491,a,b,4135,a),flip(a)].">
      <j1 rule="hyper" parents="41 1491 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(4135(a,1),50(a,2)),flip(b)].">
      <j1 rule="para" parents="4135 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      T(K(x,y) / (1 / y),x) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),4146(a,1,1,1,2))].">
      <j1 rule="para" parents="81 4146"/>
    </justification>
  </clause>

  <clause id="4403">
    <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(4152(a,2),1118(a,2,2))].">
      <j1 rule="para" parents="4152 1118"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),4153(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(3298(a,1),4153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3298 4153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4153(a,1),3424(a,1,2))].">
      <j1 rule="para" parents="4153 3424"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      T(x,y) * T(x,y) = x * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4165(a,1),4036(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4165 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(244,a,4183,a(flip),b,4076,a(flip))].">
      <j1 rule="hyper" parents="244 4183 4076"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,z,K(y,x)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,4220,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="131 4220 18"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3075,a,4242,a)].">
      <j1 rule="hyper" parents="3075 4242"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(4244(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4244 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(3357(a,1),4244(a,2,2))].">
      <j1 rule="para" parents="3357 4244"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      K(R(x,y,y \ 1),y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(790(a,1),4245(a,2,2))].">
      <j1 rule="para" parents="790 4245"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4016(a,1),4245(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4016 4245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      x \ y != K(z \ u,z) * (z * (u / z))
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(4258(a,1),329(a,2,2))].">
      <j1 rule="para" parents="4258 329"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      (T(x,y) * T(K(x,y) \ z,u)) / T(x,y) = T((x * z) / T(x,y),u)
    ]]></literal>
    <justification jstring="[para(4284(a,1),447(a,1,1,2,1))].">
      <j1 rule="para" parents="4284 447"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      T(x,x \ 1) \ (x * y) = (x * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1628(a,1),4284(a,2,1))].">
      <j1 rule="para" parents="1628 4284"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(4285(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4285 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(4285(a,1),302(a,1,1,2))].">
      <j1 rule="para" parents="4285 302"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      (x * (1 / x)) \ (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1628(a,1),4285(a,1,1))].">
      <j1 rule="para" parents="1628 4285"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4287(a,1),586(a,1))].">
      <j1 rule="para" parents="4287 586"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      K(T(x,y) \ (x * z),u) = K(K(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4287(a,1),683(a,1,1,2))].">
      <j1 rule="para" parents="4287 683"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a,b,4288,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 4288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1344,a(flip),b,4289,a)].">
      <j1 rule="hyper" parents="64 1344 4289"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,4363,a,b,4289,a)].">
      <j1 rule="hyper" parents="35 4363 4289"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,4289,a(flip),b,4356,a)].">
      <j1 rule="hyper" parents="206 4289 4356"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(4292(a,1),44(a,1))].">
      <j1 rule="para" parents="4292 44"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) = K(w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),4307(a,1,2,1))].">
      <j1 rule="para" parents="27 4307"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      ((x \ 1) * x) \ (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(263(a,1),4308(a,1,1))].">
      <j1 rule="para" parents="263 4308"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      T(x,y) * (y \ z) = x * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4292,a(flip),b,4312,a)].">
      <j1 rule="hyper" parents="131 4292 4312"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,4065,a(flip),b,4312,a)].">
      <j1 rule="hyper" parents="131 4065 4312"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4312,a(flip),b,4309,a),flip(a)].">
      <j1 rule="hyper" parents="131 4312 4309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      T(x / y,z) \ x = K(z,x / y) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),4312(a,1,2))].">
      <j1 rule="para" parents="12 4312"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (L(x,z,u) * w) = K(y,L(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),4312(a,1,1))].">
      <j1 rule="para" parents="25 4312"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4312(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4312 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[para(4004(a,1),4312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4004 4312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4019(a,2),4312(a,1,2))].">
      <j1 rule="para" parents="4019 4312"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      T(x,y) \ (K(z,x) * u) = K(y,x) * (T(x,z) \ u)
    ]]></literal>
    <justification jstring="[para(4040(a,1),4312(a,1,2))].">
      <j1 rule="para" parents="4040 4312"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(4162(a,1),4314(a,1,1))].">
      <j1 rule="para" parents="4162 4314"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      ((x * y) * z) / (K(u,R(x,y,z)) * (y * z)) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(105(a,1),4316(a,1,1))].">
      <j1 rule="para" parents="105 4316"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(3441,a,4317,a),flip(a)].">
      <j1 rule="hyper" parents="3441 4317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4317(a,1),3626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4317 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,4343,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="131 4343 91"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(78(a,1),4343(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 4343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      x * K(y,1 / (x \ z)) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(4343(a,1),1826(a,1,2))].">
      <j1 rule="para" parents="4343 1826"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      K(x,y) * (z * R(T(K(y,x),z),u,w)) = (K(x,y) * R(K(x,y) \ 1,u,w)) * z
    ]]></literal>
    <justification jstring="[para(4357(a,1),1512(a,1,2,2,1))].">
      <j1 rule="para" parents="4357 1512"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,w),y,z) \ u) = K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),4360(a,1,2,1))].">
      <j1 rule="para" parents="25 4360"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      K(x,y) \ (y * z) = y * (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4308,a,b,4383,a)].">
      <j1 rule="hyper" parents="319 4308 4383"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      K(x,y) \ T(x,y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3435,a(flip),b,4383,a),flip(a)].">
      <j1 rule="hyper" parents="35 3435 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      K(x,y) \ T(x,x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3434,a(flip),b,4383,a),flip(a)].">
      <j1 rule="hyper" parents="35 3434 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      K(x,x * y) \ T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3345,a(flip),b,4383,a),flip(a)].">
      <j1 rule="hyper" parents="35 3345 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(199,a,4417,a)].">
      <j1 rule="hyper" parents="199 4417"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2917(a,2),4417(a,2,1))].">
      <j1 rule="para" parents="2917 4417"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4429(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4429 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4450,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 4450 197"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(4450(a,1),194(a,1,2,1))].">
      <j1 rule="para" parents="4450 194"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3895(a,1),4191(a,1,1))].">
      <j1 rule="para" parents="3895 4191"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2836,a,4295,a)].">
      <j1 rule="hyper" parents="2836 4295"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4295,a(flip),b,2833,a),flip(a)].">
      <j1 rule="hyper" parents="127 4295 2833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      K(T(x,y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(4287(a,1),4345(a,1,1,2))].">
      <j1 rule="para" parents="4287 4345"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(3682(a,1),4375(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3682 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4399(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4399 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,4461,a(flip),b,4101,a),flip(a)].">
      <j1 rule="hyper" parents="127 4461 4101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      K(x,y) \ T(x,x \ y) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4461(a,1,1,2))].">
      <j1 rule="para" parents="10 4461"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x,x * y),z,u) * T(x,y)) = L(K(x,x * y),z,u) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4461(a,1),1165(a,2,2))].">
      <j1 rule="para" parents="4461 1165"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(T(x,x * y),y) * z
    ]]></literal>
    <justification jstring="[para(616(a,1),4039(a,1,2,1))].">
      <j1 rule="para" parents="616 4039"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(3349(a,1),4039(a,1,2,1))].">
      <j1 rule="para" parents="3349 4039"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(4054(a,2),1322(a,2,1))].">
      <j1 rule="para" parents="4054 1322"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4069(a,1,1,2,1))].">
      <j1 rule="para" parents="9 4069"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2202,a(flip),b,4074,a)].">
      <j1 rule="hyper" parents="64 2202 4074"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(4074(a,1),1004(a,2,2))].">
      <j1 rule="para" parents="4074 1004"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(4074(a,1),2076(a,2,1))].">
      <j1 rule="para" parents="4074 2076"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(4074(a,1),3602(a,1,1))].">
      <j1 rule="para" parents="4074 3602"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,4092,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 4092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      K(x,((y \ z) / z) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4105,a,4111,a)].">
      <j1 rule="hyper" parents="4105 4111"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),4490(a,1,2,1,1))].">
      <j1 rule="para" parents="81 4490"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y) * 1
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a,b,4491,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3886,a,b,4491,a)].">
      <j1 rule="hyper" parents="64 3886 4491"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),4491(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),4491(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 4493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(4494(a,1),4116(a,1,1))].">
      <j1 rule="para" parents="4494 4116"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      ((x * y) \ y) * K(x * y,1 / x) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4497,a(flip),b,4028,a)].">
      <j1 rule="hyper" parents="131 4497 4028"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(4497(a,2),4344(a,1))].">
      <j1 rule="para" parents="4497 4344"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,4130,a,b,4136,a)].">
      <j1 rule="hyper" parents="41 4130 4136"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      a((x \ y) * K(y / (y / x),x \ y),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(3387(a,1),4199(a,2,2))].">
      <j1 rule="para" parents="3387 4199"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      x \ (x \ (T(x,y) * z)) = (K(x,y) \ x) \ z
    ]]></literal>
    <justification jstring="[para(4427(a,2),4248(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4427 4248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4279,a,b,xx)].">
      <j1 rule="hyper" parents="131 4279"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(4016(a,2),4280(a,1,3))].">
      <j1 rule="para" parents="4016 4280"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(127,a,4290,a,b,10,a)].">
      <j1 rule="hyper" parents="127 4290 10"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(4290(a,2),96(a,2,2))].">
      <j1 rule="para" parents="4290 96"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      x \ (y * K(x,y)) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(4016(a,1),4290(a,1,2))].">
      <j1 rule="para" parents="4016 4290"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),4293(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(3349(a,1),4293(a,1,1))].">
      <j1 rule="para" parents="3349 4293"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4016(a,1),4293(a,1,1))].">
      <j1 rule="para" parents="4016 4293"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      K(x / y,y) * (z * (x / y)) = (y \ x) * T(z,x / y)
    ]]></literal>
    <justification jstring="[para(111(a,1),4294(a,2,1))].">
      <j1 rule="para" parents="111 4294"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2936,a,4311,a(flip))].">
      <j1 rule="hyper" parents="2936 4311"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2935,a,4311,a(flip))].">
      <j1 rule="hyper" parents="2935 4311"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[hyper(206,a,3853,a(flip),b,4355,a)].">
      <j1 rule="hyper" parents="206 3853 4355"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(206,a,1359,a(flip),b,4355,a)].">
      <j1 rule="hyper" parents="206 1359 4355"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(131,a,936,a(flip),b,4355,a)].">
      <j1 rule="hyper" parents="131 936 4355"/>
    </justification>
  </clause>

  <clause id="4523">
    <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(345(a,2),4362(a,1,2,2,1))].">
      <j1 rule="para" parents="345 4362"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) / (T((x \ 1) \ 1,y) * K(z,(x \ 1) \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,2920,a(flip),b,4369,a),flip(a)].">
      <j1 rule="hyper" parents="319 2920 4369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3172,a,b,4437,a)].">
      <j1 rule="hyper" parents="64 3172 4437"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,4437,a(flip),b,516,a),flip(a)].">
      <j1 rule="hyper" parents="130 4437 516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4437(a,1),331(a,1))].">
      <j1 rule="para" parents="4437 331"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (K(y,x) * (x * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4437(a,1),484(a,1,1))].">
      <j1 rule="para" parents="4437 484"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,2099,a,b,4442,a),flip(a)].">
      <j1 rule="hyper" parents="319 2099 4442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      T(x,y) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4442(a,2),4393(a,1))].">
      <j1 rule="para" parents="4442 4393"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4492(a,2),138(a,1)),flip(b)].">
      <j1 rule="para" parents="4492 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      T(x,(x / y) / x) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,4343,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 4343 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,4526,a)].">
      <j1 rule="hyper" parents="529 4526"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,4526,a)].">
      <j1 rule="hyper" parents="488 4526"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(3979(a,2),4526(a,1,1))].">
      <j1 rule="para" parents="3979 4526"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4016(a,2),4526(a,1,1))].">
      <j1 rule="para" parents="4016 4526"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(4097(a,1),4526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4097 4526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(4537(a,1),433(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4537 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(4537(a,1),430(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4537 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(1741,a,4538,a)].">
      <j1 rule="hyper" parents="1741 4538"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      ((x \ 1) * K(y,x)) \ z = K(y,x) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1595,a(flip),b,4538,a)].">
      <j1 rule="hyper" parents="64 1595 4538"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(4538(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="4538 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4538(a,1),51(a,2))].">
      <j1 rule="para" parents="4538 51"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(4538(a,1),300(a,1,2))].">
      <j1 rule="para" parents="4538 300"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1143,a,4544,a),flip(a)].">
      <j1 rule="hyper" parents="1143 4544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      L(x,K(y,z),1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1581(a,2),4547(a,1))].">
      <j1 rule="para" parents="1581 4547"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(571,a,4540,a)].">
      <j1 rule="hyper" parents="571 4540"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4540,a(flip),b,825,a)].">
      <j1 rule="hyper" parents="130 4540 825"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(127,a,4036,a(flip),b,4540,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 4036 4540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,1200,a,b,4540,a(flip))].">
      <j1 rule="hyper" parents="35 1200 4540"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(4175(a,1),4540(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4175 4540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[para(4450(a,1),4540(a,2,2))].">
      <j1 rule="para" parents="4450 4540"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(3349(a,1),4552(a,1,2,1))].">
      <j1 rule="para" parents="3349 4552"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),4555(a,1,1,1))].">
      <j1 rule="para" parents="10 4555"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(81(a,1),4102(a,1,2))].">
      <j1 rule="para" parents="81 4102"/>
    </justification>
  </clause>

  <clause id="4563">
    <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(2223(a,1),4253(a,1))].">
      <j1 rule="para" parents="2223 4253"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),4310(a,1,2))].">
      <j1 rule="para" parents="10 4310"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = w
    ]]></literal>
    <justification jstring="[para(4309(a,1),4338(a,1,2))].">
      <j1 rule="para" parents="4309 4338"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(2154(a,1),4440(a,1,2))].">
      <j1 rule="para" parents="2154 4440"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      T(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4363(a,1),4440(a,1,2))].">
      <j1 rule="para" parents="4363 4440"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4532,a(flip),b,4476,a)].">
      <j1 rule="hyper" parents="64 4532 4476"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4442,a(flip),b,4476,a)].">
      <j1 rule="hyper" parents="64 4442 4476"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y),z)) \ (T(K(x,y),z) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(4477(a,1),510(a,2,1))].">
      <j1 rule="para" parents="4477 510"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(76(a,1),4535(a,1,2,1))].">
      <j1 rule="para" parents="76 4535"/>
    </justification>
  </clause>

  <clause id="4572">
    <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(106(a,2),4535(a,1,2,1))].">
      <j1 rule="para" parents="106 4535"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (1 / y)) = z
    ]]></literal>
    <justification jstring="[para(81(a,1),4571(a,1,2))].">
      <j1 rule="para" parents="81 4571"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z / y)) = u
    ]]></literal>
    <justification jstring="[para(4491(a,1),4571(a,1))].">
      <j1 rule="para" parents="4491 4571"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      T(x,y) \ R(x,y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4292,a,b,4568,a)].">
      <j1 rule="hyper" parents="35 4292 4568"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,4288,a,b,4568,a(flip))].">
      <j1 rule="hyper" parents="39 4288 4568"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      x \ y != K(x,z) * K(x * z,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(4568(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="4568 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4281(a,2),4568(a,1,2))].">
      <j1 rule="para" parents="4281 4568"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4575(a,1),96(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4575 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4575(a,1),4421(a,1,2))].">
      <j1 rule="para" parents="4575 4421"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(4576(a,1),4298(a,1,2))].">
      <j1 rule="para" parents="4576 4298"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4569(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4281(a,2),4569(a,1,1))].">
      <j1 rule="para" parents="4281 4569"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4012(a,2),4072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4012 4072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(81(a,1),4584(a,2,1,2))].">
      <j1 rule="para" parents="81 4584"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3883(a,1),4584(a,2,1))].">
      <j1 rule="para" parents="3883 4584"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(4584(a,1),4089(a,1,2))].">
      <j1 rule="para" parents="4584 4089"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4571,a,4586,a)].">
      <j1 rule="hyper" parents="4571 4586"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2310(a,1),4586(a,1,2))].">
      <j1 rule="para" parents="2310 4586"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(4586(a,1),2937(a,1,2,1))].">
      <j1 rule="para" parents="4586 2937"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      T(x,y) != K(z,1 / T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,1 / u) = x
    ]]></literal>
    <justification jstring="[para(4590(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="4590 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,4110,a)].">
      <j1 rule="hyper" parents="35 4019 4110"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * (1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4594(a,2,2))].">
      <j1 rule="para" parents="12 4594"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(78(a,1),4594(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 4594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2737(a,1),4595(a,1,2))].">
      <j1 rule="para" parents="2737 4595"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2738(a,1),4595(a,1,2))].">
      <j1 rule="para" parents="2738 4595"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1631(a,2),4597(a,1,2,1))].">
      <j1 rule="para" parents="1631 4597"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1640(a,1),4597(a,1,2,1))].">
      <j1 rule="para" parents="1640 4597"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1704(a,1),4597(a,1,2))].">
      <j1 rule="para" parents="1704 4597"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1715(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1715 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      K(x,(1 / y) / z) = K(x,(y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(1717(a,1),4597(a,1,2))].">
      <j1 rule="para" parents="1717 4597"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      K(x,(1 / (1 / y)) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2139(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2139 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2525(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2525 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2527(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2527 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2721(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2721 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      K(x,y * (K(z,z \ 1) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(3693(a,1),4597(a,1,2))].">
      <j1 rule="para" parents="3693 4597"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      K(x,y / (K(z \ 1,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3776(a,2),4597(a,1,2))].">
      <j1 rule="para" parents="3776 4597"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3694(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3694 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3695(a,1),4597(a,1,2))].">
      <j1 rule="para" parents="3695 4597"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3696(a,1),4597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3696 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(3857(a,2),4597(a,1,2))].">
      <j1 rule="para" parents="3857 4597"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      K(x,y / (1 / (1 / z))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2745(a,1),4598(a,1,2))].">
      <j1 rule="para" parents="2745 4598"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3781(a,2),4598(a,1,2))].">
      <j1 rule="para" parents="3781 4598"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(1666(a,1),4599(a,1,2))].">
      <j1 rule="para" parents="1666 4599"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3864(a,1),4599(a,1,2))].">
      <j1 rule="para" parents="3864 4599"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(490(a,1),4600(a,1,2))].">
      <j1 rule="para" parents="490 4600"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(1674(a,2),4600(a,1,2))].">
      <j1 rule="para" parents="1674 4600"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3689(a,1),4600(a,1,2))].">
      <j1 rule="para" parents="3689 4600"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3698(a,2),4600(a,1,2))].">
      <j1 rule="para" parents="3698 4600"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      K(x,y \ (1 / z)) = K(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3716(a,1),4605(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3716 4605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y * T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(2312(a,1),4596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2312 4596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ u) = K(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2058(a,2),4606(a,1,2,1))].">
      <j1 rule="para" parents="2058 4606"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,4095,a,b,4139,a)].">
      <j1 rule="hyper" parents="36 4095 4139"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(206,a,4192,a,b,4155,a)].">
      <j1 rule="hyper" parents="206 4192 4155"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,4192,a,b,4082,a(flip))].">
      <j1 rule="hyper" parents="128 4192 4082"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,4193,a,b,4016,a(flip))].">
      <j1 rule="hyper" parents="127 4193 4016"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ y = R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(4193(a,2),3530(a,1,1))].">
      <j1 rule="para" parents="4193 3530"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4193(a,2),4006(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4193 4006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      (T(x,y) * R(y,z,u)) / T(x,y) = R(K(y,x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(4249(a,1),4193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4249 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1238(a,1),4216(a,1,2))].">
      <j1 rule="para" parents="1238 4216"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1359(a,1),4216(a,1,2))].">
      <j1 rule="para" parents="1359 4216"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(3847,a,4265,a),flip(a)].">
      <j1 rule="hyper" parents="3847 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(736,a,4265,a),flip(a)].">
      <j1 rule="hyper" parents="736 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(244,a,4038,a,b,4265,a(flip))].">
      <j1 rule="hyper" parents="244 4038 4265"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4265,a(flip),b,885,a(flip))].">
      <j1 rule="hyper" parents="131 4265 885"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4265,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="128 4265 443"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      T(x * y,z) / y = K(((1 / y) / x) \ 1,z) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,945,a(flip),b,4266,a)].">
      <j1 rule="hyper" parents="319 945 4266"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,936,a(flip),b,4266,a),flip(a)].">
      <j1 rule="hyper" parents="319 936 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,4038,a,b,4266,a),flip(a)].">
      <j1 rule="hyper" parents="36 4038 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4266(a,2,2,1))].">
      <j1 rule="para" parents="9 4266"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4167,a(flip),b,4645,a),flip(a)].">
      <j1 rule="hyper" parents="319 4167 4645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2917,a,b,4645,a)].">
      <j1 rule="hyper" parents="64 2917 4645"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4645(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 4645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4645(a,2,1))].">
      <j1 rule="para" parents="11 4645"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),4645(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 4645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(78(a,1),4647(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 4647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(4648(a,1),2918(a,1))].">
      <j1 rule="para" parents="4648 2918"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4649(a,1),4237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4649 4237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      (x * K(y \ 1,x)) \ (y \ x) = (y \ x) / x
    ]]></literal>
    <justification jstring="[para(4652(a,1),3989(a,1,1,2))].">
      <j1 rule="para" parents="4652 3989"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4469,a(flip),b,4299,a),flip(a)].">
      <j1 rule="hyper" parents="127 4469 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2849,a,4325,a)].">
      <j1 rule="hyper" parents="2849 4325"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(945(a,1),4333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="945 4333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(4374,a,4348,a)].">
      <j1 rule="hyper" parents="4374 4348"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,4398,a)].">
      <j1 rule="hyper" parents="134 4398"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4398(a,1),330(a,1,2))].">
      <j1 rule="para" parents="4398 330"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      L(((x * (1 / x)) \ 1) * y,x * (1 / x),x) = (x * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2589,a,b,4420,a)].">
      <j1 rule="hyper" parents="64 2589 4420"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      ((x \ 1) * x) \ (T(x,y) * z) = T(T(x,y),T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(2857(a,1),4433(a,1,1))].">
      <j1 rule="para" parents="2857 4433"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      T(T(x,y),y) \ x = K(y,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4162(a,1),4441(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4162 4441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((x * y) * (K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4452(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4452 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(4374,a,4510,a)].">
      <j1 rule="hyper" parents="4374 4510"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      K(x \ y,x) \ ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(134,a,4510,a)].">
      <j1 rule="hyper" parents="134 4510"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,4510,a(flip),b,4040,a),flip(a)].">
      <j1 rule="hyper" parents="127 4510 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(22(a,2),4510(a,1,2))].">
      <j1 rule="para" parents="22 4510"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(131,a,4512,a,b,4356,a)].">
      <j1 rule="hyper" parents="131 4512 4356"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      (x / (x / y)) * z = (y * (K(y \ x,y) * z)) * 1
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a,b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) / ((K(x,x \ y) * z) / K(x,x \ y))) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(3980(a,2),4541(a,1,2))].">
      <j1 rule="para" parents="3980 4541"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,192,a(flip),b,4557,a),flip(a)].">
      <j1 rule="hyper" parents="64 192 4557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(4559(a,1),586(a,1))].">
      <j1 rule="para" parents="4559 586"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(1711(a,1),4608(a,1,2,2))].">
      <j1 rule="para" parents="1711 4608"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(2673(a,1),4608(a,1,2,2))].">
      <j1 rule="para" parents="2673 4608"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(1639(a,1),4609(a,1,2,2,1))].">
      <j1 rule="para" parents="1639 4609"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(1721(a,1),4609(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1721 4609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2717(a,1),4609(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2717 4609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2354(a,1),4613(a,1,2,1))].">
      <j1 rule="para" parents="2354 4613"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(1704(a,1),4615(a,1,2,2))].">
      <j1 rule="para" parents="1704 4615"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(1705(a,1),4615(a,1,2,2))].">
      <j1 rule="para" parents="1705 4615"/>
    </justification>
  </clause>

  <clause id="4691">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2725(a,1),4615(a,1,2,2))].">
      <j1 rule="para" parents="2725 4615"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(3694(a,1),4615(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3694 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(1722(a,1),4619(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1722 4619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      K(x,y * (z \ (1 / u))) = K(x,y * (z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3716(a,1),4620(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3716 4620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2725(a,1),4621(a,1,2,1))].">
      <j1 rule="para" parents="2725 4621"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) / (x \ y) = (y / x) \ ((x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(4347(a,1),4655(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4347 4655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      T(x,y) \ T(z / (z / x),y) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(3979(a,2),4662(a,1,2,1))].">
      <j1 rule="para" parents="3979 4662"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(4281(a,1),4662(a,1,2,1,2))].">
      <j1 rule="para" parents="4281 4662"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,4670,a(flip),b,4482,a),flip(a)].">
      <j1 rule="hyper" parents="127 4670 4482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      K(x,y / (z * (u / (1 / w)))) = K(x,y / (z * (u / (w \ 1))))
    ]]></literal>
    <justification jstring="[para(3696(a,1),4685(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3696 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2968(a,1),4087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2968 4087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      K(R(x \ (y / z),x,y / (y / z)),x) = K(((z \ y) * z) / (x * (y / (y / z))),x)
    ]]></literal>
    <justification jstring="[para(3189(a,1),4170(a,2,1,1))].">
      <j1 rule="para" parents="3189 4170"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,27,a,b,4475,a),flip(a)].">
      <j1 rule="hyper" parents="319 27 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      T(x,y) / T(x,z) = K(x,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4533,a,3823,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4533 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      (K(x,y) \ K(x,z)) \ T(x,z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(199,a,4708,a)].">
      <j1 rule="hyper" parents="199 4708"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      K(x,y) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(3172(a,1),4548(a,1))].">
      <j1 rule="para" parents="3172 4548"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4012(a,2),4071(a,1,1))].">
      <j1 rule="para" parents="4012 4071"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3741,a(flip),b,4712,a),flip(a)].">
      <j1 rule="hyper" parents="64 3741 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,y,z) \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(127,a,4712,a(flip),b,2641,a)].">
      <j1 rule="hyper" parents="127 4712 2641"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(81(a,1),4712(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="81 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3883(a,1),4712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3883 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      K(x,L(L(y \ 1,z,u),w,v5) \ 1) = L(L(K(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4717(a,1),4712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4717 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3824,a(flip),b,4119,a),flip(a)].">
      <j1 rule="hyper" parents="319 3824 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4722">
    <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(4195(a,1),393(a,1,1))].">
      <j1 rule="para" parents="4195 393"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(584,a,4262,a)].">
      <j1 rule="hyper" parents="584 4262"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1386,a(flip),b,4262,a)].">
      <j1 rule="hyper" parents="64 1386 4262"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(885(a,1),4262(a,1,2))].">
      <j1 rule="para" parents="885 4262"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(4013(a,1),4264(a,1,1))].">
      <j1 rule="para" parents="4013 4264"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4054(a,2),4264(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4054 4264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3171,a(flip),b,4726,a),flip(a)].">
      <j1 rule="hyper" parents="64 3171 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,4726,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 4726 20"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2920(a,1),4726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2920 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      K(((x * (y * z)) / z) \ 1,z / (y * z)) = K((x / R(1 / y,y,z)) \ 1,z / (y * z))
    ]]></literal>
    <justification jstring="[para(760(a,1),4728(a,1,1,1))].">
      <j1 rule="para" parents="760 4728"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(4727(a,1),4213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4727 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(4730(a,1),4356(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4730 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4267,a,b,885,a(flip))].">
      <j1 rule="hyper" parents="131 4267 885"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,109,a(flip),b,4269,a)].">
      <j1 rule="hyper" parents="319 109 4269"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(2920(a,1),4735(a,2,2))].">
      <j1 rule="para" parents="2920 4735"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(2900(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="2900 4271"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(4271(a,2),4273(a,1,2))].">
      <j1 rule="para" parents="4271 4273"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      L(x \ (K(y,z) \ (T(y,z) * x)),x,K(y,z)) = T(y,K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(800,a,4286,a)].">
      <j1 rule="hyper" parents="800 4286"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(4653,a,4318,a)].">
      <j1 rule="hyper" parents="4653 4318"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      x * (y * (K(z,y) * (T(y,u) \ w))) = x * (K(z,y) * (K(u,y) * w))
    ]]></literal>
    <justification jstring="[para(4443(a,1),4315(a,1,2,2))].">
      <j1 rule="para" parents="4443 4315"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(134,a,4455,a)].">
      <j1 rule="hyper" parents="134 4455"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(3886(a,1),4455(a,1,2))].">
      <j1 rule="para" parents="3886 4455"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1145(a,1),4485(a,1,1))].">
      <j1 rule="para" parents="1145 4485"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2113(a,1),4485(a,1,1))].">
      <j1 rule="para" parents="2113 4485"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3852(a,1),4521(a,1,2))].">
      <j1 rule="para" parents="3852 4521"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      T(x,y) * (K(x * y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(4576(a,1),4542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4576 4542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      K(x,y) \ ((y \ 1) \ z) = (y \ K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(2851(a,1),4545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2851 4545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (x \ K(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(4384,a,4749,a)].">
      <j1 rule="hyper" parents="4384 4749"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4750(a,1),215(a,1))].">
      <j1 rule="para" parents="4750 215"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (T(x,y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(4024(a,2),4750(a,2,1))].">
      <j1 rule="para" parents="4024 4750"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4281(a,2),4580(a,1,2))].">
      <j1 rule="para" parents="4281 4580"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(4153(a,2),4610(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4153 4610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4213(a,1),4638(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="4213 4638"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),4643(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      (x / (x / y)) * z = (y * (K(y \ x,y) * z)) * a(u,K(w \ 1,w),v5)
    ]]></literal>
    <justification jstring="[para(3683(a,2),4677(a,2,2))].">
      <j1 rule="para" parents="3683 4677"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(3981(a,1),4688(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3981 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1588(a,1),4689(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1588 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2312(a,1),4690(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2312 4690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(129,a,4691,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 4691 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      K(x \ 1,y) * (x * z) = x * (K(x \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4739(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(81(a,1),4739(a,1,2,1,1))].">
      <j1 rule="para" parents="81 4739"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2920(a,1),4739(a,1,2,1))].">
      <j1 rule="para" parents="2920 4739"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      x \ (R(1 / y,y,x) * ((z * (y * x)) / z)) = K(z,1 / (x \ R(1 / y,y,x)))
    ]]></literal>
    <justification jstring="[para(381(a,1),4743(a,1,2,2,1,2))].">
      <j1 rule="para" parents="381 4743"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      ((((x * x) \ y) * K(x * x,y)) * x) * x = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(415(a,1),4141(a,1,1,1))].">
      <j1 rule="para" parents="415 4141"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      (K(x,y) \ (z * u)) / L(u,z,K(y,x)) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,4356,a,b,4371,a)].">
      <j1 rule="hyper" parents="128 4356 4371"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,4356,a,b,4371,a)].">
      <j1 rule="hyper" parents="127 4356 4371"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(y,z)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(4221,a,4378,a)].">
      <j1 rule="hyper" parents="4221 4378"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      L(K(x,y) * (K(z,u) * w),K(y,x),K(u,z)) = (K(u,z) * K(y,x)) \ w
    ]]></literal>
    <justification jstring="[para(4356(a,1),4378(a,1,1))].">
      <j1 rule="para" parents="4356 4378"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(3472,a,4379,a),flip(a)].">
      <j1 rule="hyper" parents="3472 4379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4379(a,1),4546(a,1)),flip(b)].">
      <j1 rule="para" parents="4379 4546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      T((1 / x) * K(y * R(1 / x,x,z),1 / x),y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(225(a,1),4400(a,2,3))].">
      <j1 rule="para" parents="225 4400"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3926,a(flip),b,4625,a),flip(a)].">
      <j1 rule="hyper" parents="35 3926 4625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      (x * y) * K(z \ 1,L(z,u,w)) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[para(4779(a,2),3704(a,1,2))].">
      <j1 rule="para" parents="4779 3704"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(4437(a,1),4681(a,1))].">
      <j1 rule="para" parents="4437 4681"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      ((x / (y * y)) * y) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(4134(a,1),4771(a,1,1,1))].">
      <j1 rule="para" parents="4134 4771"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(642(a,1),4782(a,1,1))].">
      <j1 rule="para" parents="642 4782"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      R(x / (1 / y),y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(324,a,4783,a),flip(a)].">
      <j1 rule="hyper" parents="324 4783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,3199,a(flip),b,4783,a),flip(a)].">
      <j1 rule="hyper" parents="128 3199 4783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      (x * y) * L(z,y * x,K(x,y)) = K(y,x) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3997,a(flip),b,4772,a)].">
      <j1 rule="hyper" parents="130 3997 4772"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 4773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      (K(x,y) \ (z * u)) \ (K(x,y) \ (z * (u * w))) = L(L(w,u,z),z * u,K(y,x))
    ]]></literal>
    <justification jstring="[para(94(a,1),4773(a,1,2,2))].">
      <j1 rule="para" parents="94 4773"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(4335(a,1),4781(a,1,2))].">
      <j1 rule="para" parents="4335 4781"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(3997(a,1),4787(a,2,2))].">
      <j1 rule="para" parents="3997 4787"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(4179(a,1),4787(a,2,2))].">
      <j1 rule="para" parents="4179 4787"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      T(x,y \ ((1 / z) \ u)) = T(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(37,a,4007,a(flip),b,4048,a)].">
      <j1 rule="hyper" parents="37 4007 4048"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4144(a,1),4231(a,1,2))].">
      <j1 rule="para" parents="4144 4231"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,4047,a(flip),b,4793,a),flip(a)].">
      <j1 rule="hyper" parents="319 4047 4793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4013(a,1),4275(a,1,1,2))].">
      <j1 rule="para" parents="4013 4275"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,4795,a)].">
      <j1 rule="hyper" parents="134 4795"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4797(a,1),1003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4797 1003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3276,a(flip),b,4339,a),flip(a)].">
      <j1 rule="hyper" parents="319 3276 4339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(3340,a,4340,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3340 4340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(3896(a,1),4464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3896 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2065,a(flip),b,4486,a)].">
      <j1 rule="hyper" parents="64 2065 4486"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),4486(a,1,2,1))].">
      <j1 rule="para" parents="10 4486"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ z,y,x) / z)) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(4486(a,1),2111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4486 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(81(a,1),4805(a,2,2,2))].">
      <j1 rule="para" parents="81 4805"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2835(a,1),4543(a,1,1))].">
      <j1 rule="para" parents="2835 4543"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      K(x,y * ((z / u) * (K(u,u \ z) * (1 / w)))) = K(x,y * (((u * (z / u)) / u) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(4556(a,2),4611(a,1,2,2))].">
      <j1 rule="para" parents="4556 4611"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(2978(a,1),4634(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2978 4634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4811">
    <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),4635(a,2,2))].">
      <j1 rule="para" parents="27 4635"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(110(a,2),4680(a,1,2,2,1))].">
      <j1 rule="para" parents="110 4680"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4663,a,4701,a),flip(a)].">
      <j1 rule="hyper" parents="4663 4701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,68,a(flip),b,4705,a),flip(a)].">
      <j1 rule="hyper" parents="319 68 4705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),4725(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="81 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1728,a(flip),b,4738,a),flip(a)].">
      <j1 rule="hyper" parents="64 1728 4738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      K(x,((y \ 1) / (z / y)) \ 1) \ (z / y) = T(z,x) / y
    ]]></literal>
    <justification jstring="[hyper(4392,a,4741,a)].">
      <j1 rule="hyper" parents="4392 4741"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4520,a(flip),b,4747,a),flip(a)].">
      <j1 rule="hyper" parents="64 4520 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,4757,a),flip(a)].">
      <j1 rule="hyper" parents="142 4757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) != v5 * (R(x,y,z) * w)
    ]]></literal>
    <literal><![CDATA[
      R(K(u,x),R(x,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(4808(a,1),529(a,1))].">
      <j1 rule="para" parents="4808 529"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,2005,a,b,4158,a)].">
      <j1 rule="hyper" parents="64 2005 4158"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,R(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(4337(a,1),4377(a,1,2))].">
      <j1 rule="para" parents="4337 4377"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3877(a,1),4468(a,1,1,1))].">
      <j1 rule="para" parents="3877 4468"/>
    </justification>
  </clause>

  <clause id="4826">
    <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(4013(a,1),4563(a,1,1))].">
      <j1 rule="para" parents="4013 4563"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(4826,a,xx),flip(a)].">
      <j1 rule="hyper" parents="4826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,4827,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 4827 18"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(1545(a,1),4827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1545 4827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2917(a,2),4827(a,1,1))].">
      <j1 rule="para" parents="2917 4827"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2920(a,1),4827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2920 4827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2917,a,b,4830,a),flip(a)].">
      <j1 rule="hyper" parents="319 2917 4830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(4831(a,1),4213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4831 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(4831(a,1),4356(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4831 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4717,a(flip),b,4833,a),flip(a)].">
      <j1 rule="hyper" parents="64 4717 4833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      L(K(x,y),z,u) != w \ 1
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(4835(a,1),49(a,1))].">
      <j1 rule="para" parents="4835 49"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(4717(a,1),4834(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4717 4834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(332,a,4838,a)].">
      <j1 rule="hyper" parents="332 4838"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      L(K(x,y),z,u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) * v5 = w
    ]]></literal>
    <justification jstring="[para(4838(a,1),145(a,1))].">
      <j1 rule="para" parents="4838 145"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) * w = v5
    ]]></literal>
    <justification jstring="[para(4839(a,1),330(a,1,2))].">
      <j1 rule="para" parents="4839 330"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      (x * y) * K(z \ 1,L(z,u,w)) = x * (y * K(z \ 1,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(4779(a,2),4780(a,2,2,2))].">
      <j1 rule="para" parents="4779 4780"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      L(x \ (y * z),x,K(T(y,y * z) * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(3131(a,1),4791(a,1,1,2))].">
      <j1 rule="para" parents="3131 4791"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      K(x \ y,x) * ((y \ 1) \ 1) = T((x \ y) * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3917,a(flip),b,3995,a),flip(a)].">
      <j1 rule="hyper" parents="319 3917 3995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1490,a,4188,a),flip(a)].">
      <j1 rule="hyper" parents="1490 4188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,u) * L(x \ K(u,x),y,z)) = w
    ]]></literal>
    <justification jstring="[para(4204(a,1),4567(a,1))].">
      <j1 rule="para" parents="4204 4567"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(433(a,1),4326(a,1,2))].">
      <j1 rule="para" parents="433 4326"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(433(a,1),4331(a,1,1))].">
      <j1 rule="para" parents="433 4331"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      ((x \ 1) * x) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((T(x,y) \ 1) \ 1) * z = u
    ]]></literal>
    <justification jstring="[para(4665(a,2),691(a,1))].">
      <j1 rule="para" parents="4665 691"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      R(x,x \ 1,(x \ 1) \ (x \ y)) = (y / x) \ ((x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(806,a,4697,a)].">
      <j1 rule="hyper" parents="806 4697"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      K(x,y / (K((z \ 1) \ u,z \ 1) \ u)) = K(x,y / ((z \ 1) * (u / (1 / z))))
    ]]></literal>
    <justification jstring="[para(4258(a,2),4703(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4258 4703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(923(a,1),4746(a,1,1,1))].">
      <j1 rule="para" parents="923 4746"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4265(a,2),4756(a,1,2))].">
      <j1 rule="para" parents="4265 4756"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(4636(a,1),4756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4636 4756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(81(a,1),4766(a,2,1,1))].">
      <j1 rule="para" parents="81 4766"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4859(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      (K(x,y) * ((1 / x) * z)) / (K(x,y) * z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(574,a,4860,a)].">
      <j1 rule="hyper" parents="574 4860"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(417,a,4860,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="417 4860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = u
    ]]></literal>
    <justification jstring="[para(4862(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4862 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2920(a,1),4767(a,2,1))].">
      <j1 rule="para" parents="2920 4767"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4865(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),4865(a,1,2,2))].">
      <j1 rule="para" parents="22 4865"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,4867,a(flip),b,4356,a)].">
      <j1 rule="hyper" parents="206 4867 4356"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),4870(a,1,2,2))].">
      <j1 rule="para" parents="4363 4870"/>
    </justification>
  </clause>

  <clause id="4872">
    <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(3322(a,1),4802(a,1,2))].">
      <j1 rule="para" parents="3322 4802"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4633,a(flip),b,4810,a),flip(a)].">
      <j1 rule="hyper" parents="319 4633 4810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4724,a,b,4816,a)].">
      <j1 rule="hyper" parents="64 4724 4816"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4171(a,1),4846(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4171 4846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4180,a(flip),b,4875,a),flip(a)].">
      <j1 rule="hyper" parents="319 4180 4875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),4876(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,4857,a)].">
      <j1 rule="hyper" parents="134 4857"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(130,a,4878,a(flip),b,3797,a)].">
      <j1 rule="hyper" parents="130 4878 3797"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4879(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(4363(a,1),4414(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4363 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      L(((x \ 1) * x) * y,x * (1 / x),x) = (x * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(3638(a,1),4664(a,1,1,1))].">
      <j1 rule="para" parents="3638 4664"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      L(x \ (y * x),x,K(y,z)) = T(y,K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(4100(a,1),4740(a,1,1,2))].">
      <j1 rule="para" parents="4100 4740"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      L(T(x,y),y,K(x,z)) = T(x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),4883(a,1,1))].">
      <j1 rule="para" parents="22 4883"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ z) / z),y,x) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3937(a,2),4806(a,1,2))].">
      <j1 rule="para" parents="3937 4806"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,359,a(flip),b,4829,a),flip(a)].">
      <j1 rule="hyper" parents="319 359 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1063(a,1),4887(a,1,2))].">
      <j1 rule="para" parents="1063 4887"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(57,a,4889,a)].">
      <j1 rule="hyper" parents="57 4889"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,4890,a)].">
      <j1 rule="hyper" parents="55 4890"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1065(a,2),4891(a,1,1))].">
      <j1 rule="para" parents="1065 4891"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(206,a,4892,a(flip),b,3230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 4892 3230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,2616,a(flip),b,4893,a),flip(a)].">
      <j1 rule="hyper" parents="319 2616 4893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1065(a,1),4894(a,1,1))].">
      <j1 rule="para" parents="1065 4894"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ 1,(((x \ y) * x) \ 1) \ K(x,x \ y)) = (y / ((x \ y) * x)) \ ((((x \ y) * x) \ 1) \ (((x \ y) * x) \ y))
    ]]></literal>
    <justification jstring="[para(90(a,1),4853(a,1,3,2))].">
      <j1 rule="para" parents="90 4853"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(3331(a,1),4877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3331 4877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3139,a(flip),b,4897,a),flip(a)].">
      <j1 rule="hyper" parents="319 3139 4897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4897(a,2),3140(a,1))].">
      <j1 rule="para" parents="4897 3140"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,4200,a,b,4898,a),flip(a)].">
      <j1 rule="hyper" parents="36 4200 4898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,4247,a,b,4900,a),flip(a)].">
      <j1 rule="hyper" parents="319 4247 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4509,a(flip),b,4900,a),flip(a)].">
      <j1 rule="hyper" parents="319 4509 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(3341(a,1),4901(a,1,2))].">
      <j1 rule="para" parents="3341 4901"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(199,a,4903,a)].">
      <j1 rule="hyper" parents="199 4903"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4247(a,1),4904(a,1,1))].">
      <j1 rule="para" parents="4247 4904"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4016(a,2),4905(a,1,1,2))].">
      <j1 rule="para" parents="4016 4905"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      x * (y * (z * ((y \ z) / z))) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(300,a,4886,a)].">
      <j1 rule="hyper" parents="300 4886"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * y = x * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(3039(a,1),4907(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3039 4907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3883(a,1),4908(a,1,1,2))].">
      <j1 rule="para" parents="3883 4908"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(2758(a,1),4910(a,2,2))].">
      <j1 rule="para" parents="2758 4910"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,4912,a)].">
      <j1 rule="hyper" parents="417 4912"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,4912,a)].">
      <j1 rule="hyper" parents="142 4912"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,4053,a,b,4912,a),flip(a)].">
      <j1 rule="hyper" parents="128 4053 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      (((x * x) \ y) * x) / y = (1 / x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,842,a,b,4912,a)].">
      <j1 rule="hyper" parents="128 842 4912"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,4912,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      ((x * y) * K(L(z,y,x),u)) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,438,a(flip),b,4912,a)].">
      <j1 rule="hyper" parents="127 438 4912"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      (x * K(T(y,x),z)) \ (T(y,z) * x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,241,a(flip),b,4912,a)].">
      <j1 rule="hyper" parents="127 241 4912"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1276,a,b,4912,a)].">
      <j1 rule="hyper" parents="36 1276 4912"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1272,a,b,4912,a),flip(a)].">
      <j1 rule="hyper" parents="36 1272 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(4912(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4912 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(4912(a,1),224(a,2,1))].">
      <j1 rule="para" parents="4912 224"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z,y * K(z,u),x) = w
    ]]></literal>
    <justification jstring="[para(4912(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="4912 489"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * (T(z,K(x,y) * K(x,y)) * x) = z * (K(x,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(4912(a,1),916(a,2,2))].">
      <j1 rule="para" parents="4912 916"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4017(a,1),4912(a,1,1))].">
      <j1 rule="para" parents="4017 4912"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      K(x,y * K(x,z)) * K(y * T(x,z),x) = x \ R(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(4912(a,1),4578(a,1,2,1))].">
      <j1 rule="para" parents="4912 4578"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,4915,a(flip),b,1279,a(flip))].">
      <j1 rule="hyper" parents="127 4915 1279"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      (x * x) \ T(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,4090,a,b,4916,a)].">
      <j1 rule="hyper" parents="64 4090 4916"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),1 / x) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4916,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 4916 197"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      (T(x,y) / y) * K(y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(3303,a,4918,a)].">
      <j1 rule="hyper" parents="3303 4918"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(570,a,4921,a)].">
      <j1 rule="hyper" parents="570 4921"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,313,a(flip),b,4921,a)].">
      <j1 rule="hyper" parents="64 313 4921"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4921,a(flip),b,4912,a)].">
      <j1 rule="hyper" parents="128 4921 4912"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4921,a(flip),b,446,a)].">
      <j1 rule="hyper" parents="128 4921 446"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,193,a(flip),b,4921,a(flip))].">
      <j1 rule="hyper" parents="127 193 4921"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(127,a,4921,a(flip),b,4912,a)].">
      <j1 rule="hyper" parents="127 4921 4912"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,4921,a(flip),b,193,a(flip))].">
      <j1 rule="hyper" parents="127 4921 193"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(197(a,1),4921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="197 4921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4114,a,4922,a)].">
      <j1 rule="hyper" parents="4114 4922"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,4922,a),flip(a)].">
      <j1 rule="hyper" parents="417 4922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(244,a,4922,a,b,4363,a),flip(a)].">
      <j1 rule="hyper" parents="244 4922 4363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,4922,a)].">
      <j1 rule="hyper" parents="134 4922"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,4109,a,b,4922,a)].">
      <j1 rule="hyper" parents="35 4109 4922"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) / (y * T(z,u)) = R(x,y * z,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(206,a,4922,a(flip),b,194,a)].">
      <j1 rule="hyper" parents="206 4922 194"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(4922(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      (x * y) * K(y,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4922(a,2),44(a,1))].">
      <j1 rule="para" parents="4922 44"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4922(a,1),324(a,1))].">
      <j1 rule="para" parents="4922 324"/>
    </justification>
  </clause>

  <clause id="4953">
    <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(4922(a,1),550(a,1,2))].">
      <j1 rule="para" parents="4922 550"/>
    </justification>
  </clause>

  <clause id="4954">
    <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(4922(a,1),527(a,1,1))].">
      <j1 rule="para" parents="4922 527"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      R(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4943(a,1),52(a,2))].">
      <j1 rule="para" parents="4943 52"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,4213,a,b,4948,a),flip(a)].">
      <j1 rule="hyper" parents="319 4213 4948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      a(x,y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,4948,a)].">
      <j1 rule="hyper" parents="54 4948"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4948,a(flip),b,1896,a)].">
      <j1 rule="hyper" parents="127 4948 1896"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      (x * y) * T(K(y,z),u) = x * (y * T(K(y,z),u))
    ]]></literal>
    <justification jstring="[para(4948(a,1),438(a,1,2,1))].">
      <j1 rule="para" parents="4948 438"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4837,a,4957,a)].">
      <j1 rule="hyper" parents="4837 4957"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4957(a,2),4229(a,1))].">
      <j1 rule="para" parents="4957 4229"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4963,a,b,4963,a)].">
      <j1 rule="hyper" parents="319 4963 4963"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,4963,a)].">
      <j1 rule="hyper" parents="54 4963"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4963,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="131 4963 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,4963,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 4963 18"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      T(x,y) \ ((x * x) * z) = (K(x,y) / x) \ z
    ]]></literal>
    <justification jstring="[para(4931(a,1),638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4931 638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4947(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4947 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4965(a,1),499(a,1))].">
      <j1 rule="para" parents="4965 499"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(965,a,4934,a)].">
      <j1 rule="hyper" parents="965 4934"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4038,a,b,4934,a)].">
      <j1 rule="hyper" parents="64 4038 4934"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(244,a,4038,a,b,4934,a(flip))].">
      <j1 rule="hyper" parents="244 4038 4934"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(244,a,4302,a(flip),b,4934,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="244 4302 4934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      x * (y * K((x \ 1) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4934,a(flip),b,885,a(flip))].">
      <j1 rule="hyper" parents="131 4934 885"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4934,a(flip),b,941,a)].">
      <j1 rule="hyper" parents="130 4934 941"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4934,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="128 4934 443"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,1359,a(flip),b,4934,a(flip))].">
      <j1 rule="hyper" parents="127 1359 4934"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      K(x \ (x / y),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4269,a,b,4934,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4269 4934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4268,a(flip),b,4934,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4268 4934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4265,a(flip),b,4934,a(flip))].">
      <j1 rule="hyper" parents="35 4265 4934"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4934(a,2),330(a,1,2))].">
      <j1 rule="para" parents="4934 330"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(4934(a,1),1790(a,2,1))].">
      <j1 rule="para" parents="4934 1790"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(2847,a,4985,a)].">
      <j1 rule="hyper" parents="2847 4985"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2861,a(flip),b,4985,a)].">
      <j1 rule="hyper" parents="64 2861 4985"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(4985(a,1),212(a,1)),flip(b)].">
      <j1 rule="para" parents="4985 212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),5001(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 5001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(110(a,2),4987(a,1,1))].">
      <j1 rule="para" parents="110 4987"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4987(a,2),2847(a,1))].">
      <j1 rule="para" parents="4987 2847"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      K(x \ (x / y),z) = T(z,y \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(319,a,4001,a(flip),b,4993,a),flip(a)].">
      <j1 rule="hyper" parents="319 4001 4993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(198(a,1),4993(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="198 4993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(4359(a,1),4993(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4359 4993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,2917,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="319 2917 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      K(L(x \ 1,x,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(224(a,2),4995(a,1,1))].">
      <j1 rule="para" parents="224 4995"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      K((x \ (x / y)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,684,a(flip),b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="319 684 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,683,a(flip),b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="319 683 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2917,a,b,4996,a)].">
      <j1 rule="hyper" parents="64 2917 4996"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4873,a(flip),b,4996,a)].">
      <j1 rule="hyper" parents="64 4873 4996"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(4996(a,1),4030(a,2,1))].">
      <j1 rule="para" parents="4996 4030"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(4996(a,1),4654(a,2,2))].">
      <j1 rule="para" parents="4996 4654"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      K((x * y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5022(a,2),2918(a,1))].">
      <j1 rule="para" parents="5022 2918"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = K(y,z) \ (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(5025(a,1),4277(a,2,1))].">
      <j1 rule="para" parents="5025 4277"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5027(a,1),2918(a,1))].">
      <j1 rule="para" parents="5027 2918"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(4649(a,2),5003(a,1))].">
      <j1 rule="para" parents="4649 5003"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      K(x,(y / (z * K(y,u))) \ 1) = K(x,(z / y) * K(y,u))
    ]]></literal>
    <justification jstring="[para(4936(a,1),4491(a,2,2))].">
      <j1 rule="para" parents="4936 4491"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      (x / y) * ((z * y) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4150,a,b,4969,a)].">
      <j1 rule="hyper" parents="64 4150 4969"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(4097(a,1),4969(a,1,2))].">
      <j1 rule="para" parents="4097 4969"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,4970,a)].">
      <j1 rule="hyper" parents="529 4970"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4150,a,b,4970,a),flip(a)].">
      <j1 rule="hyper" parents="319 4150 4970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,4970,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="130 4970 4915"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(4097(a,1),4970(a,2,2))].">
      <j1 rule="para" parents="4097 4970"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,4001,a(flip),b,5011,a(flip))].">
      <j1 rule="hyper" parents="40 4001 5011"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      K(x \ (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5011(a,2),4046(a,1))].">
      <j1 rule="para" parents="5011 4046"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      x * K(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4124,a,5049,a)].">
      <j1 rule="hyper" parents="4124 5049"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      T(T(x \ (x / y),z),y \ 1) = T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(394,a,5049,a),flip(a)].">
      <j1 rule="hyper" parents="394 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      (x / y) / T(x,y \ 1) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(206,a,5049,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="206 5049 110"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      (x \ (x / y)) * T(x,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(131,a,5049,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="131 5049 110"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5049(a,1,2,2))].">
      <j1 rule="para" parents="11 5049"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),5049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(198(a,1),5049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="198 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(396(a,1),5049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="396 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(404,a,5057,a),flip(a)].">
      <j1 rule="hyper" parents="404 5057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      T(x / ((y * z) \ y),z \ 1) = ((y * z) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,5057,a),flip(a)].">
      <j1 rule="hyper" parents="393 5057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5057,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 5057 22"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5058(a,2,2))].">
      <j1 rule="para" parents="9 5058"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5058(a,1),3058(a,1,1))].">
      <j1 rule="para" parents="5058 3058"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(5058(a,1),3397(a,1,1))].">
      <j1 rule="para" parents="5058 3397"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = ((((x * y) \ x) \ 1) \ z) * (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,5068,a(flip),b,934,a)].">
      <j1 rule="hyper" parents="127 5068 934"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(5068(a,1),2760(a,1,2))].">
      <j1 rule="para" parents="5068 2760"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5029(a,2),4050(a,1))].">
      <j1 rule="para" parents="5029 4050"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(570,a,5042,a),flip(a)].">
      <j1 rule="hyper" parents="570 5042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,5052,a),flip(a)].">
      <j1 rule="hyper" parents="35 4019 5052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,u / (z * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4494,a,b,5079,a),flip(a)].">
      <j1 rule="hyper" parents="319 4494 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3886,a,b,5079,a),flip(a)].">
      <j1 rule="hyper" parents="319 3886 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5079(a,1,2,2))].">
      <j1 rule="para" parents="11 5079"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),5079(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(474(a,1),5079(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="474 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(195(a,1),5079(a,1,2,2))].">
      <j1 rule="para" parents="195 5079"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4359(a,1),5079(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4359 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4316(a,1),5079(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4316 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),5081(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 5081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(197(a,1),5081(a,1,2,2))].">
      <j1 rule="para" parents="197 5081"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5081(a,2),4344(a,1))].">
      <j1 rule="para" parents="5081 4344"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(767(a,1),5083(a,1,2,1))].">
      <j1 rule="para" parents="767 5083"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4963,a,b,5084,a)].">
      <j1 rule="hyper" parents="319 4963 5084"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5084(a,2,2))].">
      <j1 rule="para" parents="9 5084"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(4356(a,1),5084(a,2,2))].">
      <j1 rule="para" parents="4356 5084"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      T((x \ y) \ K(z,y \ x),z) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(5084(a,1),4143(a,1,1,2))].">
      <j1 rule="para" parents="5084 4143"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) = x
    ]]></literal>
    <justification jstring="[para(5084(a,1),4544(a,1,2))].">
      <j1 rule="para" parents="5084 4544"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5084(a,1),4568(a,1,1))].">
      <j1 rule="para" parents="5084 4568"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5084(a,1),4712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5084 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      T(x \ y,z) * T(x,x \ y) = K(z,(y \ x) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(5084(a,2),4327(a,2,1))].">
      <j1 rule="para" parents="5084 4327"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),5098(a,1,2,2))].">
      <j1 rule="para" parents="81 5098"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      ((x \ y) * K(z,y \ x)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (K(z,y \ x) * u) = w
    ]]></literal>
    <justification jstring="[para(5098(a,1),300(a,1,2))].">
      <j1 rule="para" parents="5098 300"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(5102(a,1),51(a,2))].">
      <j1 rule="para" parents="5102 51"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * T(x,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2758(a,1),5056(a,1,2))].">
      <j1 rule="para" parents="2758 5056"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      x / T(y * x,T(y,x) \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(206,a,5059,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="206 5059 110"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,372,a,b,5062,a)].">
      <j1 rule="hyper" parents="319 372 5062"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,5062,a(flip),b,560,a)].">
      <j1 rule="hyper" parents="131 5062 560"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(81(a,1),5062(a,1,2))].">
      <j1 rule="para" parents="81 5062"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),5069(a,2,2))].">
      <j1 rule="para" parents="11 5069"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      (x * (y / x)) * (y \ x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5069(a,1),326(a,1,1))].">
      <j1 rule="para" parents="5069 326"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      T(x,y / x) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3274(a,2),5069(a,1,1))].">
      <j1 rule="para" parents="3274 5069"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,((z * u) \ u) * K(z * u,1 / z))
    ]]></literal>
    <justification jstring="[para(4500(a,2),5080(a,2,2))].">
      <j1 rule="para" parents="4500 5080"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      T(x,(x / y) / x) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4453,a,b,5113,a),flip(a)].">
      <j1 rule="hyper" parents="319 4453 5113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,u) = w
    ]]></literal>
    <justification jstring="[para(20(a,2),4952(a,1,1))].">
      <j1 rule="para" parents="20 4952"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * K(x,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(650(a,1),4976(a,1,1))].">
      <j1 rule="para" parents="650 4976"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),5077(a,1,2,1))].">
      <j1 rule="para" parents="22 5077"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      K(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),5091(a,1,2,2))].">
      <j1 rule="para" parents="11 5091"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,3856,a(flip),b,5108,a)].">
      <j1 rule="hyper" parents="206 3856 5108"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5108(a,1),3217(a,1,2,2))].">
      <j1 rule="para" parents="5108 3217"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4336,a(flip),b,4944,a),flip(a)].">
      <j1 rule="hyper" parents="64 4336 4944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      T(x * (y * z),K(z * y,z)) = (y * z) * T(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(4281(a,1),5125(a,1,2))].">
      <j1 rule="para" parents="4281 5125"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4983(a,1),3818(a,1,1))].">
      <j1 rule="para" parents="4983 3818"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      (x \ 1) * (y * K(x \ y,z)) = T((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3870(a,1),4988(a,1,2,2))].">
      <j1 rule="para" parents="3870 4988"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5046,a(flip),b,105,a)].">
      <j1 rule="hyper" parents="128 5046 105"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,T(y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(4055(a,1),5046(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4055 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2066,a(flip),b,5078,a)].">
      <j1 rule="hyper" parents="319 2066 5078"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(206,a,5110,a,b,xx)].">
      <j1 rule="hyper" parents="206 5110"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),5111(a,1,1,2))].">
      <j1 rule="para" parents="22 5111"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(3252(a,1),5133(a,1,1))].">
      <j1 rule="para" parents="3252 5133"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(340,a,5134,a),flip(a)].">
      <j1 rule="hyper" parents="340 5134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(199,a,5134,a)].">
      <j1 rule="hyper" parents="199 5134"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(144,a,5134,a),flip(a)].">
      <j1 rule="hyper" parents="144 5134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,3350,a,b,5136,a)].">
      <j1 rule="hyper" parents="64 3350 5136"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5136,a(flip),b,4303,a)].">
      <j1 rule="hyper" parents="131 5136 4303"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5136(a,1),3465(a,1,1))].">
      <j1 rule="para" parents="5136 3465"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(3252(a,1),5130(a,1,2))].">
      <j1 rule="para" parents="3252 5130"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(127,a,94,a(flip),b,5141,a)].">
      <j1 rule="hyper" parents="127 94 5141"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(36,a,4912,a,b,5141,a(flip))].">
      <j1 rule="hyper" parents="36 4912 5141"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[para(5141(a,1),3308(a,1,2))].">
      <j1 rule="para" parents="5141 3308"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(630,a,5144,a)].">
      <j1 rule="hyper" parents="630 5144"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(324,a,5144,a),flip(a)].">
      <j1 rule="hyper" parents="324 5144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      T(x * T(y,z),K(z,y)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(244,a,5144,a,b,4363,a)].">
      <j1 rule="hyper" parents="244 5144 4363"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,5144,a)].">
      <j1 rule="hyper" parents="142 5144"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,5144,a)].">
      <j1 rule="hyper" parents="134 5144"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,5144,a)].">
      <j1 rule="hyper" parents="127 10 5144"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[para(110(a,1),5144(a,1,1,2))].">
      <j1 rule="para" parents="110 5144"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = (((x * y) * T(z,u)) * K(u,z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5144(a,1),527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5144 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5146(a,1),538(a,1,1))].">
      <j1 rule="para" parents="5146 538"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(417,a,4922,a(flip),b,5147,a)].">
      <j1 rule="hyper" parents="417 4922 5147"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1273,a,b,5147,a)].">
      <j1 rule="hyper" parents="64 1273 5147"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(130,a,5147,a(flip),b,1273,a)].">
      <j1 rule="hyper" parents="130 5147 1273"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      x * K(y,z) != z * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(z,y),z) = u
    ]]></literal>
    <justification jstring="[para(5147(a,1),245(a,2)),flip(a)].">
      <j1 rule="para" parents="5147 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(5147(a,1),335(a,1,2))].">
      <j1 rule="para" parents="5147 335"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(392,a,5158,a),flip(a)].">
      <j1 rule="hyper" parents="392 5158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(199,a,5158,a)].">
      <j1 rule="hyper" parents="199 5158"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3442,a(flip),b,5158,a),flip(a)].">
      <j1 rule="hyper" parents="64 3442 5158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,156,a(flip),b,5158,a)].">
      <j1 rule="hyper" parents="64 156 5158"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,155,a(flip),b,5158,a(flip))].">
      <j1 rule="hyper" parents="128 155 5158"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,155,a(flip),b,5158,a(flip))].">
      <j1 rule="hyper" parents="127 155 5158"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5158(a,1),392(a,1))].">
      <j1 rule="para" parents="5158 392"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,5159,a)].">
      <j1 rule="hyper" parents="127 10 5159"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,4912,a(flip),b,5159,a),flip(a)].">
      <j1 rule="hyper" parents="36 4912 5159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,5172,a)].">
      <j1 rule="hyper" parents="417 5172"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(324,a,5172,a),flip(a)].">
      <j1 rule="hyper" parents="324 5172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(244,a,5172,a,b,4363,a)].">
      <j1 rule="hyper" parents="244 5172 4363"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,5172,a)].">
      <j1 rule="hyper" parents="134 5172"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      (((x \ y) \ y) * K(z,u)) \ T(x,x \ y) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,110,a,b,5172,a)].">
      <j1 rule="hyper" parents="127 110 5172"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5047,a,b,5172,a),flip(a)].">
      <j1 rule="hyper" parents="36 5047 5172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(36,a,4933,a,b,5172,a),flip(a)].">
      <j1 rule="hyper" parents="36 4933 5172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,4428,a,b,5172,a),flip(a)].">
      <j1 rule="hyper" parents="36 4428 5172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2099,a,b,5172,a),flip(a)].">
      <j1 rule="hyper" parents="36 2099 5172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(130,a,5172,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 5172 197"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      L(K(x,y),z * K(y,x),u) = (u * (z * K(y,x))) \ (u * z)
    ]]></literal>
    <justification jstring="[para(5172(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="5172 18"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5172(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5172 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5172(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5172 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5172(a,1),330(a,1,2))].">
      <j1 rule="para" parents="5172 330"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      R((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(5172(a,1),106(a,2,1))].">
      <j1 rule="para" parents="5172 106"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(z,y),x * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5172(a,1),489(a,1,1))].">
      <j1 rule="para" parents="5172 489"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5172(a,1),713(a,1,1,2))].">
      <j1 rule="para" parents="5172 713"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      K((x * K(y,z)) \ 1,u) = K(K(z,y) / x,u)
    ]]></literal>
    <justification jstring="[para(5172(a,1),4649(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5172 4649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5047,a(flip),b,5174,a),flip(a)].">
      <j1 rule="hyper" parents="319 5047 5174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5174(a,1),254(a,1,1))].">
      <j1 rule="para" parents="5174 254"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(5174(a,1),303(a,1,1))].">
      <j1 rule="para" parents="5174 303"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) != w
    ]]></literal>
    <literal><![CDATA[
      x / (K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(5174(a,1),601(a,1,1))].">
      <j1 rule="para" parents="5174 601"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      R(x / (y * K(1 / z,z)),y / K(z,1 / z),K(z,1 / z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[para(5174(a,1),2409(a,1,1,2))].">
      <j1 rule="para" parents="5174 2409"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(5174(a,1),4493(a,2,2))].">
      <j1 rule="para" parents="5174 4493"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4717,a(flip),b,5176,a),flip(a)].">
      <j1 rule="hyper" parents="319 4717 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      (((x * x) \ y) * x) / y = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4917,a,b,5163,a)].">
      <j1 rule="hyper" parents="64 4917 5163"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4540,a(flip),b,5163,a)].">
      <j1 rule="hyper" parents="64 4540 5163"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,5163,a(flip),b,4539,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 5163 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),5165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(5165(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5165 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      x \ y != (z / u) * K(w,u)
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(u,w)) = y
    ]]></literal>
    <justification jstring="[para(5167(a,1),583(a,2,1))].">
      <j1 rule="para" parents="5167 583"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,4540,a(flip),b,5179,a)].">
      <j1 rule="hyper" parents="64 4540 5179"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      R(x / (y \ K(y,z)),y \ K(y,z),K(z,y)) = (x * K(z,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(206,a,5180,a(flip),b,520,a),flip(a)].">
      <j1 rule="hyper" parents="206 5180 520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5210">
    <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(4502(a,1),5187(a,1,1))].">
      <j1 rule="para" parents="4502 5187"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(4934(a,2),5187(a,1,1))].">
      <j1 rule="para" parents="4934 5187"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ z)) = (y \ T(z,x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(936(a,1),5151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="936 5151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(875(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="875 5151"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(1238(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="1238 5151"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1271(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="1271 5151"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(1792(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="1792 5151"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) * R(R(x * T(x \ 1,y),z,u) \ 1,w,v5) = R((x * T(x \ 1,y)) * R(K(y,x \ 1),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(5151(a,1),3590(a,2,1,2,1))].">
      <j1 rule="para" parents="5151 3590"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(3853(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="3853 5151"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      T(x,K(y,z)) != K(y,z) \ u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5173(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="5173 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(5173(a,2),4384(a,1))].">
      <j1 rule="para" parents="5173 4384"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * K(z,y) = K(z,y) * L(K(y,z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(5175(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5175 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      (x * x) \ ((y * x) / y) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,721,a(flip),b,5200,a)].">
      <j1 rule="hyper" parents="64 721 5200"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4983,a(flip),b,5205,a(flip))].">
      <j1 rule="hyper" parents="35 4983 5205"/>
    </justification>
  </clause>

  <clause id="5226">
    <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(5205(a,2),4157(a,1,1))].">
      <j1 rule="para" parents="5205 4157"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      K((1 / x) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3873,a,b,5225,a)].">
      <j1 rule="hyper" parents="64 3873 5225"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3870,a(flip),b,5225,a),flip(a)].">
      <j1 rule="hyper" parents="64 3870 5225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(198(a,1),5169(a,1,1))].">
      <j1 rule="para" parents="198 5169"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4011(a,2),5169(a,1,1))].">
      <j1 rule="para" parents="4011 5169"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4540(a,1),5169(a,1))].">
      <j1 rule="para" parents="4540 5169"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      x * K(y \ z,y) != u * y
    ]]></literal>
    <literal><![CDATA[
      u * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(5153(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5153 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(324,a,5178,a),flip(a)].">
      <j1 rule="hyper" parents="324 5178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      x * (K(R(y,z,u),x) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),5201(a,2,2))].">
      <j1 rule="para" parents="27 5201"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      (((x * y) \ x) * z) / T((x * y) \ x,u) = z * (K(y \ 1,z) * K(u,(x * y) \ x))
    ]]></literal>
    <justification jstring="[para(4995(a,1),5201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4995 5201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4281,a,b,5228,a)].">
      <j1 rule="hyper" parents="64 4281 5228"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5084,a(flip),b,5228,a)].">
      <j1 rule="hyper" parents="64 5084 5228"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1315,a,b,5233,a)].">
      <j1 rule="hyper" parents="64 1315 5233"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(392,a,5239,a),flip(a)].">
      <j1 rule="hyper" parents="392 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      ((x / y) * (y * K(y \ z,y))) * (z / y) = x * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4969,a,b,5239,a)].">
      <j1 rule="hyper" parents="130 4969 5239"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[hyper(5185,a,5241,a)].">
      <j1 rule="hyper" parents="5185 5241"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(906(a,1),4998(a,1,2))].">
      <j1 rule="para" parents="906 4998"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4216(a,1),4998(a,1))].">
      <j1 rule="para" parents="4216 4998"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(4356(a,1),5247(a,1,1,1))].">
      <j1 rule="para" parents="4356 5247"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4637(a,2),5247(a,1))].">
      <j1 rule="para" parents="4637 5247"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(2823(a,1),5249(a,1))].">
      <j1 rule="para" parents="2823 5249"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(5094(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5094 25"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5094(a,1),499(a,1))].">
      <j1 rule="para" parents="5094 499"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),5253(a,1,2,1))].">
      <j1 rule="para" parents="22 5253"/>
    </justification>
  </clause>

  <clause id="5255">
    <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(96(a,2),5253(a,1,2,1))].">
      <j1 rule="para" parents="96 5253"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3886(a,2),5253(a,1))].">
      <j1 rule="para" parents="3886 5253"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(4356(a,1),5253(a,1,2,1))].">
      <j1 rule="para" parents="4356 5253"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(875(a,1),5211(a,1,1))].">
      <j1 rule="para" parents="875 5211"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      T(x * T(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(4922(a,1),5222(a,1,1))].">
      <j1 rule="para" parents="4922 5222"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4960(a,1),4222(a,1,2))].">
      <j1 rule="para" parents="4960 4222"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(4548,a,4989,a)].">
      <j1 rule="hyper" parents="4548 4989"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(3974(a,1),4991(a,1,2))].">
      <j1 rule="para" parents="3974 4991"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5247,a,5028,a),flip(a)].">
      <j1 rule="hyper" parents="5247 5028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5087,a(flip),b,5088,a),flip(a)].">
      <j1 rule="hyper" parents="64 5087 5088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(5266(a,1),4430(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5266 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(4568(a,1),5208(a,1,2))].">
      <j1 rule="para" parents="4568 5208"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x \ R(x,y \ 1,x)) = z
    ]]></literal>
    <justification jstring="[para(5269(a,1),604(a,1,2))].">
      <j1 rule="para" parents="5269 604"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(131,a,5213,a,b,xx)].">
      <j1 rule="hyper" parents="131 5213"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ y = u
    ]]></literal>
    <justification jstring="[para(5213(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5213 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5100,a(flip),b,5085,a)].">
      <j1 rule="hyper" parents="64 5100 5085"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(4964,a,5273,a),flip(a)].">
      <j1 rule="hyper" parents="4964 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),5273(a,2,2,1))].">
      <j1 rule="para" parents="10 5273"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5273(a,2,2,2))].">
      <j1 rule="para" parents="10 5273"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(96(a,2),5273(a,2,2))].">
      <j1 rule="para" parents="96 5273"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      T(x,(y * z) \ (y * x)) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,5274,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5274 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),5274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),5274(a,1,2,2))].">
      <j1 rule="para" parents="10 5274"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(4363(a,1),5274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4363 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),5278(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(4526(a,1),5280(a,2,2,2))].">
      <j1 rule="para" parents="4526 5280"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5273,a(flip),b,5277,a),flip(a)].">
      <j1 rule="hyper" parents="64 5273 5277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(1591(a,1),5277(a,2,2))].">
      <j1 rule="para" parents="1591 5277"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(131,a,5275,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 5275 18"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(5275(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5275 25"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5275(a,1),4546(a,1)),flip(b)].">
      <j1 rule="para" parents="5275 4546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(5275(a,1),4964(a,1))].">
      <j1 rule="para" parents="5275 4964"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      K(x,L(a(y \ 1,y,z) \ u,a(y \ 1,y,z),L(z,y,y \ 1))) = K(x,z \ (L(z,y,y \ 1) * u))
    ]]></literal>
    <justification jstring="[para(1965(a,1),5285(a,2,2,1))].">
      <j1 rule="para" parents="1965 5285"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,((y * z) \ y) \ y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(5109(a,1),5285(a,2,2,1))].">
      <j1 rule="para" parents="5109 5285"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4601,a(flip),b,5286,a),flip(a)].">
      <j1 rule="hyper" parents="319 4601 5286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(401(a,2),5090(a,1,2))].">
      <j1 rule="para" parents="401 5090"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(713,a,5145,a),flip(a)].">
      <j1 rule="hyper" parents="713 5145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,5188,a(flip),b,5044,a(flip))].">
      <j1 rule="hyper" parents="130 5188 5044"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4195,a,b,5296,a)].">
      <j1 rule="hyper" parents="64 4195 5296"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(4016(a,2),5296(a,1,1,2))].">
      <j1 rule="para" parents="4016 5296"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(392,a,5298,a)].">
      <j1 rule="hyper" parents="392 5298"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(130,a,4346,a(flip),b,5298,a)].">
      <j1 rule="hyper" parents="130 4346 5298"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / ((z * y) / z),y) = y \ u
    ]]></literal>
    <justification jstring="[para(5299(a,1),285(a,1))].">
      <j1 rule="para" parents="5299 285"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(130,a,5300,a,b,5174,a)].">
      <j1 rule="hyper" parents="130 5300 5174"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),5300(a,1,2,1))].">
      <j1 rule="para" parents="12 5300"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(3349(a,1),5300(a,1,2))].">
      <j1 rule="para" parents="3349 5300"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4016(a,1),5300(a,1,2))].">
      <j1 rule="para" parents="4016 5300"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) \ 1) = K(x,((u * z) / u) / y)
    ]]></literal>
    <justification jstring="[para(5300(a,1),4491(a,1,2,1))].">
      <j1 rule="para" parents="5300 4491"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      K(x,1 / ((y * (1 / z)) / y)) = K(x,z * K(1 / z,y))
    ]]></literal>
    <justification jstring="[para(5300(a,2),4604(a,1,2))].">
      <j1 rule="para" parents="5300 4604"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((((y * z) / y) \ K(y,z)) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5306(a,1),908(a,2,1,2))].">
      <j1 rule="para" parents="5306 908"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ T(x / z,1 / (x / ((y * z) / y))) = ((1 / (x / ((y * z) / y))) \ K(y,z)) * (1 / (x / ((y * z) / y)))
    ]]></literal>
    <justification jstring="[para(5306(a,1),3814(a,1,2,1))].">
      <j1 rule="para" parents="5306 3814"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ x = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(199,a,5309,a)].">
      <j1 rule="hyper" parents="199 5309"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      (x / (y * K(z,y))) * u != w
    ]]></literal>
    <literal><![CDATA[
      ((x / y) * K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(5314(a,1),570(a,1,1,2))].">
      <j1 rule="para" parents="5314 570"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,2337,a,b,5307,a)].">
      <j1 rule="hyper" parents="319 2337 5307"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(5316(a,1),3863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5316 3863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      R((x / R(K(y,z),u,u \ 1)) * K(y,z),K(z,y),R(K(y,z),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4366(a,1),5194(a,2,2))].">
      <j1 rule="para" parents="4366 5194"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5088(a,1),5257(a,1))].">
      <j1 rule="para" parents="5088 5257"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(4356(a,1),5276(a,1,1,2))].">
      <j1 rule="para" parents="4356 5276"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,5000,a(flip),b,4934,a(flip))].">
      <j1 rule="hyper" parents="127 5000 4934"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(81(a,1),5325(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 5325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),y \ 1,z * y)) = K(x,a(z,y,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2504(a,2),5093(a,1,2))].">
      <j1 rule="para" parents="2504 5093"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      K(x,((y / z) \ y) \ 1) \ (y / z) = T(y \ (y / z),x) * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5049(a,1),5101(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5049 5101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,5143,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 5143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(4831(a,1),5198(a,1,1,2))].">
      <j1 rule="para" parents="4831 5198"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(207,a,5330,a)].">
      <j1 rule="hyper" parents="207 5330"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(40,a,18,a(flip),b,5330,a),flip(a)].">
      <j1 rule="hyper" parents="40 18 5330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      x * L(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * L(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(5330(a,1),140(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5330 140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),5330(a,1,1))].">
      <j1 rule="para" parents="94 5330"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(437(a,1),5330(a,1,1))].">
      <j1 rule="para" parents="437 5330"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w != x * y
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(5332(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5332 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(5332(a,1),330(a,1,2))].">
      <j1 rule="para" parents="5332 330"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),5214(a,1,1,2))].">
      <j1 rule="para" parents="109 5214"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(875(a,1),5214(a,1,1,2))].">
      <j1 rule="para" parents="875 5214"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1359(a,1),5214(a,1,1,2))].">
      <j1 rule="para" parents="1359 5214"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5219,a(flip),b,5338,a),flip(a)].">
      <j1 rule="hyper" parents="64 5219 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4214,a,b,5341,a)].">
      <j1 rule="hyper" parents="319 4214 5341"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,4214,a,b,5342,a)].">
      <j1 rule="hyper" parents="37 4214 5342"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5319(a,1),4617(a,1,2))].">
      <j1 rule="para" parents="5319 4617"/>
    </justification>
  </clause>

  <clause id="5345">
    <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(4130(a,1),5329(a,2,1))].">
      <j1 rule="para" parents="4130 5329"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(4924(a,2),4212(a,1))].">
      <j1 rule="para" parents="4924 4212"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(514(a,2),5086(a,1,2))].">
      <j1 rule="para" parents="514 5086"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      (x \ y) \ T(y,y \ x) = y * (T(x,x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,3802,a(flip))].">
      <j1 rule="hyper" parents="5112 3802"/>
    </justification>
  </clause>

  <clause id="5349">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(81(a,1),5121(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 5121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5061,a(flip),b,5122,a),flip(a)].">
      <j1 rule="hyper" parents="319 5061 5122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),5350(a,1,2,2,1))].">
      <j1 rule="para" parents="12 5350"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,5352,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 5352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(206,a,5353,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="206 5353 110"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2758(a,1),5354(a,2,2))].">
      <j1 rule="para" parents="2758 5354"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      L(K(x,y),z * K(y,x),u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5334,a(flip),b,5184,a),flip(a)].">
      <j1 rule="hyper" parents="319 5334 5184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5245,a,5264,a),flip(a)].">
      <j1 rule="hyper" parents="5245 5264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4584,a,b,5252,a),flip(a)].">
      <j1 rule="hyper" parents="319 4584 5252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3899,a,b,5294,a)].">
      <j1 rule="hyper" parents="64 3899 5294"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,438,a(flip),b,4941,a),flip(a)].">
      <j1 rule="hyper" parents="319 438 4941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(127,a,438,a(flip),b,4941,a)].">
      <j1 rule="hyper" parents="127 438 4941"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      (x * (y * T(z,u))) * K(u,L(z,y,x)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(5185,a,5360,a)].">
      <j1 rule="hyper" parents="5185 5360"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4950,a(flip),b,5361,a)].">
      <j1 rule="hyper" parents="64 4950 5361"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(4982,a,5363,a),flip(a)].">
      <j1 rule="hyper" parents="4982 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      K(L(x,x,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(495,a,5363,a),flip(a)].">
      <j1 rule="hyper" parents="495 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5363(a,1,2))].">
      <j1 rule="para" parents="10 5363"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),5363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4394,a(flip),b,5364,a),flip(a)].">
      <j1 rule="hyper" parents="319 4394 5364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(5364(a,2),4395(a,1))].">
      <j1 rule="para" parents="5364 4395"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,18,a(flip),b,5367,a),flip(a)].">
      <j1 rule="hyper" parents="319 18 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5367(a,1),4213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5367 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(96(a,1),5366(a,2,1))].">
      <j1 rule="para" parents="96 5366"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(302(a,1),5366(a,2,1))].">
      <j1 rule="para" parents="302 5366"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(504(a,1),5366(a,2,1))].">
      <j1 rule="para" parents="504 5366"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1568(a,2),5366(a,2,1))].">
      <j1 rule="para" parents="1568 5366"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(1591(a,1),5366(a,2,1))].">
      <j1 rule="para" parents="1591 5366"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4835,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="319 4835 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      K(x,L(y,1 / y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,494,a(flip),b,5377,a),flip(a)].">
      <j1 rule="hyper" parents="319 494 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),5377(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(4915(a,1),5377(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4915 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      K(x,L(y,z * z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(497(a,2),5378(a,1,2))].">
      <j1 rule="para" parents="497 5378"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      K(x,L(y,y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(495,a,5379,a),flip(a)].">
      <j1 rule="hyper" parents="495 5379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3742,a(flip),b,5379,a),flip(a)].">
      <j1 rule="hyper" parents="64 3742 5379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      K(x,L(y,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5379(a,1),495(a,1))].">
      <j1 rule="para" parents="5379 495"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      T(x,L(y,y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5382,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5382 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(5383(a,1),4832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5383 4832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      L(K((K(x,y) * z) \ u,w),u,K(y,x)) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),5372(a,2,1,1))].">
      <j1 rule="para" parents="4363 5372"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(5225(a,1),5372(a,1,1))].">
      <j1 rule="para" parents="5225 5372"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(4982,a,5374,a)].">
      <j1 rule="hyper" parents="4982 5374"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5275,a(flip),b,5374,a)].">
      <j1 rule="hyper" parents="64 5275 5374"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(5374(a,1),4982(a,1))].">
      <j1 rule="para" parents="5374 4982"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(4982,a,5376,a),flip(a)].">
      <j1 rule="hyper" parents="4982 5376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3871,a(flip),b,5376,a),flip(a)].">
      <j1 rule="hyper" parents="319 3871 5376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3871,a(flip),b,5393,a)].">
      <j1 rule="hyper" parents="64 3871 5393"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(4282,a,5395,a)].">
      <j1 rule="hyper" parents="4282 5395"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      L(x,y,z \ 1) != K((z \ 1) * y,u)
    ]]></literal>
    <literal><![CDATA[
      K(z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(5394(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="5394 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      (x * (y * T(T(z,y),u))) \ (x * (z * y)) = K(u,L(T(z,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,229,a(flip),b,5362,a)].">
      <j1 rule="hyper" parents="127 229 5362"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5362(a,1,1,2))].">
      <j1 rule="para" parents="109 5362"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(5370(a,2),489(a,1))].">
      <j1 rule="para" parents="5370 489"/>
    </justification>
  </clause>

  <clause id="5402">
    <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(78(a,1),5401(a,1,1,2))].">
      <j1 rule="para" parents="78 5401"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,5373,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="131 5373 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(5225(a,1),5373(a,1,1))].">
      <j1 rule="para" parents="5225 5373"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(5357(a,1),5373(a,1,1))].">
      <j1 rule="para" parents="5357 5373"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3742,a(flip),b,5387,a),flip(a)].">
      <j1 rule="hyper" parents="319 3742 5387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5406(a,1),1695(a,1,2))].">
      <j1 rule="para" parents="5406 1695"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * y) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(L(z,y,x) \ u,w),u,x * y) = v5
    ]]></literal>
    <justification jstring="[para(513(a,1),5402(a,1,1))].">
      <j1 rule="para" parents="513 5402"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      T(x,1 / y) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(4536(a,1),5115(a,1,1))].">
      <j1 rule="para" parents="4536 5115"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = T(x,1 / y) / y
    ]]></literal>
    <justification jstring="[para(81(a,1),5410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="81 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(81(a,1),5216(a,1,1,1,2,1))].">
      <j1 rule="para" parents="81 5216"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(4302(a,1),5217(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4302 5217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5084,a(flip),b,5238,a),flip(a)].">
      <j1 rule="hyper" parents="319 5084 5238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(5100(a,1),5255(a,1))].">
      <j1 rule="para" parents="5100 5255"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(5277(a,1),5415(a,1))].">
      <j1 rule="para" parents="5277 5415"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4430,a(flip),b,5267,a),flip(a)].">
      <j1 rule="hyper" parents="319 4430 5267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(5267(a,2),4465(a,1))].">
      <j1 rule="para" parents="5267 4465"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) = K(y \ T(x,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5417(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5420">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ K(y,z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(3123(a,2),5419(a,1,1,1))].">
      <j1 rule="para" parents="3123 5419"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(4513(a,1),5284(a,1,2,1))].">
      <j1 rule="para" parents="4513 5284"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,(x \ w) \ y))
    ]]></literal>
    <literal><![CDATA[
      K(u,w \ (x * y)) = z
    ]]></literal>
    <justification jstring="[para(5287(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5287 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2758(a,1),5355(a,1,1))].">
      <j1 rule="para" parents="2758 5355"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(66(a,1),5391(a,2,1))].">
      <j1 rule="para" parents="66 5391"/>
    </justification>
  </clause>

  <clause id="5425">
    <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(1124(a,1),5391(a,2,1))].">
      <j1 rule="para" parents="1124 5391"/>
    </justification>
  </clause>

  <clause id="5426">
    <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(5403(a,2),5187(a,1,1))].">
      <j1 rule="para" parents="5403 5187"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x \ z,u) \ T(z,u)) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,5413,a,b,xx)].">
      <j1 rule="hyper" parents="131 5413"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(3447(a,1),4932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3447 4932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(4864,a,5428,a)].">
      <j1 rule="hyper" parents="4864 5428"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4081(a,1),5428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4081 5428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(3626(a,1),5430(a,2,2))].">
      <j1 rule="para" parents="3626 5430"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y * z,x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(5431(a,2),1657(a,1))].">
      <j1 rule="para" parents="5431 1657"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(4912(a,1),5129(a,1,2))].">
      <j1 rule="para" parents="4912 5129"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(531,a,5433,a),flip(a)].">
      <j1 rule="hyper" parents="531 5433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4097(a,1),5434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4097 5434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,(x * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),5259(a,1,1,2))].">
      <j1 rule="para" parents="109 5259"/>
    </justification>
  </clause>

  <clause id="5437">
    <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(906(a,1),5259(a,1,1,2))].">
      <j1 rule="para" parents="906 5259"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5219(a,1),5436(a,1))].">
      <j1 rule="para" parents="5219 5436"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      (x * (T(y,z) * u)) \ (x * (y * u)) = K(z,L(T(y,u),u,x))
    ]]></literal>
    <justification jstring="[para(241(a,1),5399(a,1,1,2))].">
      <j1 rule="para" parents="241 5399"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      (x * (T(y,z) * u)) \ (x * (y * u)) = K(z,T(L(y,u,x),u))
    ]]></literal>
    <justification jstring="[para(25(a,1),5439(a,2,2))].">
      <j1 rule="para" parents="25 5439"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5373,a(flip),b,5405,a),flip(a)].">
      <j1 rule="hyper" parents="64 5373 5405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5441(a,2,1,1))].">
      <j1 rule="para" parents="10 5441"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),5442(a,1,1,1,2))].">
      <j1 rule="para" parents="78 5442"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = (u * K(x \ z,x)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(5443(a,1),5164(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5443 5164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,5164,a(flip),b,5444,a),flip(a)].">
      <j1 rule="hyper" parents="319 5164 5444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5135(a,1),5445(a,1,2))].">
      <j1 rule="para" parents="5135 5445"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(206,a,5446,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="206 5446 110"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(692,a,5447,a)].">
      <j1 rule="hyper" parents="692 5447"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5070,a(flip),b,5448,a),flip(a)].">
      <j1 rule="hyper" parents="64 5070 5448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4156,a,5149,a),flip(a)].">
      <j1 rule="hyper" parents="4156 5149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5450,a(flip),b,4912,a)].">
      <j1 rule="hyper" parents="128 5450 4912"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5450(a,1),2735(a,1))].">
      <j1 rule="para" parents="5450 2735"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(4341,a,4849,a)].">
      <j1 rule="hyper" parents="4341 4849"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      K(R(x,K(x,y) * (x \ z),u),w) = R(K(x,w),K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4305(a,1),5453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4305 5453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,535,a(flip),b,5454,a),flip(a)].">
      <j1 rule="hyper" parents="319 535 5454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,5454,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="130 5454 20"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),5454(a,1,1))].">
      <j1 rule="para" parents="102 5454"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(5454(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5454 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(81(a,1),5458(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 5458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(204(a,1),5458(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="204 5458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3171,a(flip),b,5461,a),flip(a)].">
      <j1 rule="hyper" parents="64 3171 5461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5001,a(flip),b,5462,a),flip(a)].">
      <j1 rule="hyper" parents="319 5001 5462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(5136(a,1),4415(a,1,2,2))].">
      <j1 rule="para" parents="5136 4415"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      x * (K(y,z) * (K(y,z) * u)) = x * (z * (T(T(z,y),y) \ u))
    ]]></literal>
    <justification jstring="[para(4447(a,1),4742(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4447 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),4745(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 4745"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4491,a(flip),b,5467,a),flip(a)].">
      <j1 rule="hyper" parents="319 4491 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(5468(a,1),540(a,1,1))].">
      <j1 rule="para" parents="5468 540"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4486(a,1),4804(a,1,1))].">
      <j1 rule="para" parents="4486 4804"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(417,a,4019,a,b,5470,a)].">
      <j1 rule="hyper" parents="417 4019 5470"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(3883(a,1),5470(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3883 5470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3883(a,1),5472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3883 5472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * (y \ 1)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5156,a,b,5473,a)].">
      <j1 rule="hyper" parents="64 5156 5473"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      ((x * T(y,z)) * (y \ 1)) * K(z,y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(35,a,4828,a,b,4842,a)].">
      <j1 rule="hyper" parents="35 4828 4842"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) * (x / L(x,u,w)) = x * T(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5476(a,1),2387(a,1,1))].">
      <j1 rule="para" parents="5476 2387"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) * (u / L(x,w,v5)) = u / ((L(x,w,v5) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(5476(a,1),2694(a,1,1))].">
      <j1 rule="para" parents="5476 2694"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(4555(a,1),4856(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4555 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3797,a(flip),b,5479,a),flip(a)].">
      <j1 rule="hyper" parents="319 3797 5479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(4535,a,5480,a)].">
      <j1 rule="hyper" parents="4535 5480"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3485(a,1),5481(a,1,2))].">
      <j1 rule="para" parents="3485 5481"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5326,a,b,5482,a)].">
      <j1 rule="hyper" parents="319 5326 5482"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(743,a,4863,a)].">
      <j1 rule="hyper" parents="743 4863"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(3974(a,1),5340(a,1,1,2))].">
      <j1 rule="para" parents="3974 5340"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(4921(a,1),5412(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4921 5412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(131,a,5486,a,b,xx)].">
      <j1 rule="hyper" parents="131 5486"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(4939(a,1),5487(a,1,2,2))].">
      <j1 rule="para" parents="4939 5487"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(5487(a,1),5176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5487 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * K(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(5488(a,2),571(a,1))].">
      <j1 rule="para" parents="5488 571"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5172(a,1),5488(a,1,1,1))].">
      <j1 rule="para" parents="5172 5488"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5491,a(flip),b,5147,a)].">
      <j1 rule="hyper" parents="128 5491 5147"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,y)) * K(z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(u,y) = w
    ]]></literal>
    <justification jstring="[para(5491(a,2),5193(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5491 5193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4936,a(flip),b,5492,a)].">
      <j1 rule="hyper" parents="64 4936 5492"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5146(a,1),5494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5146 5494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(296,a,5495,a),flip(a)].">
      <j1 rule="hyper" parents="296 5495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(1 / u,u)))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3739(a,1),3924(a,1,2,2))].">
      <j1 rule="para" parents="3739 3924"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(3156(a,1),4052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3156 4052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(4294(a,2),5498(a,1,2))].">
      <j1 rule="para" parents="4294 5498"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(y \ (y * x),w),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(4196(a,1),925(a,1,1,1))].">
      <j1 rule="para" parents="4196 925"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      R(x * K(y,x),y,L(x,z,u)) = x * K(y * L(x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(4230,a,4197,a)].">
      <j1 rule="hyper" parents="4230 4197"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4197(a,1),765(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4197 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5504">
    <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(64,a,4398,a,b,5503,a)].">
      <j1 rule="hyper" parents="64 4398 5503"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * (y * K(z * L(y,u,w),y))) / (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(5502(a,1),1485(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5502 1485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5506">
    <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(824(a,2),4403(a,1,2,2,1))].">
      <j1 rule="para" parents="824 4403"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      (x / (x / (x / y))) * z = ((x / y) * (K(y,x / y) * z)) * a(u,K(w \ 1,w),v5)
    ]]></literal>
    <justification jstring="[para(81(a,1),4759(a,2,1,2,1,1))].">
      <j1 rule="para" parents="81 4759"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      (x * (y * T(z,y))) \ ((x * y) * T(z,y)) = a(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(5046(a,1),4923(a,1,2))].">
      <j1 rule="para" parents="5046 4923"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      a(x,y * K(z,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5508(a,1),713(a,1))].">
      <j1 rule="para" parents="5508 713"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5396(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="5396 5099"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5390(a,1),5511(a,1,2))].">
      <j1 rule="para" parents="5390 5511"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(3043(a,1),5349(a,2,2))].">
      <j1 rule="para" parents="3043 5349"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,3060,a(flip),b,5513,a),flip(a)].">
      <j1 rule="hyper" parents="64 3060 5513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2758(a,1),5514(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2758 5514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(2758(a,1),5515(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2758 5515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(199,a,5516,a)].">
      <j1 rule="hyper" parents="199 5516"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      (((x \ y) / (x \ 1)) \ (y / x)) \ (y / x) = (x \ 1) \ T(y / x,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),5517(a,1,1,1,1))].">
      <j1 rule="para" parents="111 5517"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      (((x \ y) / (x \ 1)) \ (y / x)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),5518(a,2,2))].">
      <j1 rule="para" parents="111 5518"/>
    </justification>
  </clause>

  <clause id="5520">
    <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(5335(a,1),5426(a,1))].">
      <j1 rule="para" parents="5335 5426"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(z,y)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(4356(a,1),5520(a,1,1,2))].">
      <j1 rule="para" parents="4356 5520"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) * (x / L(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      (L(x,u,w) \ 1) * x = v5
    ]]></literal>
    <justification jstring="[para(5477(a,2),291(a,1))].">
      <j1 rule="para" parents="5477 291"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) * (u / L(x,w,v5)) = u / L((x \ 1) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(2652(a,2),5478(a,2,2))].">
      <j1 rule="para" parents="2652 5478"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(489,a,5497,a)].">
      <j1 rule="hyper" parents="489 5497"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * K(1 / x,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4043(a,1),5525(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4043 5525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(5185,a,5526,a)].">
      <j1 rule="hyper" parents="5185 5526"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5527(a,1),3864(a,2,2))].">
      <j1 rule="para" parents="5527 3864"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1976(a,1),5506(a,1,2))].">
      <j1 rule="para" parents="1976 5506"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(x,x \ y),z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(127,a,4128,a(flip),b,4040,a),flip(a)].">
      <j1 rule="hyper" parents="127 4128 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) / (T((x \ 1) \ 1,y) * K(z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3883(a,1),4524(a,1,2,2))].">
      <j1 rule="para" parents="3883 4524"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(4959(a,1),4755(a,2,2,2))].">
      <j1 rule="para" parents="4959 4755"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(945(a,1),4874(a,1,1))].">
      <j1 rule="para" parents="945 4874"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1248(a,1),5533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1248 5533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5536">
    <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(4922(a,1),4954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4922 4954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,5536,a),flip(a)].">
      <j1 rule="hyper" parents="319 20 5536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5538">
    <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(5536(a,2),531(a,1))].">
      <j1 rule="para" parents="5536 531"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      T(x \ (x / y),z) * T(x,y \ 1) = K(z,y \ 1) \ (x / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),5328(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),5339(a,1,1,2,2))].">
      <j1 rule="para" parents="109 5339"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3972(a,2),5540(a,1,1))].">
      <j1 rule="para" parents="3972 5540"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4145(a,1),5345(a,1,1,2))].">
      <j1 rule="para" parents="4145 5345"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4047(a,1),5542(a,1,2,2))].">
      <j1 rule="para" parents="4047 5542"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      x / L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(5522,a,5524,a),flip(a)].">
      <j1 rule="hyper" parents="5522 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * x) \ x = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(199,a,5544,a)].">
      <j1 rule="hyper" parents="199 5544"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5545(a,1),3955(a,1,1))].">
      <j1 rule="para" parents="5545 3955"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      (L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1)) * (x \ 1) = ((L(x,y,z) \ 1) * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5546(a,1),3859(a,2,1))].">
      <j1 rule="para" parents="5546 3859"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(3842(a,1),5534(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3842 5534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4183,a,b,5548,a)].">
      <j1 rule="hyper" parents="319 4183 5548"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),5549(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(4356(a,1),5550(a,1,2))].">
      <j1 rule="para" parents="4356 5550"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5482(a,2),5551(a,1,1))].">
      <j1 rule="para" parents="5482 5551"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(585,a,5552,a)].">
      <j1 rule="hyper" parents="585 5552"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,3837,a(flip),b,3849,a),flip(a)].">
      <j1 rule="hyper" parents="64 3837 3849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(2961(a,2),3855(a,1,1))].">
      <j1 rule="para" parents="2961 3855"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(4487(a,1),4488(a,2,1))].">
      <j1 rule="para" parents="4487 4488"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,105,a,b,5556,a)].">
      <j1 rule="hyper" parents="36 105 5556"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,3202,a(flip),b,5556,a),flip(a)].">
      <j1 rule="hyper" parents="36 3202 5556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5559">
    <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),5558(a,1,2,1))].">
      <j1 rule="para" parents="31 5558"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(81(a,1),5557(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="81 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3883(a,1),5557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3883 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(4491(a,1),5557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4491 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5084(a,1),5557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5084 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4732,a(flip),b,5560,a)].">
      <j1 rule="hyper" parents="64 4732 5560"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5561(a,1),4733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5561 4733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(319,a,105,a(flip),b,5565,a),flip(a)].">
      <j1 rule="hyper" parents="319 105 5565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4467,a(flip),b,5565,a),flip(a)].">
      <j1 rule="hyper" parents="64 4467 5565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(4572,a,5562,a),flip(a)].">
      <j1 rule="hyper" parents="4572 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(517(a,1),5562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="517 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(5562(a,1),4572(a,1))].">
      <j1 rule="para" parents="5562 4572"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),5568(a,2,2,1))].">
      <j1 rule="para" parents="12 5568"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),5568(a,2,2,2))].">
      <j1 rule="para" parents="12 5568"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),5568(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 5568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      R(K(x,R(y,z,u) \ y),y,w) = K(x,(y * w) / (R(y,z,u) * w))
    ]]></literal>
    <justification jstring="[para(2967(a,1),5568(a,1,1,2))].">
      <j1 rule="para" parents="2967 5568"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(4350(a,1),5572(a,1,1))].">
      <j1 rule="para" parents="4350 5572"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),5573(a,1,2))].">
      <j1 rule="para" parents="102 5573"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5459,a(flip),b,5576,a)].">
      <j1 rule="hyper" parents="64 5459 5576"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      x / R(K(y,z),u,w) = x * R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(206,a,5576,a(flip),b,5459,a(flip))].">
      <j1 rule="hyper" parents="206 5576 5459"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,5576,a(flip),b,5459,a(flip))].">
      <j1 rule="hyper" parents="131 5576 5459"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(22(a,2),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      R(K(x,R(y,z,u)),(y * z) * u,w) = K(x,R(R(y,z,u),z * u,w))
    ]]></literal>
    <justification jstring="[para(194(a,1),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="194 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1908(a,1),5576(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1908 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(4309(a,1),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4309 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(3238,a,5580,a),flip(a)].">
      <j1 rule="hyper" parents="3238 5580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4726,a(flip),b,5580,a)].">
      <j1 rule="hyper" parents="64 4726 5580"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(5580(a,1),27(a,2,1))].">
      <j1 rule="para" parents="5580 27"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5580(a,1),4527(a,1,1))].">
      <j1 rule="para" parents="5580 4527"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(3238,a,5575,a),flip(a)].">
      <j1 rule="hyper" parents="3238 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4491,a,b,5575,a),flip(a)].">
      <j1 rule="hyper" parents="319 4491 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(5575(a,1),3238(a,1))].">
      <j1 rule="para" parents="5575 3238"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1525(a,1),5589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1525 5589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(548(a,1),5559(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="548 5559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = T(K(x,(y / (x * z)) \ 1),u)
    ]]></literal>
    <justification jstring="[para(5590(a,1),27(a,2,1))].">
      <j1 rule="para" parents="5590 27"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / ((y \ z) * u)) = w
    ]]></literal>
    <justification jstring="[para(78(a,1),5570(a,1,1,2))].">
      <j1 rule="para" parents="78 5570"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3951(a,1),5593(a,1,2,1))].">
      <j1 rule="para" parents="3951 5593"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5280,a(flip),b,5597,a)].">
      <j1 rule="hyper" parents="64 5280 5597"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1168(a,1),5598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1168 5598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(5437,a,5485,a),flip(a)].">
      <j1 rule="hyper" parents="5437 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5600(a,2,2,1))].">
      <j1 rule="para" parents="10 5600"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(78(a,1),5600(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(357(a,1),5602(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="357 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5147(a,1),5603(a,1,2,1))].">
      <j1 rule="para" parents="5147 5603"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4020(a,1),5604(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4020 5604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),5501(a,2,1,1))].">
      <j1 rule="para" parents="9 5501"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[para(3937(a,2),5554(a,1,2))].">
      <j1 rule="para" parents="3937 5554"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(290,a,5555,a),flip(a)].">
      <j1 rule="hyper" parents="290 5555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4491,a(flip),b,5594,a),flip(a)].">
      <j1 rule="hyper" parents="319 4491 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5562,a(flip),b,5609,a)].">
      <j1 rule="hyper" parents="64 5562 5609"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(4350(a,1),5610(a,1,1))].">
      <j1 rule="para" parents="4350 5610"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5453,a(flip),b,5611,a),flip(a)].">
      <j1 rule="hyper" parents="64 5453 5611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5613">
    <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),5612(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5614">
    <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(4553(a,1),5612(a,1,2,1))].">
      <j1 rule="para" parents="4553 5612"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5454,a(flip),b,5613,a),flip(a)].">
      <j1 rule="hyper" parents="64 5454 5613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[hyper(300,a,5607,a),flip(a)].">
      <j1 rule="hyper" parents="300 5607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(232(a,1),3835(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4001(a,2),5617(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4001 5617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4001(a,2),5619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4001 5619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = (x \ y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4922,a(flip),b,5620,a),flip(a)].">
      <j1 rule="hyper" parents="319 4922 5620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,4912,a,b,5621,a),flip(a)].">
      <j1 rule="hyper" parents="36 4912 5621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5622,a)].">
      <j1 rule="hyper" parents="145 5622"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4509,a(flip),b,5622,a)].">
      <j1 rule="hyper" parents="64 4509 5622"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(244,a,5622,a(flip),b,4292,a),flip(a)].">
      <j1 rule="hyper" parents="244 5622 4292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),5623(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(5422,a,5626,a),flip(a)].">
      <j1 rule="hyper" parents="5422 5626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,5626,a)].">
      <j1 rule="hyper" parents="529 5626"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(488,a,5626,a)].">
      <j1 rule="hyper" parents="488 5626"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,5626,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="130 5626 4915"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      (x * (y * K(x,z))) / T(x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,5626,a(flip),b,4921,a)].">
      <j1 rule="hyper" parents="128 5626 4921"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,5626,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="126 5626 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5626(a,1),4936(a,1,1))].">
      <j1 rule="para" parents="5626 4936"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      x * (L(x \ y,z,u) * K(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5626(a,1),5118(a,1))].">
      <j1 rule="para" parents="5626 5118"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      R(R(x,y,z),u,K(x,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5628(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5628 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(5628(a,1),433(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5628 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(5628(a,1),430(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5628 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(5628(a,1),432(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5628 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(5628(a,1),5457(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5628 5457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5520,a,5629,a)].">
      <j1 rule="hyper" parents="5520 5629"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1741,a,5629,a)].">
      <j1 rule="hyper" parents="1741 5629"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      L(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1740,a,5629,a)].">
      <j1 rule="hyper" parents="1740 5629"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5379,a(flip),b,5629,a)].">
      <j1 rule="hyper" parents="64 5379 5629"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5363,a(flip),b,5629,a)].">
      <j1 rule="hyper" parents="64 5363 5629"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      K(x,L(y,z,x)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4214,a,b,5644,a),flip(a)].">
      <j1 rule="hyper" parents="319 4214 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5644,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5644 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="30 5644"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      K(x,(x \ 1) \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(503(a,1),5644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(747(a,1),5644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="747 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1584(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="1584 5644"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1584(a,2),5644(a,1,2))].">
      <j1 rule="para" parents="1584 5644"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(4881(a,1),5644(a,1,2))].">
      <j1 rule="para" parents="4881 5644"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(5644(a,1),5363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5644 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(L(x,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5629,a,b,5645,a)].">
      <j1 rule="hyper" parents="319 5629 5645"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5645,a(flip),b,4086,a)].">
      <j1 rule="hyper" parents="131 5645 4086"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3495(a,1),5645(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3495 5645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4401,a,5647,a(flip))].">
      <j1 rule="hyper" parents="4401 5647"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(504(a,1),5647(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 5647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      x * K(R(x,y,x),z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,5658,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 5658 4012"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5454,a(flip),b,5658,a)].">
      <j1 rule="hyper" parents="64 5454 5658"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,5658,a(flip),b,4213,a),flip(a)].">
      <j1 rule="hyper" parents="206 5658 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,5658,a(flip),b,4061,a)].">
      <j1 rule="hyper" parents="130 5658 4061"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(5658(a,1),4337(a,1,1))].">
      <j1 rule="para" parents="5658 4337"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(5658(a,1),5457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5658 5457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5580,a(flip),b,5663,a)].">
      <j1 rule="hyper" parents="64 5580 5663"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5572,a(flip),b,5663,a)].">
      <j1 rule="hyper" parents="64 5572 5663"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(5663(a,1),4527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5663 4527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      K(L(x,x,y),z) = K(x,R(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,5365,a,b,5668,a)].">
      <j1 rule="hyper" parents="319 5365 5668"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5668,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5668 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(540(a,1),5673(a,1,2))].">
      <j1 rule="para" parents="540 5673"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (z / x),u))
    ]]></literal>
    <justification jstring="[para(758(a,1),5673(a,1,2))].">
      <j1 rule="para" parents="758 5673"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5293,a(flip),b,5643,a)].">
      <j1 rule="hyper" parents="64 5293 5643"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(4227,a,5646,a)].">
      <j1 rule="hyper" parents="4227 5646"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      K(x,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5646(a,2),4219(a,1))].">
      <j1 rule="para" parents="5646 4219"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5401,a,5680,a)].">
      <j1 rule="hyper" parents="5401 5680"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,5680,a(flip),b,5370,a(flip))].">
      <j1 rule="hyper" parents="131 5680 5370"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),5680(a,1,1))].">
      <j1 rule="para" parents="30 5680"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(466(a,1),5680(a,1,1))].">
      <j1 rule="para" parents="466 5680"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[para(302(a,1),5680(a,1,1))].">
      <j1 rule="para" parents="302 5680"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[para(504(a,1),5680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="504 5680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1584(a,2),5680(a,1,1))].">
      <j1 rule="para" parents="1584 5680"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = R(z,u,w) \ R(z * K(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(5680(a,1),4628(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5680 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(4881(a,1),5680(a,1,1))].">
      <j1 rule="para" parents="4881 5680"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5379,a(flip),b,5682,a)].">
      <j1 rule="hyper" parents="64 5379 5682"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5682(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="5682 481"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5692,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5692 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5692,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 5692 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3295(a,1),5692(a,1,2))].">
      <j1 rule="para" parents="3295 5692"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3296(a,1),5692(a,1,2))].">
      <j1 rule="para" parents="3296 5692"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3495(a,1),5692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3495 5692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,5696,a),flip(a)].">
      <j1 rule="hyper" parents="393 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      x * T(y,L(x,z,x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(131,a,5696,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="131 5696 22"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5696,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 5696 22"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3296(a,1),5696(a,1,2))].">
      <j1 rule="para" parents="3296 5696"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3495(a,1),5696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3495 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5576,a(flip),b,5700,a)].">
      <j1 rule="hyper" parents="64 5576 5700"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5700,a(flip),b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="131 5700 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3414(a,1),5700(a,1,2))].">
      <j1 rule="para" parents="3414 5700"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,5706,a),flip(a)].">
      <j1 rule="hyper" parents="393 5706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5706,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 5706 22"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3341(a,1),5706(a,1,2))].">
      <j1 rule="para" parents="3341 5706"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3414(a,1),5706(a,1,2))].">
      <j1 rule="para" parents="3414 5706"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(3514(a,1),5706(a,1,2))].">
      <j1 rule="para" parents="3514 5706"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      K(R(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5453,a(flip),b,5707,a)].">
      <j1 rule="hyper" parents="64 5453 5707"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(130,a,5707,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 5707 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      K(x,y) * ((x * z) * y) = (T(x,y) * z) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,5715,a(flip),b,4849,a)].">
      <j1 rule="hyper" parents="130 5715 4849"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,u,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5456,a,b,5653,a)].">
      <j1 rule="hyper" parents="64 5456 5653"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,5662,a(flip),b,5529,a),flip(a)].">
      <j1 rule="hyper" parents="127 5662 5529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5664(a,2),4219(a,1))].">
      <j1 rule="para" parents="5664 4219"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[para(509(a,1),5688(a,1,1))].">
      <j1 rule="para" parents="509 5688"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5697(a,2),4089(a,1))].">
      <j1 rule="para" parents="5697 4089"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(111(a,1),5703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(5650(a,1),5276(a,1,1))].">
      <j1 rule="para" parents="5650 5276"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5656(a,1),496(a,1)),flip(b)].">
      <j1 rule="para" parents="5656 496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      K(x,x \ ((x \ 1) \ y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,((x / (y * x)) \ 1) \ z) = K((x / (y * x)) \ 1,R(y \ 1,y,x) * z)
    ]]></literal>
    <justification jstring="[para(2058(a,2),5679(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2058 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(302(a,1),5681(a,1,2))].">
      <j1 rule="para" parents="302 5681"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * (y \ w))) = K(x,T(y,L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[para(1166(a,1),5698(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1166 5698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1453(a,1),5698(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1453 5698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3327(a,2),5698(a,1,2))].">
      <j1 rule="para" parents="3327 5698"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(78(a,1),5699(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      T(T(x,y),x / z) = T(T(x,y),z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3354,a(flip),b,5705,a)].">
      <j1 rule="hyper" parents="64 3354 5705"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(78(a,1),5705(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 5705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1332(a,1),5720(a,1,2))].">
      <j1 rule="para" parents="1332 5720"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1622(a,1),5720(a,1,2))].">
      <j1 rule="para" parents="1622 5720"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3414(a,1),5720(a,1,2))].">
      <j1 rule="para" parents="3414 5720"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3296(a,1),5723(a,1,2))].">
      <j1 rule="para" parents="3296 5723"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(3389(a,2),5728(a,1,1))].">
      <j1 rule="para" parents="3389 5728"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(3495(a,1),5728(a,1,1))].">
      <j1 rule="para" parents="3495 5728"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      K(x,R(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5672(a,1),5728(a,1))].">
      <j1 rule="para" parents="5672 5728"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ y) = x * (((x \ 1) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(130,a,5729,a(flip),b,4261,a)].">
      <j1 rule="hyper" parents="130 5729 4261"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4647,a,b,5732,a)].">
      <j1 rule="hyper" parents="64 4647 5732"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4162,a(flip),b,5735,a),flip(a)].">
      <j1 rule="hyper" parents="319 4162 5735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      T(x,T(y,z * y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,5735,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5735 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(5736(a,1),5273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5736 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y \ z)) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(5736(a,1),5415(a,1,1))].">
      <j1 rule="para" parents="5736 5415"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,5738,a),flip(a)].">
      <j1 rule="hyper" parents="393 5738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) \ 1) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5058,a,b,5738,a)].">
      <j1 rule="hyper" parents="64 5058 5738"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5750(a,1),3352(a,1))].">
      <j1 rule="para" parents="5750 3352"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5538,a,5636,a)].">
      <j1 rule="hyper" parents="5538 5636"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * K(x,u) = R(x,y,z) \ K(x,u)
    ]]></literal>
    <justification jstring="[para(5636(a,1),402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5636 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = T(R(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(5757(a,1),27(a,2,1))].">
      <j1 rule="para" parents="5757 27"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(111(a,1),5757(a,1,3)),flip(a)].">
      <j1 rule="para" parents="111 5757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      T(x,R(y,z,T(y,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5757(a,2),5706(a,1,2))].">
      <j1 rule="para" parents="5757 5706"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,z)) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(249(a,1),5764(a,1,2,3))].">
      <j1 rule="para" parents="249 5764"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(4826,a,5642,a)].">
      <j1 rule="hyper" parents="4826 5642"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,5642,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 5642 18"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2489(a,2),5740(a,1,2))].">
      <j1 rule="para" parents="2489 5740"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3870(a,2),5740(a,1))].">
      <j1 rule="para" parents="3870 5740"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3495(a,1),5766(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3495 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      (K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(5770(a,1),4729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5770 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5438,a,5641,a)].">
      <j1 rule="hyper" parents="5438 5641"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5215,a,b,5641,a)].">
      <j1 rule="hyper" parents="64 5215 5641"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z)
    ]]></literal>
    <justification jstring="[para(262(a,1),5641(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 5641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5641(a,1),5131(a,2,2))].">
      <j1 rule="para" parents="5641 5131"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(2939,a,5657,a)].">
      <j1 rule="hyper" parents="2939 5657"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(5657(a,1),4776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5657 4776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      K(x,y) \ R(y,z,y) = R(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(4393,a,5665,a)].">
      <j1 rule="hyper" parents="4393 5665"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,5665,a(flip),b,4037,a)].">
      <j1 rule="hyper" parents="127 5665 4037"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,5667,a)].">
      <j1 rule="hyper" parents="488 5667"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4294,a(flip),b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="319 4294 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,4412,a,b,5667,a)].">
      <j1 rule="hyper" parents="35 4412 5667"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5667(a,1),400(a,1,1))].">
      <j1 rule="para" parents="5667 400"/>
    </justification>
  </clause>

  <clause id="5788">
    <literal><![CDATA[
      (K(x,y) * z) / x = K(x,y) * (z / x)
    ]]></literal>
    <justification jstring="[hyper(206,a,5783,a(flip),b,98,a(flip))].">
      <j1 rule="hyper" parents="206 5783 98"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5783(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5783 25"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      L(L(x,y,z),u,K(x,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5783(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5783 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(5783(a,1),436(a,1,2,1))].">
      <j1 rule="para" parents="5783 436"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5783(a,1),5367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5783 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      L(L(x,y,z),u,K(w,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5786(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5786 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(5786(a,1),438(a,1,2,1))].">
      <j1 rule="para" parents="5786 438"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5786(a,1),5367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5786 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5786(a,1),5377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5786 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4884,a(flip),b,5789,a)].">
      <j1 rule="hyper" parents="64 4884 5789"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,2860,a(flip),b,5800,a),flip(a)].">
      <j1 rule="hyper" parents="319 2860 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4286,a,b,5800,a)].">
      <j1 rule="hyper" parents="64 4286 5800"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      K(K(x,y) * z,x) = x / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,5800,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 5800 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,5800,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 5800 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5808">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(5800(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5800 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4363(a,1),5800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      T(x,T(x,y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4292(a,1),5800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,K(x,u) * y)) = T(x * K(z,x),K(x,u) * y)
    ]]></literal>
    <justification jstring="[para(5800(a,1),4398(a,1,1))].">
      <j1 rule="para" parents="5800 4398"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(4670(a,1),5800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4670 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      T(x,y \ T(z,x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4522(a,1),5800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4522 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      T(x,K(y,x) * z) = x * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      T(((K(x,y) * z) \ y) \ T(y,z),y) = ((K(x,y) * z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(5809(a,1),1219(a,1,1,2))].">
      <j1 rule="para" parents="5809 1219"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      T(x,y * T(z,x)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(4646(a,1),5809(a,1,2))].">
      <j1 rule="para" parents="4646 5809"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5379,a(flip),b,5794,a)].">
      <j1 rule="hyper" parents="64 5379 5794"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      L(T(K(x,y),z),u,K(x,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5794(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5794 25"/>
    </justification>
  </clause>

  <clause id="5822">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(5794(a,1),3370(a,1,1,1))].">
      <j1 rule="para" parents="5794 3370"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[para(5794(a,1),4412(a,1,2))].">
      <j1 rule="para" parents="5794 4412"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5379,a(flip),b,5798,a)].">
      <j1 rule="hyper" parents="64 5379 5798"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5363,a(flip),b,5799,a)].">
      <j1 rule="hyper" parents="64 5363 5799"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(4774(a,1),5820(a,1,2))].">
      <j1 rule="para" parents="4774 5820"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5824,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5824 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5828">
    <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),5824(a,1,2))].">
      <j1 rule="para" parents="30 5824"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[para(4378(a,1),5825(a,1,1))].">
      <j1 rule="para" parents="4378 5825"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(96(a,1),5827(a,1,2))].">
      <j1 rule="para" parents="96 5827"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,5806,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 5806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(5806(a,2),4117(a,1))].">
      <j1 rule="para" parents="5806 4117"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4081(a,1),5832(a,1,1))].">
      <j1 rule="para" parents="4081 5832"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(4363(a,1),5832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 5832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4522(a,1),5832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4522 5832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(5832(a,1),4948(a,1,1))].">
      <j1 rule="para" parents="5832 4948"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(5560(a,1),5832(a,1,1,1))].">
      <j1 rule="para" parents="5560 5832"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4646(a,1),5837(a,1,1))].">
      <j1 rule="para" parents="4646 5837"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,5807,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 5807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5807(a,2),4106(a,1))].">
      <j1 rule="para" parents="5807 4106"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      K(x,K(x,y) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(4081(a,1),5843(a,1,2))].">
      <j1 rule="para" parents="4081 5843"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4356(a,2),5843(a,1,2))].">
      <j1 rule="para" parents="4356 5843"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4363(a,1),5843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 5843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4292(a,1),5843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 5843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4314(a,1),5843(a,1,2))].">
      <j1 rule="para" parents="4314 5843"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4361(a,1),5843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4361 5843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5560(a,1),5843(a,1,2,1))].">
      <j1 rule="para" parents="5560 5843"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      (x * y) / T((y \ x) * y,y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3502,a,b,5810,a)].">
      <j1 rule="hyper" parents="64 3502 5810"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      T(x,y \ (z / x)) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(111(a,1),5815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 5815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5816(a,2),4089(a,1))].">
      <j1 rule="para" parents="5816 4089"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      T(x,y * (z / x)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(111(a,1),5819(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 5819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3313,a,b,5838,a)].">
      <j1 rule="hyper" parents="64 3313 5838"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5838,a(flip),b,3978,a),flip(a)].">
      <j1 rule="hyper" parents="131 5838 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),5838(a,1,1,2))].">
      <j1 rule="para" parents="22 5838"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      K(x * (y / z),z) = K(x * (z \ y),z)
    ]]></literal>
    <justification jstring="[para(111(a,1),5842(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 5842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(5074(a,1),5842(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5074 5842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      K(x,R(y / x,z,u) \ w) = K(x,R(x \ y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(252(a,1),5850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="252 5850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(3999(a,1),5833(a,1,1))].">
      <j1 rule="para" parents="3999 5833"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      K(T(x,y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(4314(a,1),5833(a,1,1))].">
      <j1 rule="para" parents="4314 5833"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),5840(a,1,1))].">
      <j1 rule="para" parents="105 5840"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(5453(a,1),5840(a,1,1,1))].">
      <j1 rule="para" parents="5453 5840"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      K(x,T(y,x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4314(a,1),5844(a,1,2))].">
      <j1 rule="para" parents="4314 5844"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),5852(a,1,2))].">
      <j1 rule="para" parents="105 5852"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5453(a,1),5852(a,1,2,1))].">
      <j1 rule="para" parents="5453 5852"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(4659(a,1),5857(a,1,2))].">
      <j1 rule="para" parents="4659 5857"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      T(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4644(a,1),5857(a,1,2))].">
      <j1 rule="para" parents="4644 5857"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(3999(a,1),5868(a,1,1))].">
      <j1 rule="para" parents="3999 5868"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(4041(a,1),5868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4041 5868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4021(a,1),5871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4021 5871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(3999(a,1),5871(a,1,2))].">
      <j1 rule="para" parents="3999 5871"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),5871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 5871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(4116(a,1),5871(a,1,2))].">
      <j1 rule="para" parents="4116 5871"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(4292(a,1),5871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 5871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(4670(a,1),5871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4670 5871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(4337(a,1),5871(a,1,2))].">
      <j1 rule="para" parents="4337 5871"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      T((x * y) / T(x,z),x) = y * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(5160,a,5683,a)].">
      <j1 rule="hyper" parents="5160 5683"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,5683,a)].">
      <j1 rule="hyper" parents="529 5683"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      (x * (y * K(z,x))) * z = (x * y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,5683,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="130 5683 4915"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5683,a(flip),b,5147,a)].">
      <j1 rule="hyper" parents="128 5683 5147"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,27,a(flip),b,5884,a(flip))].">
      <j1 rule="hyper" parents="41 27 5884"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5884(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5884 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1800(a,1),5884(a,1,3))].">
      <j1 rule="para" parents="1800 5884"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      (x * y) * K(z,T(x,u)) = x * (y * K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(130,a,5888,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 5888 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,T(x,v5)) = L(x,y,z) * (u * K(w,T(x,v5)))
    ]]></literal>
    <justification jstring="[para(5888(a,1),432(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5888 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(5891(a,1),519(a,1,1))].">
      <j1 rule="para" parents="5891 519"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = ((x * K(y,z)) * R(z,u,w)) / K(y,z)
    ]]></literal>
    <justification jstring="[para(5890(a,1),825(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5890 825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(4274,a,5686,a)].">
      <j1 rule="hyper" parents="4274 5686"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5343,a,b,5686,a)].">
      <j1 rule="hyper" parents="64 5343 5686"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5265,a,b,5686,a)].">
      <j1 rule="hyper" parents="64 5265 5686"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5686(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(5161,a,5693,a)].">
      <j1 rule="hyper" parents="5161 5693"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),5704(a,1,2))].">
      <j1 rule="para" parents="111 5704"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5710,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 5710 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(5710(a,1),5842(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5710 5842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),5711(a,1,2))].">
      <j1 rule="para" parents="111 5711"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(4722,a,5714,a),flip(a)].">
      <j1 rule="hyper" parents="4722 5714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(244,a,5716,a,b,4040,a)].">
      <j1 rule="hyper" parents="244 5716 4040"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      (K(x,y) * T(z * K(y,z),u)) * y = K(x,y) * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4138(a,1),5716(a,2,2))].">
      <j1 rule="para" parents="4138 5716"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3962(a,1),5734(a,2,2))].">
      <j1 rule="para" parents="3962 5734"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(5058(a,1),5734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5058 5734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,27,a,b,5761,a),flip(a)].">
      <j1 rule="hyper" parents="319 27 5761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3328,a(flip),b,5761,a),flip(a)].">
      <j1 rule="hyper" parents="319 3328 5761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5285,a,b,5773,a)].">
      <j1 rule="hyper" parents="64 5285 5773"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (x * z)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),5773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 5773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(237(a,1),5773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="237 5773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(244,a,5784,a,b,4036,a)].">
      <j1 rule="hyper" parents="244 5784 4036"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(4037(a,2),5784(a,1,1))].">
      <j1 rule="para" parents="4037 5784"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(4292(a,1),5784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4292 5784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      K(x,y) * ((x * z) / x) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(4081(a,1),5788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4081 5788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,4920,a,b,5805,a)].">
      <j1 rule="hyper" parents="40 4920 5805"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(5185,a,5925,a)].">
      <j1 rule="hyper" parents="5185 5925"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a,b,5925,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(245,a,5925,a),flip(a)].">
      <j1 rule="hyper" parents="245 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2833,a,b,5925,a),flip(a)].">
      <j1 rule="hyper" parents="35 2833 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2099,a,b,5925,a),flip(a)].">
      <j1 rule="hyper" parents="35 2099 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5932">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),5925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),5925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(5925(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="5925 5176"/>
    </justification>
  </clause>

  <clause id="5935">
    <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(5925(a,1),5337(a,1,1,2))].">
      <j1 rule="para" parents="5925 5337"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(130,a,5928,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 5928 4011"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2924(a,1),5928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2924 5928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(5928(a,1),4213(a,1,1))].">
      <j1 rule="para" parents="5928 4213"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      T(x,T(y,z)) * K(x,y) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,5929,a(flip),b,4078,a)].">
      <j1 rule="hyper" parents="131 5929 4078"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(T(x,K(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(130,a,5930,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 5930 4011"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(5930(a,1),4213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5930 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5937(a,1),291(a,1,2))].">
      <j1 rule="para" parents="5937 291"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,5181,a,b,5926,a),flip(a)].">
      <j1 rule="hyper" parents="35 5181 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,4368,a,b,5927,a(flip))].">
      <j1 rule="hyper" parents="40 4368 5927"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5927(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="5927 5176"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,5938,a(flip),b,4024,a(flip))].">
      <j1 rule="hyper" parents="131 5938 4024"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5941(a,2),4229(a,1))].">
      <j1 rule="para" parents="5941 4229"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5944,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5944 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),5944(a,1,2,2,1))].">
      <j1 rule="para" parents="108 5944"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,T(x,z) \ y)
    ]]></literal>
    <justification jstring="[para(3123(a,1),5944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3123 5944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5950,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 5950 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5950,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 5950 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,5952,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 5952 22"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(249(a,1),5952(a,1,2,2))].">
      <j1 rule="para" parents="249 5952"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5945(a,1),4351(a,1,2))].">
      <j1 rule="para" parents="5945 4351"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(4130(a,1),5948(a,1,2,2,1))].">
      <j1 rule="para" parents="4130 5948"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5953(a,2),4089(a,1))].">
      <j1 rule="para" parents="5953 4089"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      K(x,K(T(y,K(x,z)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5928(a,2),5947(a,1,2))].">
      <j1 rule="para" parents="5928 5947"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(5705(a,1),5959(a,1))].">
      <j1 rule="para" parents="5705 5959"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,5661,a(flip),b,5814,a),flip(a)].">
      <j1 rule="hyper" parents="319 5661 5814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5174,a,b,5822,a),flip(a)].">
      <j1 rule="hyper" parents="319 5174 5822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),5822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),K(x,y)) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(5822(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5822 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4363(a,1),5822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 5822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      T((x \ K(y,x)) \ z,K(x,y)) = ((x \ 1) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4750(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="4750 5822"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(3999(a,1),5870(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3999 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(4041(a,1),5870(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4041 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(4522(a,1),5870(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4522 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K((y * x) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(5897(a,1),4627(a,1,1,1,2))].">
      <j1 rule="para" parents="5897 4627"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5861,a(flip),b,5899,a)].">
      <j1 rule="hyper" parents="64 5861 5899"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),5908(a,2,2))].">
      <j1 rule="para" parents="10 5908"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),5908(a,2,2))].">
      <j1 rule="para" parents="12 5908"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2731(a,1),5908(a,2,2))].">
      <j1 rule="para" parents="2731 5908"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,3375,a(flip),b,5912,a),flip(a)].">
      <j1 rule="hyper" parents="319 3375 5912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5977">
    <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(5912(a,1),1133(a,1,1))].">
      <j1 rule="para" parents="5912 1133"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      R(T(x * K(y,x),y),z,x * K(y,x)) = R(x,z,T(x * K(y,x),u))
    ]]></literal>
    <justification jstring="[para(4130(a,1),5912(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4130 5912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      K(x,R(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5912(a,1),5700(a,1,2))].">
      <j1 rule="para" parents="5912 5700"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4674,a(flip),b,5920,a),flip(a)].">
      <j1 rule="hyper" parents="319 4674 5920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4858,a(flip),b,5920,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4858 5920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x) = K(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),5920(a,2,2))].">
      <j1 rule="para" parents="25 5920"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,2844,a,b,5932,a),flip(a)].">
      <j1 rule="hyper" parents="36 2844 5932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2154,a,b,5932,a),flip(a)].">
      <j1 rule="hyper" parents="36 2154 5932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5933(a,1),5809(a,1,2))].">
      <j1 rule="para" parents="5933 5809"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5933(a,1),5837(a,1,1))].">
      <j1 rule="para" parents="5933 5837"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5933(a,1),5848(a,1,2))].">
      <j1 rule="para" parents="5933 5848"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5933(a,1),5878(a,1,2))].">
      <j1 rule="para" parents="5933 5878"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      T(T(x,y),z * K(u,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5989(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5989 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      T(x,(y / T(x,z)) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5147(a,2),5989(a,1,2))].">
      <j1 rule="para" parents="5147 5989"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5172(a,1),5989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5172 5989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(5241(a,1),5989(a,1,2))].">
      <j1 rule="para" parents="5241 5989"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4214,a,b,5990,a),flip(a)].">
      <j1 rule="hyper" parents="319 4214 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4831(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="4831 5990"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(5144(a,1),5990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5144 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5172(a,1),5990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(5991(a,1),3171(a,1,1))].">
      <j1 rule="para" parents="5991 3171"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      K(x,y / T(z,x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(4918(a,1),5991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4918 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(5144(a,1),5991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5144 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5172(a,1),5991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5172 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(5241(a,1),5991(a,1,2))].">
      <j1 rule="para" parents="5241 5991"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,5997,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 5997 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(5997(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="5997 242"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x * K(y,z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5997(a,1),3273(a,1,2,1))].">
      <j1 rule="para" parents="5997 3273"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4716(a,1),5997(a,1,2,2))].">
      <j1 rule="para" parents="4716 5997"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(5400(a,1),5997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5400 5997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z * K(x,u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5832,a,b,6002,a)].">
      <j1 rule="hyper" parents="319 5832 6002"/>
    </justification>
  </clause>

  <clause id="6015">
    <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(6002(a,1),4630(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6002 4630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[para(6006(a,2),2829(a,1,2))].">
      <j1 rule="para" parents="6006 2829"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4716(a,1),6006(a,1,2,2))].">
      <j1 rule="para" parents="4716 6006"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5427(a,1),6006(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5427 6006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(6006(a,1),4929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6006 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3348,a,5996,a)].">
      <j1 rule="hyper" parents="3348 5996"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5999(a,2),4219(a,1))].">
      <j1 rule="para" parents="5999 4219"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4281,a(flip),b,6001,a),flip(a)].">
      <j1 rule="hyper" parents="319 4281 6001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      K(x,y / T(z / T(u,z),x)) = K(x,y / (T(z,u) / u))
    ]]></literal>
    <justification jstring="[para(3381(a,1),6004(a,1,2,2))].">
      <j1 rule="para" parents="3381 6004"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4394,a(flip),b,6005,a),flip(a)].">
      <j1 rule="hyper" parents="319 4394 6005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6008(a,2),4106(a,1))].">
      <j1 rule="para" parents="6008 4106"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),6022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 6022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(5241(a,1),5992(a,1,2))].">
      <j1 rule="para" parents="5241 5992"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(94(a,1),6000(a,1,1))].">
      <j1 rule="para" parents="94 6000"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(5332(a,1),6000(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5332 6000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5379(a,1),6000(a,1,1,2))].">
      <j1 rule="para" parents="5379 6000"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),6011(a,1,2))].">
      <j1 rule="para" parents="94 6011"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5363(a,1),6011(a,1,2,2))].">
      <j1 rule="para" parents="5363 6011"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),6017(a,1,2))].">
      <j1 rule="para" parents="94 6017"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5332(a,1),6017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5332 6017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1187(a,1),6021(a,1,1))].">
      <j1 rule="para" parents="1187 6021"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      K(K(x,y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5925(a,1),6021(a,1,1))].">
      <j1 rule="para" parents="5925 6021"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      K(x,y / T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5163(a,1),6025(a,1,2))].">
      <j1 rule="para" parents="5163 6025"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(5244(a,1),6025(a,1,2))].">
      <j1 rule="para" parents="5244 6025"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(5400(a,1),6025(a,1,2))].">
      <j1 rule="para" parents="5400 6025"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(305(a,1),6031(a,1,1))].">
      <j1 rule="para" parents="305 6031"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(479(a,1),6033(a,1,2))].">
      <j1 rule="para" parents="479 6033"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(4670(a,1),6037(a,1,1))].">
      <j1 rule="para" parents="4670 6037"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4374,a,5946,a)].">
      <j1 rule="hyper" parents="4374 5946"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(5946(a,1),5181(a,1,1))].">
      <j1 rule="para" parents="5946 5181"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5849,a(flip),b,5951,a),flip(a)].">
      <j1 rule="hyper" parents="319 5849 5951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(6046(a,1),4324(a,2,1))].">
      <j1 rule="para" parents="6046 4324"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[para(4356(a,2),5963(a,1,1))].">
      <j1 rule="para" parents="4356 5963"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5963(a,2),5186(a,1))].">
      <j1 rule="para" parents="5963 5186"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(5185,a,5966,a)].">
      <j1 rule="hyper" parents="5185 5966"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      T(x,K(y,z)) * T(z,y) = (K(z,y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,5966,a(flip),b,5158,a)].">
      <j1 rule="hyper" parents="130 5966 5158"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5899,a(flip),b,5972,a),flip(a)].">
      <j1 rule="hyper" parents="64 5899 5972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(736,a,5983,a),flip(a)].">
      <j1 rule="hyper" parents="736 5983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5983,a(flip),b,4878,a),flip(a)].">
      <j1 rule="hyper" parents="131 5983 4878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(5983(a,1),1321(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5983 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(5983(a,1),5214(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5983 5214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5675,a,b,5998,a)].">
      <j1 rule="hyper" parents="64 5675 5998"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5669,a,b,6007,a)].">
      <j1 rule="hyper" parents="64 5669 6007"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6014(a,1),5833(a,1))].">
      <j1 rule="para" parents="6014 5833"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      K(x,T(K(x,y) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(4363(a,1),6018(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4363 6018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(4918(a,1),6029(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4918 6029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      K(x * (K(y,z) * u),z) = K(x * u,z)
    ]]></literal>
    <justification jstring="[para(5925(a,1),6029(a,1,1,2))].">
      <j1 rule="para" parents="5925 6029"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      K(x,y * (z / T(u,x))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(5163(a,1),6034(a,1,2,2))].">
      <j1 rule="para" parents="5163 6034"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      K(x / y,z * (y * (x / y))) = K(x / y,z * x)
    ]]></literal>
    <justification jstring="[para(306(a,1),6035(a,1,2,2))].">
      <j1 rule="para" parents="306 6035"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      K(x,y * (T(z,x) / u)) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(1191(a,1),6035(a,1,2,2))].">
      <j1 rule="para" parents="1191 6035"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      K(x,K(y,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,4353,a(flip),b,6044,a),flip(a)].">
      <j1 rule="hyper" parents="126 4353 6044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      T(x,K(y,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,6070,a)].">
      <j1 rule="hyper" parents="57 6070"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),6071(a,1,2,2))].">
      <j1 rule="para" parents="12 6071"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6072,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 6072 22"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(244,a,6052,a,b,xx)].">
      <j1 rule="hyper" parents="244 6052"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,4095,a,b,6052,a)].">
      <j1 rule="hyper" parents="36 4095 6052"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2099,a(flip),b,6052,a),flip(a)].">
      <j1 rule="hyper" parents="36 2099 6052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,6052,a(flip),b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="244 6052 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(6074(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="6074 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,6076,a(flip),b,4357,a),flip(a)].">
      <j1 rule="hyper" parents="131 6076 4357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,6075,a),flip(a)].">
      <j1 rule="hyper" parents="35 4019 6075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6075(a,1),4187(a,1,1))].">
      <j1 rule="para" parents="6075 4187"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6075(a,1),4186(a,1))].">
      <j1 rule="para" parents="6075 4186"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(4385,a,6080,a)].">
      <j1 rule="hyper" parents="4385 6080"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6080,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6080 4012"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,6080,a(flip),b,4070,a)].">
      <j1 rule="hyper" parents="130 6080 4070"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6080(a,1),4229(a,1,1))].">
      <j1 rule="para" parents="6080 4229"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(6083(a,1),4229(a,1))].">
      <j1 rule="para" parents="6083 4229"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4921,a,b,6055,a)].">
      <j1 rule="hyper" parents="319 4921 6055"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4913,a(flip),b,6055,a)].">
      <j1 rule="hyper" parents="64 4913 6055"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) = (y \ x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),6055(a,2,1))].">
      <j1 rule="para" parents="111 6055"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6055(a,2),4298(a,1,2))].">
      <j1 rule="para" parents="6055 4298"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(6055(a,2),5846(a,1,2))].">
      <j1 rule="para" parents="6055 5846"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(4568(a,1),6056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4568 6056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(4041(a,1),6066(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4041 6066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(4363(a,1),6066(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 6066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5300,a,b,6073,a)].">
      <j1 rule="hyper" parents="319 5300 6073"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4985,a(flip),b,6077,a),flip(a)].">
      <j1 rule="hyper" parents="319 4985 6077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6045,a(flip),b,6077,a)].">
      <j1 rule="hyper" parents="64 6045 6077"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6077(a,1),5193(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6077 5193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      K(T(x,y),z) \ 1 = T(K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(4385,a,6099,a)].">
      <j1 rule="hyper" parents="4385 6099"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,5928,a,b,6099,a)].">
      <j1 rule="hyper" parents="319 5928 6099"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,5595,a,b,6099,a)].">
      <j1 rule="hyper" parents="319 5595 6099"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(319,a,5587,a,b,6099,a)].">
      <j1 rule="hyper" parents="319 5587 6099"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,5288,a,b,6099,a)].">
      <j1 rule="hyper" parents="319 5288 6099"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4987,a,b,6099,a)].">
      <j1 rule="hyper" parents="319 4987 6099"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4584,a,b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="319 4584 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,4357,a,b,6099,a)].">
      <j1 rule="hyper" parents="319 4357 6099"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4985,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="319 4985 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      K(x * y,T(z,y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3828,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="319 3828 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,2938,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="319 2938 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,6099,a,b,9,a)].">
      <j1 rule="hyper" parents="131 6099 9"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,6099,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="131 6099 22"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5938,a,b,6099,a)].">
      <j1 rule="hyper" parents="64 5938 6099"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5709,a,b,6099,a)].">
      <j1 rule="hyper" parents="64 5709 6099"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5735,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="64 5735 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5699,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="64 5699 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5698,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="64 5698 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4354,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="64 4354 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(206,a,6099,a(flip),b,5938,a)].">
      <j1 rule="hyper" parents="206 6099 5938"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6099,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6099 4012"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      T(T(K(x,y),z),u) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(6099(a,2),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6099 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),6099(a,1,2))].">
      <j1 rule="para" parents="23 6099"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6099(a,2),291(a,1,2))].">
      <j1 rule="para" parents="6099 291"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6099(a,2),229(a,1,2,2))].">
      <j1 rule="para" parents="6099 229"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,w) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(6099(a,2),242(a,1,2,1))].">
      <j1 rule="para" parents="6099 242"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(6099(a,2),646(a,1,2,2))].">
      <j1 rule="para" parents="6099 646"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      L(K(x,T(y,z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      u \ (z * (K(x,y) * (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(6099(a,2),728(a,1,1))].">
      <j1 rule="para" parents="6099 728"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(u / (u / K(x,y)),z) = K(K(x,y) \ u,T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(6099(a,2),4700(a,1,1))].">
      <j1 rule="para" parents="6099 4700"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      x * (K(x,T(y,z)) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6099(a,2),4300(a,1,2,1))].">
      <j1 rule="para" parents="6099 4300"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(6099(a,2),4760(a,2,2))].">
      <j1 rule="para" parents="6099 4760"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6099(a,2),5249(a,1))].">
      <j1 rule="para" parents="6099 5249"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(6099(a,2),5358(a,1,1))].">
      <j1 rule="para" parents="6099 5358"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6099(a,1),5739(a,1))].">
      <j1 rule="para" parents="6099 5739"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6099(a,1),5946(a,1,2))].">
      <j1 rule="para" parents="6099 5946"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      K(T(x,x * y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5749,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="319 5749 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5699,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="319 5699 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3961,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="319 3961 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(131,a,6102,a,b,5934,a)].">
      <j1 rule="hyper" parents="131 6102 5934"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6102,a,b,9,a)].">
      <j1 rule="hyper" parents="131 6102 9"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,6102,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6102 4012"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5176,a,b,6102,a)].">
      <j1 rule="hyper" parents="64 5176 6102"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5007,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="64 5007 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(206,a,6102,a(flip),b,5176,a)].">
      <j1 rule="hyper" parents="206 6102 5176"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(206,a,6102,a(flip),b,4001,a(flip))].">
      <j1 rule="hyper" parents="206 6102 4001"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,6102,a(flip),b,5168,a)].">
      <j1 rule="hyper" parents="131 6102 5168"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      T(x,x * T(y,z)) * K(y,T(x,z)) = L(x,T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(131,a,6102,a(flip),b,4470,a(flip))].">
      <j1 rule="hyper" parents="131 6102 4470"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      T(x,y) * K(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6102,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6102 4012"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,6102,a(flip),b,4364,a),flip(a)].">
      <j1 rule="hyper" parents="130 6102 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,6102,a(flip),b,4009,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 6102 4009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),6102(a,2,2))].">
      <j1 rule="para" parents="23 6102"/>
    </justification>
  </clause>

  <clause id="6154">
    <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),6102(a,1,1))].">
      <j1 rule="para" parents="25 6102"/>
    </justification>
  </clause>

  <clause id="6155">
    <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),6102(a,1,1))].">
      <j1 rule="para" parents="27 6102"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(111(a,1),6102(a,2,2))].">
      <j1 rule="para" parents="111 6102"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(222(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="222 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(187(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="187 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6161">
    <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(1491(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1491 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(6102(a,1),4130(a,1,1,2))].">
      <j1 rule="para" parents="6102 4130"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6102(a,1),4316(a,1,2,1))].">
      <j1 rule="para" parents="6102 4316"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6102(a,1),4384(a,1,1))].">
      <j1 rule="para" parents="6102 4384"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(6102(a,1),4393(a,1,1))].">
      <j1 rule="para" parents="6102 4393"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6102(a,1),4328(a,1,1))].">
      <j1 rule="para" parents="6102 4328"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      R(x,y,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(6102(a,1),5044(a,1,3))].">
      <j1 rule="para" parents="6102 5044"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6102(a,1),5185(a,1,2))].">
      <j1 rule="para" parents="6102 5185"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6102(a,1),5186(a,1,2))].">
      <j1 rule="para" parents="6102 5186"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6102(a,1),5990(a,1,1,2))].">
      <j1 rule="para" parents="6102 5990"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5997(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5997 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(6138(a,1),4481(a,2,1))].">
      <j1 rule="para" parents="6138 4481"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6101(a,1),4229(a,1))].">
      <j1 rule="para" parents="6101 4229"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[para(6108(a,1),74(a,1,2,2))].">
      <j1 rule="para" parents="6108 74"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x / y,z \ x) = K(y \ x,x / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5699,a(flip),b,6109,a)].">
      <j1 rule="hyper" parents="64 5699 6109"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      (T(x,y) * (y / z)) * K(z \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      (y / z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6109(a,1),299(a,1,2))].">
      <j1 rule="para" parents="6109 299"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * T(y / z,T(u,y)) = w
    ]]></literal>
    <justification jstring="[para(6109(a,1),4976(a,1,2))].">
      <j1 rule="para" parents="6109 4976"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y)
    ]]></literal>
    <justification jstring="[para(6109(a,1),5460(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6109 5460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      L(x / y,z,K(y \ x,u)) = x / y
    ]]></literal>
    <justification jstring="[para(6109(a,1),5783(a,1,3))].">
      <j1 rule="para" parents="6109 5783"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(5229,a,6113,a)].">
      <j1 rule="hyper" parents="5229 6113"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,4314,a(flip),b,6113,a),flip(a)].">
      <j1 rule="hyper" parents="319 4314 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      (K(x,y) * z) / T(y,z) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,6113,a(flip),b,5147,a)].">
      <j1 rule="hyper" parents="128 6113 5147"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),6113(a,1,2,2))].">
      <j1 rule="para" parents="23 6113"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) = K(y,L(z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),6113(a,1,2,2))].">
      <j1 rule="para" parents="25 6113"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6113(a,1),44(a,1))].">
      <j1 rule="para" parents="6113 44"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),6113(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2931(a,1),6113(a,1,2,2))].">
      <j1 rule="para" parents="2931 6113"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      T(x,y) * K(z,T(x * y,x)) = K(z,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3122(a,1),6113(a,1,2,2))].">
      <j1 rule="para" parents="3122 6113"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(5698(a,1),6113(a,1,2))].">
      <j1 rule="para" parents="5698 6113"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ x) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(5934(a,2),6113(a,1,2))].">
      <j1 rule="para" parents="5934 6113"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(6113(a,1),6032(a,1,2,2))].">
      <j1 rule="para" parents="6113 6032"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(6099(a,2),6113(a,1,2,2))].">
      <j1 rule="para" parents="6099 6113"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(y,z),u) \ 1) = (x * T(K(y,z),u)) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,6114,a(flip),b,411,a),flip(a)].">
      <j1 rule="hyper" parents="131 6114 411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3274(a,2),6115(a,1,2))].">
      <j1 rule="para" parents="3274 6115"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,5084,a,b,6117,a),flip(a)].">
      <j1 rule="hyper" parents="319 5084 6117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6117(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="6117 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      K(x,y \ z) * T(x,z) = T(T(x,z),z / y)
    ]]></literal>
    <justification jstring="[para(6117(a,1),5936(a,1,1))].">
      <j1 rule="para" parents="6117 5936"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6116,a,b,6118,a)].">
      <j1 rule="hyper" parents="319 6116 6118"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4587,a,b,6120,a)].">
      <j1 rule="hyper" parents="319 4587 6120"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4588,a,6121,a),flip(a)].">
      <j1 rule="hyper" parents="4588 6121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(6121(a,1),4588(a,1))].">
      <j1 rule="para" parents="6121 4588"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(222(a,1),6139(a,1,1))].">
      <j1 rule="para" parents="222 6139"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      T(T(x / y,z),u * K(w,y \ x)) = T(T(x / y,u),z)
    ]]></literal>
    <justification jstring="[para(6139(a,1),5993(a,1,2,2))].">
      <j1 rule="para" parents="6139 5993"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4325,a,b,6143,a)].">
      <j1 rule="hyper" parents="64 4325 6143"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6099,a,b,6145,a),flip(a)].">
      <j1 rule="hyper" parents="319 6099 6145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4651,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="64 4651 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(130,a,6156,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 6156 4011"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6156(a,1),4063(a,1,1))].">
      <j1 rule="para" parents="6156 4063"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      (x / y) * (K(y \ x,z) * u) = T(x / y,T(z,y)) * u
    ]]></literal>
    <justification jstring="[para(6156(a,1),4036(a,1,2,1))].">
      <j1 rule="para" parents="6156 4036"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6156(a,2),4345(a,1))].">
      <j1 rule="para" parents="6156 4345"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4495,a(flip),b,6157,a)].">
      <j1 rule="hyper" parents="64 4495 6157"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(222(a,1),6157(a,1,1))].">
      <j1 rule="para" parents="222 6157"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y / z,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6157(a,1),5169(a,1,2))].">
      <j1 rule="para" parents="6157 5169"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(6157(a,1),5927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 5927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,6158,a(flip),b,4484,a)].">
      <j1 rule="hyper" parents="130 6158 4484"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(6158(a,1),3151(a,1,3))].">
      <j1 rule="para" parents="6158 3151"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(6158(a,1),4967(a,1,3))].">
      <j1 rule="para" parents="6158 4967"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      R(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(6158(a,1),5044(a,1,3))].">
      <j1 rule="para" parents="6158 5044"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(6158(a,1),5837(a,1,1,1))].">
      <j1 rule="para" parents="6158 5837"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      L(x,T(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(4221,a,6223,a)].">
      <j1 rule="hyper" parents="4221 6223"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,6224,a)].">
      <j1 rule="hyper" parents="53 6224"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = x / (T(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5188,a(flip),b,6225,a),flip(a)].">
      <j1 rule="hyper" parents="64 5188 6225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(130,a,6225,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 6225 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      (1 / T(x,y)) \ K(z,x) = T(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(6225(a,1),381(a,1,1))].">
      <j1 rule="para" parents="6225 381"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4579,a,b,6229,a)].">
      <j1 rule="hyper" parents="64 4579 6229"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(4636(a,1),6170(a,1,1))].">
      <j1 rule="para" parents="4636 6170"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6211(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      K(x,R(T(y,x \ z),u,w)) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(27(a,2),6211(a,1,2))].">
      <j1 rule="para" parents="27 6211"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5057(a,1),6211(a,1,2))].">
      <j1 rule="para" parents="5057 6211"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(6211(a,1),5453(a,1,1))].">
      <j1 rule="para" parents="6211 5453"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a,b,6236,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 6236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      (x * y) * K(x,T(z,y)) = K(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6236(a,1),6113(a,1,2))].">
      <j1 rule="para" parents="6236 6113"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5057(a,2),6135(a,1))].">
      <j1 rule="para" parents="5057 6135"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = u
    ]]></literal>
    <justification jstring="[para(4584(a,2),6173(a,1))].">
      <j1 rule="para" parents="4584 6173"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5928(a,2),6173(a,1))].">
      <j1 rule="para" parents="5928 6173"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6145(a,2),6173(a,1))].">
      <j1 rule="para" parents="6145 6173"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      (K(x \ y,z) * u) * (y / x) = K(x \ y,z) * (u * (y / x))
    ]]></literal>
    <justification jstring="[hyper(131,a,6182,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 6182 18"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6240(a,2),6244(a,1))].">
      <j1 rule="para" parents="6240 6244"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      x \ K(y,z) != K(y,z) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(6079(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6079 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6084(a,1),4375(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6084 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4921,a,b,6089,a)].">
      <j1 rule="hyper" parents="319 4921 6089"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      T(x,y) * L(K(y,z),y,u) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(4948(a,2),6089(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4948 6089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      T(x \ (y * T(x,z)),x) = x \ (T(y,x) * T(x,z))
    ]]></literal>
    <justification jstring="[para(6089(a,2),4913(a,1,1))].">
      <j1 rule="para" parents="6089 4913"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = L(x,y,z) / L(x * K(u * v5,x),y,z)
    ]]></literal>
    <justification jstring="[para(6096(a,1),4626(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6096 4626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6255">
    <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(6096(a,1),4628(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6096 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(5254,a,6107,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5254 6107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(111(a,1),6107(a,2,2,1))].">
      <j1 rule="para" parents="111 6107"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(6107(a,2),5254(a,1))].">
      <j1 rule="para" parents="6107 5254"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      T(T(K(x,y),z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(6122(a,2),6173(a,1))].">
      <j1 rule="para" parents="6122 6173"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5262,a,b,6136,a)].">
      <j1 rule="hyper" parents="64 5262 6136"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6144(a,1),5187(a,1))].">
      <j1 rule="para" parents="6144 5187"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6099(a,1),6261(a,1))].">
      <j1 rule="para" parents="6099 6261"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      K(T(x,x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(5007(a,2),6262(a,1))].">
      <j1 rule="para" parents="5007 6262"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4311,a,b,6150,a)].">
      <j1 rule="hyper" parents="64 4311 6150"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,6150,a(flip),b,4311,a)].">
      <j1 rule="hyper" parents="127 6150 4311"/>
    </justification>
  </clause>

  <clause id="6266">
    <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(6152(a,1),1829(a,1,2))].">
      <j1 rule="para" parents="6152 1829"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a(flip),b,6171,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 6171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      a((x \ y) * K((y / x) \ y,y / x),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(6175(a,1),4503(a,1,1,2))].">
      <j1 rule="para" parents="6175 4503"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4438,a,b,6190,a)].">
      <j1 rule="hyper" parents="64 4438 6190"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,6190,a(flip),b,4438,a)].">
      <j1 rule="hyper" parents="206 6190 4438"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,4438,a,b,6190,a(flip))].">
      <j1 rule="hyper" parents="127 4438 6190"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(x * (1 / y)) \ x) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(5132(a,1),6190(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5132 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      (K(y,x) * z) \ z = u
    ]]></literal>
    <justification jstring="[para(6194(a,1),44(a,1))].">
      <j1 rule="para" parents="6194 44"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6200(a,2),5253(a,1))].">
      <j1 rule="para" parents="6200 5253"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(6203(a,2),4226(a,1,1))].">
      <j1 rule="para" parents="6203 4226"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(23(a,1),6210(a,1,2))].">
      <j1 rule="para" parents="23 6210"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(521(a,1),6212(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="521 6212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1066(a,1),6212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1066 6212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6244,a,6217,a)].">
      <j1 rule="hyper" parents="6244 6217"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(6217(a,1),6244(a,1))].">
      <j1 rule="para" parents="6217 6244"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(244,a,6222,a,b,4922,a)].">
      <j1 rule="hyper" parents="244 6222 4922"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      x \ (T(y,z) * T(x,y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,4294,a(flip),b,6222,a(flip))].">
      <j1 rule="hyper" parents="127 4294 6222"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      L((x * y) \ z,x * y,K(y,u)) = (x * T(y,T(u,x))) \ (K(y,u) * z)
    ]]></literal>
    <justification jstring="[para(6222(a,1),96(a,2,1))].">
      <j1 rule="para" parents="6222 96"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6173,a,6284,a)].">
      <j1 rule="hyper" parents="6173 6284"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,5645,a,b,6287,a)].">
      <j1 rule="hyper" parents="319 5645 6287"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6287(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      K(a(x,y,z),T(u,(x * y) * z)) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(85(a,1),6287(a,1,2,2))].">
      <j1 rule="para" parents="85 6287"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6289,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6289 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(3421(a,1),6289(a,1,2))].">
      <j1 rule="para" parents="3421 6289"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      T(x,T(y,y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),6291(a,2,2))].">
      <j1 rule="para" parents="108 6291"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(78(a,1),6291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 6291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      T(x,T(y,x \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3116(a,1),6293(a,1,2))].">
      <j1 rule="para" parents="3116 6293"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(4359(a,1),6293(a,1,2,2))].">
      <j1 rule="para" parents="4359 6293"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      T(x,T(x * y,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),6295(a,1,2,2))].">
      <j1 rule="para" parents="9 6295"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      (K(x,y) * z) * K(z,T(y,u)) = T(K(x,y) * z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,6226,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6226 4012"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(4041(a,1),6226(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4041 6226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),T(y,T(x,w))) = R(x,T(y,T(x,w)),R(x,z,u))
    ]]></literal>
    <justification jstring="[para(6235(a,1),4400(a,1,1,2))].">
      <j1 rule="para" parents="6235 4400"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(6099(a,2),6264(a,1,2,2))].">
      <j1 rule="para" parents="6099 6264"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4004(a,1),6267(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4004 6267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(5047(a,1),6267(a,1,2,2))].">
      <j1 rule="para" parents="5047 6267"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5705(a,1),6303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5705 6303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,5166,a,b,6270,a)].">
      <j1 rule="hyper" parents="319 5166 6270"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(6270(a,2),5171(a,1,1))].">
      <j1 rule="para" parents="6270 5171"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6271(a,1,2,2,2))].">
      <j1 rule="para" parents="9 6271"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),(x * K(y,x \ z)) \ z) = T(T(x * K(y,x \ z),u),T(z / x,y))
    ]]></literal>
    <justification jstring="[para(6271(a,1),3365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6271 3365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(5083(a,1),6271(a,1,2,2))].">
      <j1 rule="para" parents="5083 6271"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      x / (T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(5132(a,1),6271(a,2,1))].">
      <j1 rule="para" parents="5132 6271"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      (x * y) \ (T(R(z * K(x,z),x,y),u) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(4189(a,2),6272(a,1,2,1,1))].">
      <j1 rule="para" parents="4189 6272"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      T(x,y) \ T(y,T(z,x)) = x \ T(T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(127,a,6279,a(flip),b,4037,a)].">
      <j1 rule="hyper" parents="127 6279 4037"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6282,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6282 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6256,a(flip),b,6282,a)].">
      <j1 rule="hyper" parents="64 6256 6282"/>
    </justification>
  </clause>

  <clause id="6318">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6107,a(flip),b,6282,a)].">
      <j1 rule="hyper" parents="64 6107 6282"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(81(a,1),6282(a,2,2,2))].">
      <j1 rule="para" parents="81 6282"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4913,a,b,6285,a)].">
      <j1 rule="hyper" parents="64 4913 6285"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(6294(a,1),6303(a,1,2))].">
      <j1 rule="para" parents="6294 6303"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y \ x)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(6305(a,1),6113(a,1,2))].">
      <j1 rule="para" parents="6305 6113"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(78(a,1),6306(a,2,1,1))].">
      <j1 rule="para" parents="78 6306"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),6306(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 6306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(78(a,1),6307(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 6307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(3265(a,1),6307(a,1,1,1))].">
      <j1 rule="para" parents="3265 6307"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(6307(a,1),5736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6307 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6205,a(flip),b,6316,a)].">
      <j1 rule="hyper" parents="64 6205 6316"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(81(a,1),6316(a,2,2,2))].">
      <j1 rule="para" parents="81 6316"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6317,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6317 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4024(a,1),6318(a,1,2))].">
      <j1 rule="para" parents="4024 6318"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(110(a,2),6323(a,1,2,1))].">
      <j1 rule="para" parents="110 6323"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      x / (x / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / (x / y),z) = u
    ]]></literal>
    <justification jstring="[para(6324(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6324 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,315,a,b,6325,a)].">
      <j1 rule="hyper" parents="64 315 6325"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(6325(a,2),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6325 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      T(T(x,x \ y),z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(110(a,2),6325(a,1,1))].">
      <j1 rule="para" parents="110 6325"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      T(T(x,y),x \ y) = (x \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[para(3270(a,1),6337(a,2,1))].">
      <j1 rule="para" parents="3270 6337"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(6337(a,2),5738(a,1,2))].">
      <j1 rule="para" parents="6337 5738"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) * (x \ y)) / T(x,y)) = ((x \ T(y,x)) \ y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(6342(a,1),3103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6342 3103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ y)) = u
    ]]></literal>
    <justification jstring="[para(3217(a,1),5741(a,1,2))].">
      <j1 rule="para" parents="3217 5741"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,z)) = u
    ]]></literal>
    <justification jstring="[para(3220(a,1),5741(a,1,2))].">
      <j1 rule="para" parents="3220 5741"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ u,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5166(a,1),5742(a,1,2,1))].">
      <j1 rule="para" parents="5166 5742"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),6036(a,1,1,2))].">
      <j1 rule="para" parents="22 6036"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4213(a,1),6086(a,1))].">
      <j1 rule="para" parents="4213 6086"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      K(R(x / y,z,u) / w,y \ x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w \ R(x / y,z,u),y \ x) = v5
    ]]></literal>
    <justification jstring="[para(4349(a,1),6133(a,1,2))].">
      <j1 rule="para" parents="4349 6133"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),6216(a,1,1,1))].">
      <j1 rule="para" parents="10 6216"/>
    </justification>
  </clause>

  <clause id="6353">
    <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(2940(a,1),6277(a,1))].">
      <j1 rule="para" parents="2940 6277"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6099(a,2),6277(a,1))].">
      <j1 rule="para" parents="6099 6277"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(187(a,1),6352(a,1,2))].">
      <j1 rule="para" parents="187 6352"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = w
    ]]></literal>
    <justification jstring="[para(3797(a,1),6352(a,1,1))].">
      <j1 rule="para" parents="3797 6352"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      K(x / (y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,y) = u
    ]]></literal>
    <justification jstring="[para(5709(a,1),6352(a,1))].">
      <j1 rule="para" parents="5709 6352"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(5163(a,1),5625(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5163 5625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(5630(a,1),4923(a,1,2))].">
      <j1 rule="para" parents="5630 4923"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      T((((x * y) \ x) * (z * K((x * y) \ x,u))) / T((x * y) \ x,u),(((x * y) \ x) * z) / L(y \ 1,y,x)) = (((x * y) \ x) * z) / L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(429,a,5631,a,b,373,a)].">
      <j1 rule="hyper" parents="429 5631 373"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(L(x,y,z),w))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),5631(a,1,2))].">
      <j1 rule="para" parents="25 5631"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(R(x,y,z),w))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),5631(a,1,2))].">
      <j1 rule="para" parents="27 5631"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      (R(x \ y,z,x \ y) / (x \ y)) * (y / x) = R((x \ y) * K(x,x \ y),z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5043,a,b,5708,a)].">
      <j1 rule="hyper" parents="319 5043 5708"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = K(y,x) * R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,2835,a(flip),b,5708,a),flip(a)].">
      <j1 rule="hyper" parents="319 2835 5708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6366">
    <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(4730(a,1),5708(a,2,2))].">
      <j1 rule="para" parents="4730 5708"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4825,a,b,5762,a)].">
      <j1 rule="hyper" parents="64 4825 5762"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6072(a,2),5762(a,1,1))].">
      <j1 rule="para" parents="6072 5762"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      (T(x,y) \ y) * x != z * K(x \ y,x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5859(a,1),140(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="5859 140"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(5896(a,1),5608(a,2,1))].">
      <j1 rule="para" parents="5896 5608"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5357,a(flip),b,5898,a)].">
      <j1 rule="hyper" parents="64 5357 5898"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      (x / R(y,z,y)) * y != y * u
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(5902(a,2),44(a,1))].">
      <j1 rule="para" parents="5902 44"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5283(a,1),5911(a,1,2))].">
      <j1 rule="para" parents="5283 5911"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(244,a,5921,a,b,1013,a)].">
      <j1 rule="hyper" parents="244 5921 1013"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,3812,a(flip),b,5922,a),flip(a)].">
      <j1 rule="hyper" parents="127 3812 5922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      K(x,y) \ ((x \ z) * x) = (T(x,y) \ z) * x
    ]]></literal>
    <justification jstring="[hyper(127,a,5922,a(flip),b,4294,a)].">
      <j1 rule="hyper" parents="127 5922 4294"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      K(x,y) \ ((y * z) / y) = (T(y,x) * z) / y
    ]]></literal>
    <justification jstring="[hyper(4393,a,5923,a)].">
      <j1 rule="hyper" parents="4393 5923"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      K(x,y) * (z * K(x,z)) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,4150,a(flip),b,5923,a)].">
      <j1 rule="hyper" parents="64 4150 5923"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      (x \ T(y,x)) \ (x \ (y * T(x,T(y,z)))) = T(T(x,T(y,z)),x \ T(y,x))
    ]]></literal>
    <justification jstring="[para(5954(a,1),1029(a,1,2,2))].">
      <j1 rule="para" parents="5954 1029"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      T(T(T(x,y) / (T(x,y) / y),x),z) = L(T(y,z),y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5956(a,1),3395(a,1,1))].">
      <j1 rule="para" parents="5956 3395"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / (z \ 1)) * u) = K(x,(y * ((T(y,x) / (z \ 1)) / T(y,x))) * u)
    ]]></literal>
    <justification jstring="[para(3056(a,2),5969(a,1,2,1))].">
      <j1 rule="para" parents="3056 5969"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      K(x,(y \ (z / x)) * u) = K(x,(y \ (x \ z)) * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),5970(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="111 5970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(244,a,6053,a,b,5784,a(flip))].">
      <j1 rule="hyper" parents="244 6053 5784"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(410,a,6385,a)].">
      <j1 rule="hyper" parents="410 6385"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2096(a,1),6385(a,1,1))].">
      <j1 rule="para" parents="2096 6385"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(5175(a,1),6385(a,1,1))].">
      <j1 rule="para" parents="5175 6385"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(5822(a,1),6385(a,1,1))].">
      <j1 rule="para" parents="5822 6385"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6074(a,1),6385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6074 6385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6078,a,6386,a)].">
      <j1 rule="hyper" parents="6078 6386"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(6386(a,1),5930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6386 5930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6386(a,1),6081(a,1,1))].">
      <j1 rule="para" parents="6386 6081"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5713,a(flip),b,6388,a)].">
      <j1 rule="hyper" parents="64 5713 6388"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(695,a,6391,a),flip(a)].">
      <j1 rule="hyper" parents="695 6391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5940,a,b,6391,a)].">
      <j1 rule="hyper" parents="64 5940 6391"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      T(x,K(y,z)) * y = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6391,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 6391 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,K(y,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6391(a,1),149(a,1))].">
      <j1 rule="para" parents="6391 149"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(6391(a,1),114(a,2,1))].">
      <j1 rule="para" parents="6391 114"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6391(a,1),695(a,1))].">
      <j1 rule="para" parents="6391 695"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      T(T(x,y / z),K(y / z,T(z,y))) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3123(a,1),6392(a,2,2))].">
      <j1 rule="para" parents="3123 6392"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(6329(a,1),6393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 6393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4519,a,b,6397,a)].">
      <j1 rule="hyper" parents="64 4519 6397"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4311,a(flip),b,6397,a)].">
      <j1 rule="hyper" parents="64 4311 6397"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,5125,a,b,6398,a)].">
      <j1 rule="hyper" parents="128 5125 6398"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6406,a(flip),b,3797,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 6406 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6408">
    <literal><![CDATA[
      T(x \ y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6406(a,1),3833(a,1))].">
      <j1 rule="para" parents="6406 3833"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      T(x * T(y,K(x,z)),x) = T(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6407(a,1),6391(a,1,1))].">
      <j1 rule="para" parents="6407 6391"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(3225(a,1),6065(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3225 6065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      K(x \ y,z * (x / ((x \ y) * x))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(3356(a,1),6069(a,1,2,2))].">
      <j1 rule="para" parents="3356 6069"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      (T(x * y,y) / y) * T(y,z) = T(x * T(y,z),y)
    ]]></literal>
    <justification jstring="[para(4922(a,1),6088(a,2,1))].">
      <j1 rule="para" parents="4922 6088"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) != u * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      y \ x = u
    ]]></literal>
    <justification jstring="[para(6090(a,2),45(a,1))].">
      <j1 rule="para" parents="6090 45"/>
    </justification>
  </clause>

  <clause id="6414">
    <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(187(a,1),6155(a,2,2))].">
      <j1 rule="para" parents="187 6155"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[para(5709(a,1),6185(a,1,2))].">
      <j1 rule="para" parents="5709 6185"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(6185(a,1),6034(a,1,2,2))].">
      <j1 rule="para" parents="6185 6034"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      K(x,T(y,T(z,x) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6185(a,1),6267(a,1,2,2))].">
      <j1 rule="para" parents="6185 6267"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      (T(x,y) \ z) * K(T(x,z),y) = x \ z
    ]]></literal>
    <justification jstring="[hyper(5185,a,6415,a)].">
      <j1 rule="hyper" parents="5185 6415"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,6415,a)].">
      <j1 rule="hyper" parents="134 6415"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      T(x / T(T(y,x),z),y) = y \ (K(z,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(6186(a,1),5157(a,1,1))].">
      <j1 rule="para" parents="6186 5157"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,4348,a(flip),b,6193,a),flip(a)].">
      <j1 rule="hyper" parents="319 4348 6193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z \ x) * (x / y) = T(T(T(x,y \ x) / y,x),x / z)
    ]]></literal>
    <justification jstring="[para(3119(a,1),6202(a,1,2))].">
      <j1 rule="para" parents="3119 6202"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(4227,a,6204,a)].">
      <j1 rule="hyper" parents="4227 6204"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2921,a,b,6423,a)].">
      <j1 rule="hyper" parents="64 2921 6423"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5015,a(flip),b,6423,a)].">
      <j1 rule="hyper" parents="64 5015 6423"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(78(a,1),6424(a,1,1,1,1))].">
      <j1 rule="para" parents="78 6424"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6424(a,1),4827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6424 4827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(5017(a,1),6426(a,2,1))].">
      <j1 rule="para" parents="5017 6426"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6426(a,2),6173(a,1))].">
      <j1 rule="para" parents="6426 6173"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(5281(a,1),6213(a,1,1))].">
      <j1 rule="para" parents="5281 6213"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) \ ((T(x,y) \ 1) \ K(z,x)) = T(x,y) \ (T(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[para(6232(a,1),2559(a,2,2))].">
      <j1 rule="para" parents="6232 2559"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5910,a(flip),b,6238,a),flip(a)].">
      <j1 rule="hyper" parents="64 5910 6238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6434">
    <literal><![CDATA[
      (x * y) * K(x,T(z,y)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,4081,a(flip),b,6241,a),flip(a)].">
      <j1 rule="hyper" parents="319 4081 6241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,4081,a(flip),b,6241,a)].">
      <j1 rule="hyper" parents="127 4081 6241"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6434(a,1),330(a,1,2))].">
      <j1 rule="para" parents="6434 330"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      x \ ((y / x) * T(x,z)) = ((x \ y) / x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),6251(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 6251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6257(a,2),5253(a,1))].">
      <j1 rule="para" parents="6257 5253"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(6257(a,1),6113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6257 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,4140,a(flip),b,6308,a),flip(a)].">
      <j1 rule="hyper" parents="319 4140 6308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(111(a,1),6321(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 6321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      K(x,T(T(y / z,y),u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),6327(a,1,2))].">
      <j1 rule="para" parents="23 6327"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      K(x,T(y / z,u)) * y = y * K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(6327(a,1),6113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6327 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(9(a,1),6343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3905,a(flip),b,6373,a),flip(a)].">
      <j1 rule="hyper" parents="64 3905 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K(x,y) \ ((x \ z) * x) = (x \ (K(x,y) \ z)) * x
    ]]></literal>
    <justification jstring="[para(4304(a,2),6378(a,2,1))].">
      <j1 rule="para" parents="4304 6378"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      K(x,T(y,z)) \ ((R(z,u,w) * T(y,z)) / T(y,z)) = (T(T(y,z),x) * R(T(z,y),u,w)) / T(y,z)
    ]]></literal>
    <justification jstring="[para(3277(a,1),6379(a,1,2,1))].">
      <j1 rule="para" parents="3277 6379"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(4710,a,6380,a)].">
      <j1 rule="hyper" parents="4710 6380"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(6390(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6390 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      K(T(x * y,T(x,z)) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(6409(a,1),4472(a,1,1,1))].">
      <j1 rule="para" parents="6409 4472"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      K(x,R(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[para(925(a,1),6445(a,1,2))].">
      <j1 rule="para" parents="925 6445"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(5655(a,1),5384(a,1))].">
      <j1 rule="para" parents="5655 5384"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K(x,(K(y,z / x) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ z,y) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(4355(a,2),5731(a,1,2,1))].">
      <j1 rule="para" parents="4355 5731"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(5219(a,2),5731(a,1))].">
      <j1 rule="para" parents="5219 5731"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5363,a(flip),b,5839,a)].">
      <j1 rule="hyper" parents="64 5363 5839"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5832,a(flip),b,6460,a),flip(a)].">
      <j1 rule="hyper" parents="319 5832 6460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(302(a,1),6461(a,1,1))].">
      <j1 rule="para" parents="302 6461"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,(y \ ((1 / z) \ y)) \ (x \ ((1 / z) \ y)))
    ]]></literal>
    <justification jstring="[para(3227(a,1),5917(a,2,2,2,2))].">
      <j1 rule="para" parents="3227 5917"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,y \ (x \ ((y * L(y \ z,u,w)) * x)))
    ]]></literal>
    <justification jstring="[para(1558(a,1),5918(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1558 5918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6003(a,1),366(a,1)),flip(b)].">
      <j1 rule="para" parents="6003 366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(1187(a,1),6466(a,1,2))].">
      <j1 rule="para" parents="1187 6466"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4636(a,1),6466(a,1,2))].">
      <j1 rule="para" parents="4636 6466"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(5241(a,1),6466(a,1,2))].">
      <j1 rule="para" parents="5241 6466"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5927(a,1),6466(a,1,2))].">
      <j1 rule="para" parents="5927 6466"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),6467(a,1,2,2))].">
      <j1 rule="para" parents="22 6467"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4363(a,1),6051(a,1,1))].">
      <j1 rule="para" parents="4363 6051"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(4356(a,1),6164(a,1))].">
      <j1 rule="para" parents="4356 6164"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5174(a,1),6169(a,1))].">
      <j1 rule="para" parents="5174 6169"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = x * (L(x,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6172,a(flip),b,4308,a)].">
      <j1 rule="hyper" parents="131 6172 4308"/>
    </justification>
  </clause>

  <clause id="6477">
    <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(6118(a,1),6250(a,1,2))].">
      <j1 rule="para" parents="6118 6250"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      x / T((y \ x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T((y \ x) * y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(4260(a,1),6339(a,1,2,1))].">
      <j1 rule="para" parents="4260 6339"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5897(a,2),6349(a,1))].">
      <j1 rule="para" parents="5897 6349"/>
    </justification>
  </clause>

  <clause id="6481">
    <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(5655(a,2),6455(a,1))].">
      <j1 rule="para" parents="5655 6455"/>
    </justification>
  </clause>

  <clause id="6482">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(5669(a,2),6469(a,1))].">
      <j1 rule="para" parents="5669 6469"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(5928(a,1),6473(a,1,1))].">
      <j1 rule="para" parents="5928 6473"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5928(a,1),6474(a,1,2))].">
      <j1 rule="para" parents="5928 6474"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(6054(a,1),6479(a,1))].">
      <j1 rule="para" parents="6054 6479"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      K((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(5343(a,1),6485(a,1))].">
      <j1 rule="para" parents="5343 6485"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      K(x / ((y * z) * x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (y \ 1),y) = u
    ]]></literal>
    <justification jstring="[para(4649(a,2),6486(a,1))].">
      <j1 rule="para" parents="4649 6486"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(244,a,5637,a,b,4081,a)].">
      <j1 rule="hyper" parents="244 5637 4081"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      (T(x,y) \ 1) \ y = x * (((x \ 1) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4752,a(flip),b,5746,a)].">
      <j1 rule="hyper" parents="64 4752 5746"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(439(a,1),5753(a,1,1)),flip(a)].">
      <j1 rule="para" parents="439 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(5758(a,1),330(a,1,2))].">
      <j1 rule="para" parents="5758 330"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,5767,a)].">
      <j1 rule="hyper" parents="529 5767"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6494(a,1),27(a,2,1))].">
      <j1 rule="para" parents="6494 27"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4800,a(flip),b,6496,a),flip(a)].">
      <j1 rule="hyper" parents="64 4800 6496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,6497,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 6497 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5926(a,1),6497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 6497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6113(a,1),6497(a,1,2))].">
      <j1 rule="para" parents="6113 6497"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3886(a,2),6501(a,1,2,1))].">
      <j1 rule="para" parents="3886 6501"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      T(x \ 1,K(x,y) * z) = T(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(2920(a,1),6502(a,1,2,1))].">
      <j1 rule="para" parents="2920 6502"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,6504,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 6504 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,6500,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 6500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5172(a,1),6508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5172 6508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      K(x,K(x \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6113(a,1),6508(a,1,2))].">
      <j1 rule="para" parents="6113 6508"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      K(x,T(y,x \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6185(a,1),6508(a,1,2))].">
      <j1 rule="para" parents="6185 6508"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5084(a,1),6509(a,1,2,2))].">
      <j1 rule="para" parents="5084 6509"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(3999(a,1),6506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3999 6506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,6507,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 6507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),6515(a,1,1,1,2))].">
      <j1 rule="para" parents="78 6515"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3886(a,1),6515(a,1,1,1))].">
      <j1 rule="para" parents="3886 6515"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(3999(a,1),6515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3999 6515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(4757(a,1),6515(a,1,1))].">
      <j1 rule="para" parents="4757 6515"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(x,y \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6517,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6517 4012"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(4413(a,1),6517(a,1,1,1))].">
      <j1 rule="para" parents="4413 6517"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4644(a,1),6517(a,1,1))].">
      <j1 rule="para" parents="4644 6517"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5933(a,1),6517(a,1,1))].">
      <j1 rule="para" parents="5933 6517"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      K(x * K(y \ 1,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5172(a,1),6524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 6524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      K(x * K(y \ z,u),z \ y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4996(a,1),6525(a,1,1,2))].">
      <j1 rule="para" parents="4996 6525"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * T(y,x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(6511(a,1),5276(a,1,1))].">
      <j1 rule="para" parents="6511 5276"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,3556,a(flip),b,6513,a),flip(a)].">
      <j1 rule="hyper" parents="319 3556 6513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      x * T(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6513,a,b,4025,a)].">
      <j1 rule="hyper" parents="131 6513 4025"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      T((x / y) \ 1,y * (x / y)) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),6513(a,2,2))].">
      <j1 rule="para" parents="12 6513"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T((x \ 1) * L((x \ 1) \ 1,z,u),y * x)
    ]]></literal>
    <justification jstring="[para(6513(a,1),1999(a,1,2,1,1))].">
      <j1 rule="para" parents="6513 1999"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,z,u),x * y) = w
    ]]></literal>
    <justification jstring="[para(6513(a,2),2004(a,1,1))].">
      <j1 rule="para" parents="6513 2004"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3999(a,1),6516(a,1,1))].">
      <j1 rule="para" parents="3999 6516"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3880,a(flip),b,6518,a),flip(a)].">
      <j1 rule="hyper" parents="319 3880 6518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5685,a(flip),b,6518,a),flip(a)].">
      <j1 rule="hyper" parents="64 5685 6518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4167,a,b,6535,a),flip(a)].">
      <j1 rule="hyper" parents="319 4167 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5862,a(flip),b,6535,a)].">
      <j1 rule="hyper" parents="64 5862 6535"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(130,a,6535,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 6535 4011"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),6535(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(6535(a,1),4807(a,2,2))].">
      <j1 rule="para" parents="6535 4807"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3880,a(flip),b,6536,a),flip(a)].">
      <j1 rule="hyper" parents="64 3880 6536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2749(a,1),6519(a,2,1))].">
      <j1 rule="para" parents="2749 6519"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),6528(a,1,2))].">
      <j1 rule="para" parents="10 6528"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(88(a,1),6512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="88 6512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(5047(a,1),6512(a,1,2))].">
      <j1 rule="para" parents="5047 6512"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(4670(a,1),6522(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4670 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(5178(a,1),6526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5178 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(4253,a,6529,a)].">
      <j1 rule="hyper" parents="4253 6529"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6548(a,2),4654(a,2,2))].">
      <j1 rule="para" parents="6548 4654"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5095,a(flip),b,6539,a),flip(a)].">
      <j1 rule="hyper" parents="319 5095 6539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(6541(a,1),4237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6541 4237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      L(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,5771,a)].">
      <j1 rule="hyper" parents="488 5771"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2920(a,1),6552(a,1,3))].">
      <j1 rule="para" parents="2920 6552"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(131,a,6556,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 6556 18"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(6556(a,1),865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6556 865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,5176,a,b,5774,a),flip(a)].">
      <j1 rule="hyper" parents="40 5176 5774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),5774(a,1,1,1,1,2))].">
      <j1 rule="para" parents="11 5774"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3837,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="64 3837 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,5776,a(flip),b,3837,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5776 3837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(6564(a,1),5616(a,2,2))].">
      <j1 rule="para" parents="6564 5616"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(131,a,5778,a(flip),b,4312,a)].">
      <j1 rule="hyper" parents="131 5778 4312"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      T((K(x,y) * K(y,z)) \ (K(x,y) * (u * K(y,z))),K(x,y)) = R(T(u,K(x,y) * K(y,z)),K(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(5823(a,1),1003(a,1,1,2))].">
      <j1 rule="para" parents="5823 1003"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(27(a,2),5880(a,1,2,1))].">
      <j1 rule="para" parents="27 5880"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(488,a,5892,a)].">
      <j1 rule="hyper" parents="488 5892"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(5398,a,6569,a),flip(a)].">
      <j1 rule="hyper" parents="5398 6569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      K(x,L(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5379,a(flip),b,6569,a)].">
      <j1 rule="hyper" parents="64 5379 6569"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5374,a(flip),b,6569,a),flip(a)].">
      <j1 rule="hyper" parents="64 5374 6569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      K(x,L(y \ z,u,z / y)) = K(x,T(z / y,T(y,z)))
    ]]></literal>
    <justification jstring="[para(3123(a,1),6571(a,1,2,1))].">
      <j1 rule="para" parents="3123 6571"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(6099(a,2),5894(a,1,2,2))].">
      <j1 rule="para" parents="6099 5894"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5414,a,b,5987,a)].">
      <j1 rule="hyper" parents="319 5414 5987"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5151,a(flip),b,6059,a),flip(a)].">
      <j1 rule="hyper" parents="319 5151 6059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      T(x,(y * K(x,z)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,6576,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6576 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),6576(a,1,2,1))].">
      <j1 rule="para" parents="5047 6576"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5172(a,1),6576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5172 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(5271(a,1),6576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5271 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5926(a,1),6576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5926 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(6113(a,1),6576(a,1,2,1))].">
      <j1 rule="para" parents="6113 6576"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5926(a,1),6577(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5926 6577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a,b,6580,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5826,a(flip),b,6582,a)].">
      <j1 rule="hyper" parents="64 5826 6582"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      K(x,(y * z) \ ((K(x,u) * y) * z)) = K(x,a(K(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(14(a,2),6583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5831,a(flip),b,6585,a),flip(a)].">
      <j1 rule="hyper" parents="64 5831 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(3999(a,1),6588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3999 6588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4021(a,1),6590(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4021 6590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      T(x,y \ (z * x)) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(3999(a,1),6590(a,1,2,2))].">
      <j1 rule="para" parents="3999 6590"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4215(a,1),6590(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4215 6590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(4510(a,1),6590(a,1,2,2))].">
      <j1 rule="para" parents="4510 6590"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(5961,a,6595,a)].">
      <j1 rule="hyper" parents="5961 6595"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      T(T(x,y),z \ K(x,u)) = T(T(x,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(6597(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6597 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,5627,a,b,6592,a)].">
      <j1 rule="hyper" parents="319 5627 6592"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6592(a,2,2,2))].">
      <j1 rule="para" parents="10 6592"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,5962,a,b,6596,a)].">
      <j1 rule="hyper" parents="319 5962 6596"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,5661,a,b,6596,a)].">
      <j1 rule="hyper" parents="319 5661 6596"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 6601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(6601(a,1),5276(a,1,1))].">
      <j1 rule="para" parents="6601 5276"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      L(T(x,y \ (z * x)),u,w) \ L(x,u,w) = K((y / x) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(6604(a,1),4026(a,1,1,1))].">
      <j1 rule="para" parents="6604 4026"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6605(a,2),6375(a,1,2))].">
      <j1 rule="para" parents="6605 6375"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),6610(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6612">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6245,a,6611,a),flip(a)].">
      <j1 rule="hyper" parents="6245 6611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4813,a,b,6612,a),flip(a)].">
      <j1 rule="hyper" parents="319 4813 6612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4813,a,b,6613,a)].">
      <j1 rule="hyper" parents="64 4813 6613"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6614(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(6483,a,6085,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6483 6085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <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(6085(a,2),6483(a,1))].">
      <j1 rule="para" parents="6085 6483"/>
    </justification>
  </clause>

  <clause id="6618">
    <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),6104(a,2,2))].">
      <j1 rule="para" parents="27 6104"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ (K(y,L(z,u,w)) * x) = v6
    ]]></literal>
    <justification jstring="[para(6188(a,2),571(a,1))].">
      <j1 rule="para" parents="6188 571"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(1592(a,1),6188(a,1,2,2))].">
      <j1 rule="para" parents="1592 6188"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      (x * K(y,y * z)) / T(y,z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(4576(a,1),6230(a,2,2))].">
      <j1 rule="para" parents="4576 6230"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5495,a(flip),b,6621,a)].">
      <j1 rule="hyper" parents="64 5495 6621"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,6621,a(flip),b,5492,a),flip(a)].">
      <j1 rule="hyper" parents="130 6621 5492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(6622(a,1),6030(a,1,1,2))].">
      <j1 rule="para" parents="6622 6030"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      ((x * T(y,z)) / y) * ((u * y) / u) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5042,a,b,6231,a)].">
      <j1 rule="hyper" parents="64 5042 6231"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      K(x,R(T(y,x \ z),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),6237(a,2,2))].">
      <j1 rule="para" parents="27 6237"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6121(a,1),6260(a,1,2,2))].">
      <j1 rule="para" parents="6121 6260"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5125(a,2),6627(a,1,2))].">
      <j1 rule="para" parents="5125 6627"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(4106,a,6628,a)].">
      <j1 rule="hyper" parents="4106 6628"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(6100,a,6278,a),flip(a)].">
      <j1 rule="hyper" parents="6100 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6631">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6350,a,6630,a),flip(a)].">
      <j1 rule="hyper" parents="6350 6630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6629,a(flip),b,6631,a),flip(a)].">
      <j1 rule="hyper" parents="64 6629 6631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      1 * T((x \ 1) * y,K(z,T(u,x \ y))) = T(T((x \ 1) * y,x \ y),K(z,u))
    ]]></literal>
    <justification jstring="[para(3768(a,1),6302(a,1,1))].">
      <j1 rule="para" parents="3768 6302"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6376(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 6376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      T(T(x,y / z),K(z \ y,z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(6109(a,1),6402(a,1,2))].">
      <j1 rule="para" parents="6109 6402"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6636,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 6636 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      T((x \ y) * T(x,z),x) = (x \ T(y,x)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(1248(a,1),6412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1248 6412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      T(x / T(T(y,x),z),y) = T(y,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4309,a(flip),b,6420,a),flip(a)].">
      <j1 rule="hyper" parents="319 4309 6420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      T(x / T(T(y,z),x),y) = T(y,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(23(a,1),6639(a,1,1,2))].">
      <j1 rule="para" parents="23 6639"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(6433(a,1),5504(a,1,2))].">
      <j1 rule="para" parents="6433 5504"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4153(a,1),6442(a,1,1,2))].">
      <j1 rule="para" parents="4153 6442"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5835,a(flip),b,6463,a),flip(a)].">
      <j1 rule="hyper" parents="319 5835 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      K(T(x \ T(y,x),z) \ u,z) = K((T(x,y) \ y) \ u,z)
    ]]></literal>
    <justification jstring="[para(4042(a,1),6643(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4042 6643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(5144(a,1),6643(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5144 6643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(5400(a,1),6643(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5400 6643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),6643(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5926 6643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      K(x \ K(y,z),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(5248,a,6648,a)].">
      <j1 rule="hyper" parents="5248 6648"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5830,a(flip),b,6648,a)].">
      <j1 rule="hyper" parents="64 5830 6648"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(131,a,6649,a(flip),b,4938,a)].">
      <j1 rule="hyper" parents="131 6649 4938"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(4363(a,1),6650(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 6650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(4207(a,1),6650(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4207 6650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(4498(a,1),6653(a,1,1,2))].">
      <j1 rule="para" parents="4498 6653"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3874,a(flip),b,6534,a),flip(a)].">
      <j1 rule="hyper" parents="64 3874 6534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),6656(a,2,1))].">
      <j1 rule="para" parents="10 6656"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      K(x \ (x * (y / x)),(y \ (y / (y / x))) * z) = K(x \ (x * (y / x)),z * ((x * (y / x)) \ x))
    ]]></literal>
    <justification jstring="[para(4279(a,1),6544(a,1,2,1))].">
      <j1 rule="para" parents="4279 6544"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      K((x * (y / x)) \ x,(x \ (x * (y / x))) * z) = K(y \ (y / (y / x)),z * (x \ (x * (y / x))))
    ]]></literal>
    <justification jstring="[para(4279(a,1),6544(a,2,1))].">
      <j1 rule="para" parents="4279 6544"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(5089(a,1),6551(a,2,2))].">
      <j1 rule="para" parents="5089 6551"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(529,a,6559,a)].">
      <j1 rule="hyper" parents="529 6559"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(292,a,6559,a)].">
      <j1 rule="hyper" parents="292 6559"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(244,a,6559,a,b,4868,a)].">
      <j1 rule="hyper" parents="244 6559 4868"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5580,a(flip),b,6662,a)].">
      <j1 rule="hyper" parents="64 5580 6662"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      T(x,R(y,z,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6665,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6665 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      T(x,R(y,z,x \ 1)) \ x = K(y,x)
    ]]></literal>
    <justification jstring="[para(6667(a,2),4001(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6667 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      K(R(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(4046,a,6668,a)].">
      <j1 rule="hyper" parents="4046 6668"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      K(x,y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(6669(a,1),4416(a,1,1))].">
      <j1 rule="para" parents="6669 4416"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,6561,a(flip),b,3862,a(flip))].">
      <j1 rule="hyper" parents="130 6561 3862"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6563(a,2,2,2,1))].">
      <j1 rule="para" parents="9 6563"/>
    </justification>
  </clause>

  <clause id="6673">
    <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(1130,a,6574,a),flip(a)].">
      <j1 rule="hyper" parents="1130 6574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(6579(a,1),4430(a,1,2,2))].">
      <j1 rule="para" parents="6579 4430"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(6586(a,2),5187(a,1))].">
      <j1 rule="para" parents="6586 5187"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(4636(a,1),6675(a,1,2,1))].">
      <j1 rule="para" parents="4636 6675"/>
    </justification>
  </clause>

  <clause id="6677">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(5925(a,1),6675(a,1,2,1))].">
      <j1 rule="para" parents="5925 6675"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z \ w) = v5
    ]]></literal>
    <justification jstring="[para(6158(a,1),6675(a,1,2,1,2))].">
      <j1 rule="para" parents="6158 6675"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(5826(a,1),6677(a,1))].">
      <j1 rule="para" parents="5826 6677"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      L(T(x,y \ ((x \ z) \ u)),w,v5) \ L(x,w,v5) = K(y \ ((z / x) \ u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(6598(a,1),4026(a,1,1,1))].">
      <j1 rule="para" parents="6598 4026"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6099(a,2),6618(a,1,1))].">
      <j1 rule="para" parents="6099 6618"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      K(x,R(T(y,x * z),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),6626(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 6626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6683">
    <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(1499(a,1),6635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1499 6635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3909,a(flip),b,6647,a),flip(a)].">
      <j1 rule="hyper" parents="319 3909 6647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6685">
    <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(6654(a,1),4630(a,1,1,1,2))].">
      <j1 rule="para" parents="6654 4630"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x \ 1) = K(x,y) * L(T(z,x \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),6664(a,2,2))].">
      <j1 rule="para" parents="25 6664"/>
    </justification>
  </clause>

  <clause id="6687">
    <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),6681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 6681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(4257,a,6682,a)].">
      <j1 rule="hyper" parents="4257 6682"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,535,a(flip),b,6687,a),flip(a)].">
      <j1 rule="hyper" parents="319 535 6687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6099,a(flip),b,6689,a),flip(a)].">
      <j1 rule="hyper" parents="319 6099 6689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * (y \ z)))
    ]]></literal>
    <justification jstring="[para(1170(a,1),5751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1170 5751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4174,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="319 4174 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(5919(a,2),4255(a,1))].">
      <j1 rule="para" parents="5919 4255"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6119(a,1),6094(a,1,2))].">
      <j1 rule="para" parents="6119 6094"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4580,a,6694,a),flip(a)].">
      <j1 rule="hyper" parents="4580 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(279,a,6695,a)].">
      <j1 rule="hyper" parents="279 6695"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5269(a,1),6696(a,1,1))].">
      <j1 rule="para" parents="5269 6696"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      L(x,T(y,z),x) != u * K(y,T(x,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6149(a,1),45(a,1))].">
      <j1 rule="para" parents="6149 45"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(6371,a,5153,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6371 5153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6477,a,5946,a)].">
      <j1 rule="hyper" parents="6477 5946"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6631,a,b,6701,a)].">
      <j1 rule="hyper" parents="64 6631 6701"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6632,a(flip),b,6701,a)].">
      <j1 rule="hyper" parents="64 6632 6701"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6087,a,6703,a)].">
      <j1 rule="hyper" parents="6087 6703"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6632,a(flip),b,6703,a),flip(a)].">
      <j1 rule="hyper" parents="319 6632 6703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6629,a(flip),b,6703,a),flip(a)].">
      <j1 rule="hyper" parents="319 6629 6703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,6703,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6703 4012"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(130,a,6703,a,b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 6703 4011"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6703(a,1),4030(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6703 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(6703(a,1),4050(a,1,1))].">
      <j1 rule="para" parents="6703 4050"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y))) = 1
    ]]></literal>
    <justification jstring="[para(6703(a,1),4958(a,1,3))].">
      <j1 rule="para" parents="6703 4958"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6703(a,1),6044(a,1,2))].">
      <j1 rule="para" parents="6703 6044"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6703(a,1),6045(a,1,1))].">
      <j1 rule="para" parents="6703 6045"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6703(a,1),6083(a,1,1))].">
      <j1 rule="para" parents="6703 6083"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6703(a,1),6077(a,1,1))].">
      <j1 rule="para" parents="6703 6077"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6703(a,1),6084(a,1,2))].">
      <j1 rule="para" parents="6703 6084"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(6703(a,1),6404(a,1,1))].">
      <j1 rule="para" parents="6703 6404"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6703(a,1),6616(a,1,1))].">
      <j1 rule="para" parents="6703 6616"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4730,a(flip),b,6705,a),flip(a)].">
      <j1 rule="hyper" parents="319 4730 6705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      R(K(K(x,y),z \ 1),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,5557,a,b,6705,a)].">
      <j1 rule="hyper" parents="64 5557 6705"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,6705,a(flip),b,4947,a)].">
      <j1 rule="hyper" parents="131 6705 4947"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,6705,a(flip),b,4001,a(flip))].">
      <j1 rule="hyper" parents="131 6705 4001"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      K(x,K(y,z)) / z = 1 / T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,6705,a(flip),b,4008,a(flip))].">
      <j1 rule="hyper" parents="128 6705 4008"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(6705(a,1),4089(a,1,2))].">
      <j1 rule="para" parents="6705 4089"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6705(a,1),4314(a,1,1))].">
      <j1 rule="para" parents="6705 4314"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      T(x * T(K(y,z),u),K(u,K(y,z))) = K(y,K(z,u)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(6705(a,1),5148(a,2,1))].">
      <j1 rule="para" parents="6705 5148"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      (K(x,y) / z) * K(x,K(y,1 / z)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[para(6705(a,1),5411(a,1,2))].">
      <j1 rule="para" parents="6705 5411"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(5832(a,1),6705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5832 6705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      K(x,K(K(x,y) \ z,u)) = K(K(x,z),u)
    ]]></literal>
    <justification jstring="[para(5845(a,1),6705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5845 6705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6705(a,1),6350(a,1))].">
      <j1 rule="para" parents="6705 6350"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(y,K(y \ x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6702(a,1,1))].">
      <j1 rule="para" parents="10 6702"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6706,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6706 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6706(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 6706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(4489(a,1),6706(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4489 6706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6707,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6707 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(85(a,1),6707(a,1,2,2))].">
      <j1 rule="para" parents="85 6707"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6708(a,1),6267(a,1,2,2))].">
      <j1 rule="para" parents="6708 6267"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6086,a,6715,a)].">
      <j1 rule="hyper" parents="6086 6715"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(4229,a,6715,a)].">
      <j1 rule="hyper" parents="4229 6715"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6715(a,1),6086(a,1))].">
      <j1 rule="para" parents="6715 6086"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6707,a,b,6742,a)].">
      <j1 rule="hyper" parents="319 6707 6742"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6705,a,b,6742,a)].">
      <j1 rule="hyper" parents="319 6705 6742"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6704,a,b,6742,a)].">
      <j1 rule="hyper" parents="319 6704 6742"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6703,a,b,6742,a),flip(a)].">
      <j1 rule="hyper" parents="319 6703 6742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6742,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6742 4012"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,6742,a,b,4070,a)].">
      <j1 rule="hyper" parents="130 6742 4070"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,6742,a,b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 6742 4011"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      (x * K(y,z)) \ K(y,K(x * K(y,z),z)) = (L(K(y,z),x,K(y,z)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(6742(a,1),4405(a,1,2))].">
      <j1 rule="para" parents="6742 4405"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6742(a,1),6084(a,1,2))].">
      <j1 rule="para" parents="6742 6084"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6742(a,1),6708(a,1,2))].">
      <j1 rule="para" parents="6742 6708"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6742(a,1),6709(a,1,1))].">
      <j1 rule="para" parents="6742 6709"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6703,a,b,6743,a),flip(a)].">
      <j1 rule="hyper" parents="319 6703 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6703,a,b,6746,a),flip(a)].">
      <j1 rule="hyper" parents="319 6703 6746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6743,a(flip),b,6746,a)].">
      <j1 rule="hyper" parents="64 6743 6746"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(130,a,6746,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 6746 4011"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,6746,a(flip),b,3998,a(flip))].">
      <j1 rule="hyper" parents="130 6746 3998"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(4730(a,1),6746(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4730 6746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6746(a,1),6350(a,1))].">
      <j1 rule="para" parents="6746 6350"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6746(a,2),6708(a,1,2))].">
      <j1 rule="para" parents="6746 6708"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,6748,a,b,6715,a)].">
      <j1 rule="hyper" parents="131 6748 6715"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y))
    ]]></literal>
    <justification jstring="[hyper(131,a,6748,a,b,4938,a),flip(a)].">
      <j1 rule="hyper" parents="131 6748 4938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,6748,a,b,4070,a)].">
      <j1 rule="hyper" parents="130 6748 4070"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[hyper(130,a,6748,a,b,4820,a(flip))].">
      <j1 rule="hyper" parents="130 6748 4820"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(6748(a,2),4983(a,2,2))].">
      <j1 rule="para" parents="6748 4983"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      x * (y * K(z,K(u,(x \ 1) \ y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6748(a,2),4988(a,1,2,2))].">
      <j1 rule="para" parents="6748 4988"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(6748(a,2),5146(a,1,1,2))].">
      <j1 rule="para" parents="6748 5146"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6748(a,1),6044(a,1,2))].">
      <j1 rule="para" parents="6748 6044"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6748(a,2),6044(a,1,2))].">
      <j1 rule="para" parents="6748 6044"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6748(a,2),6045(a,1,1))].">
      <j1 rule="para" parents="6748 6045"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(6102(a,1),6748(a,1,2))].">
      <j1 rule="para" parents="6102 6748"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      x * K(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6748(a,1),6708(a,1,2))].">
      <j1 rule="para" parents="6748 6708"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(6756(a,1),4314(a,1,1))].">
      <j1 rule="para" parents="6756 4314"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6756(a,1),6350(a,1))].">
      <j1 rule="para" parents="6756 6350"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      x / K(y,K(z,u)) = x * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(206,a,6757,a(flip),b,5176,a)].">
      <j1 rule="hyper" parents="206 6757 5176"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      (x / y) * K(y,K(z,u)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,6757,a(flip),b,5168,a)].">
      <j1 rule="hyper" parents="131 6757 5168"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,6757,a(flip),b,4364,a),flip(a)].">
      <j1 rule="hyper" parents="130 6757 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * u) = T(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6757(a,1),4308(a,1,1))].">
      <j1 rule="para" parents="6757 4308"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(6757(a,1),4314(a,1,1))].">
      <j1 rule="para" parents="6757 4314"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(6757(a,1),4374(a,1,1))].">
      <j1 rule="para" parents="6757 4374"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(6757(a,1),4393(a,1,1))].">
      <j1 rule="para" parents="6757 4393"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(6757(a,1),4322(a,1,1))].">
      <j1 rule="para" parents="6757 4322"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6757(a,1),6350(a,1))].">
      <j1 rule="para" parents="6757 6350"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,5957,a,b,6758,a)].">
      <j1 rule="hyper" parents="319 5957 6758"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,6758,a,b,4518,a)].">
      <j1 rule="hyper" parents="129 6758 4518"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(4820(a,1),6758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4820 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5365(a,1),6758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5365 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6758(a,1),6044(a,1,2))].">
      <j1 rule="para" parents="6758 6044"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6472,a,6791,a)].">
      <j1 rule="hyper" parents="6472 6791"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6394,a,6791,a),flip(a)].">
      <j1 rule="hyper" parents="6394 6791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(6082,a,6791,a)].">
      <j1 rule="hyper" parents="6082 6791"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6051,a,6791,a),flip(a)].">
      <j1 rule="hyper" parents="6051 6791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(5260,a,6791,a),flip(a)].">
      <j1 rule="hyper" parents="5260 6791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(5222,a,6791,a),flip(a)].">
      <j1 rule="hyper" parents="5222 6791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(4389,a,6791,a)].">
      <j1 rule="hyper" parents="4389 6791"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(410,a,6791,a)].">
      <j1 rule="hyper" parents="410 6791"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6386,a(flip),b,6791,a),flip(a)].">
      <j1 rule="hyper" parents="319 6386 6791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6791,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="131 6791 22"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,6791,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="130 6791 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      K(x,y) \ T(z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,6791,a,b,4367,a)].">
      <j1 rule="hyper" parents="127 6791 4367"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(u,z)),y) = w
    ]]></literal>
    <justification jstring="[para(6791(a,1),410(a,1))].">
      <j1 rule="para" parents="6791 410"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = ((z * K(x,y)) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(6791(a,1),3629(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6791 3629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(6791(a,1),6052(a,1,1))].">
      <j1 rule="para" parents="6791 6052"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(6791(a,1),6078(a,1))].">
      <j1 rule="para" parents="6791 6078"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6791(a,1),6081(a,1,1))].">
      <j1 rule="para" parents="6791 6081"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6791(a,1),6385(a,1,1))].">
      <j1 rule="para" parents="6791 6385"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(6791(a,1),6391(a,1,1))].">
      <j1 rule="para" parents="6791 6391"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(6791(a,1),6407(a,2,2))].">
      <j1 rule="para" parents="6791 6407"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6791(a,1),6394(a,1))].">
      <j1 rule="para" parents="6791 6394"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5221,a,6797,a),flip(a)].">
      <j1 rule="hyper" parents="5221 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(x,y) * u) = T(R(z,K(x,y),u),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(776,a,6797,a)].">
      <j1 rule="hyper" parents="776 6797"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(698,a,6797,a),flip(a)].">
      <j1 rule="hyper" parents="698 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(41,a,6489,a,b,6797,a),flip(a)].">
      <j1 rule="hyper" parents="41 6489 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(206,a,6797,a(flip),b,3410,a)].">
      <j1 rule="hyper" parents="206 6797 3410"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6797,a(flip),b,3410,a)].">
      <j1 rule="hyper" parents="131 6797 3410"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6797(a,1),295(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="6797 295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6797(a,1),6081(a,1,1))].">
      <j1 rule="para" parents="6797 6081"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(6724(a,1),6032(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6724 6032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,6735,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 6735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6735(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 6735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6748,a,b,6736,a)].">
      <j1 rule="hyper" parents="64 6748 6736"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      T(x,K(y * z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6791,a,b,6738,a)].">
      <j1 rule="hyper" parents="64 6791 6738"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6742,a,b,6745,a)].">
      <j1 rule="hyper" parents="64 6742 6745"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6748,a,b,6747,a)].">
      <j1 rule="hyper" parents="64 6748 6747"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6742,a,b,6747,a)].">
      <j1 rule="hyper" parents="64 6742 6747"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      T(x,K(y,z)) * z = x * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,6755,a(flip),b,4288,a),flip(a)].">
      <j1 rule="hyper" parents="131 6755 4288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      T((x \ T(y,x)) \ y,K(z,x \ y)) = T(T(x,y),T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(6342(a,1),6796(a,1,1))].">
      <j1 rule="para" parents="6342 6796"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(41,a,6636,a,b,6803,a),flip(a)].">
      <j1 rule="hyper" parents="41 6636 6803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6162(a,1),6803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6162 6803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6099,a,b,6820,a),flip(a)].">
      <j1 rule="hyper" parents="319 6099 6820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,6099,a,b,6820,a)].">
      <j1 rule="hyper" parents="130 6099 6820"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,5928,a,b,6820,a)].">
      <j1 rule="hyper" parents="130 5928 6820"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      K(x,y \ z) * z = z * K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(130,a,6117,a(flip),b,6820,a)].">
      <j1 rule="hyper" parents="130 6117 6820"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,4985,a(flip),b,6820,a)].">
      <j1 rule="hyper" parents="130 4985 6820"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6820(a,1),231(a,1,1))].">
      <j1 rule="para" parents="6820 231"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6259,a,6844,a)].">
      <j1 rule="hyper" parents="6259 6844"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6201,a,6844,a),flip(a)].">
      <j1 rule="hyper" parents="6201 6844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      T(K(x,1 / T(y,z)),z) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4592,a,6844,a),flip(a)].">
      <j1 rule="hyper" parents="4592 6844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6122,a(flip),b,6844,a)].">
      <j1 rule="hyper" parents="64 6122 6844"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(6844(a,1),282(a,1,2,2,1))].">
      <j1 rule="para" parents="6844 282"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6352,a,6845,a)].">
      <j1 rule="hyper" parents="6352 6845"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6261,a,6845,a)].">
      <j1 rule="hyper" parents="6261 6845"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(6216,a,6845,a),flip(a)].">
      <j1 rule="hyper" parents="6216 6845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6133,a,6845,a)].">
      <j1 rule="hyper" parents="6133 6845"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6845,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6845 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,6155,a,b,6845,a)].">
      <j1 rule="hyper" parents="64 6155 6845"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,6154,a,b,6845,a)].">
      <j1 rule="hyper" parents="64 6154 6845"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6445,a(flip),b,6845,a)].">
      <j1 rule="hyper" parents="64 6445 6845"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(111(a,1),6845(a,1,2,1))].">
      <j1 rule="para" parents="111 6845"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),6845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 6845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(114(a,2),6845(a,1,2))].">
      <j1 rule="para" parents="114 6845"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4130(a,1),6845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 6845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      K(T(x,y),z) * (y * K(z,x)) = y
    ]]></literal>
    <justification jstring="[para(6845(a,1),6174(a,1,2,2))].">
      <j1 rule="para" parents="6845 6174"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6845(a,1),6216(a,1))].">
      <j1 rule="para" parents="6845 6216"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(41,a,6200,a,b,6848,a),flip(a)].">
      <j1 rule="hyper" parents="41 6200 6848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6848(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6848 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6848(a,1),653(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6848 653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6848(a,1),5936(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 5936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6156(a,1),6848(a,1,1))].">
      <j1 rule="para" parents="6156 6848"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(5743,a,6851,a),flip(a)].">
      <j1 rule="hyper" parents="5743 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6851,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6851 4012"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,6851,a(flip),b,6108,a),flip(a)].">
      <j1 rule="hyper" parents="131 6851 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <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),6851(a,1,2))].">
      <j1 rule="para" parents="25 6851"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(111(a,1),6851(a,1,2))].">
      <j1 rule="para" parents="111 6851"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(231(a,1),6851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * u)) = K(T(x,y),R(z,y,u))
    ]]></literal>
    <justification jstring="[para(765(a,2),6851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="765 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      K(x * T(x \ y,y),z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(1291(a,1),6851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1291 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(3190(a,1),6851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3190 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      K(x \ T(y,x),T(z,x)) = K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3265(a,1),6851(a,1,1))].">
      <j1 rule="para" parents="3265 6851"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(3387(a,1),6851(a,1,2))].">
      <j1 rule="para" parents="3387 6851"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(4130(a,1),6851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4130 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4130(a,1),6851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4130 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6851(a,1),4441(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6851 4441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(T(x,u),L(T(y,u),z,w))
    ]]></literal>
    <justification jstring="[para(6851(a,1),5379(a,1,1))].">
      <j1 rule="para" parents="6851 5379"/>
    </justification>
  </clause>

  <clause id="6887">
    <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(6851(a,1),5580(a,1,1))].">
      <j1 rule="para" parents="6851 5580"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(5659(a,1),6851(a,1,1))].">
      <j1 rule="para" parents="5659 6851"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6851(a,1),5743(a,1))].">
      <j1 rule="para" parents="6851 5743"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(6851(a,1),6650(a,1,1,2,1))].">
      <j1 rule="para" parents="6851 6650"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      T(x,T(y,z)) * T(z,x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6854,a(flip),b,6285,a),flip(a)].">
      <j1 rule="hyper" parents="131 6854 6285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6854,a(flip),b,6265,a),flip(a)].">
      <j1 rule="hyper" parents="131 6854 6265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      T(T(x,y),y) * T(z,x) = z * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6854,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 6854 22"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),6854(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 6854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(250(a,1),6854(a,1,2,1))].">
      <j1 rule="para" parents="250 6854"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(6854(a,1),6222(a,2,2))].">
      <j1 rule="para" parents="6854 6222"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      T(x,K(y * z,y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6791,a,b,6826,a)].">
      <j1 rule="hyper" parents="64 6791 6826"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(6826(a,1),6813(a,1,1))].">
      <j1 rule="para" parents="6826 6813"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      T(x * K(y \ z,y),K(y,z)) = K(y \ z,y) * x
    ]]></literal>
    <justification jstring="[hyper(5222,a,6827,a),flip(a)].">
      <j1 rule="hyper" parents="5222 6827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,6827,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 6827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6830,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6830 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6758,a,b,6831,a),flip(a)].">
      <j1 rule="hyper" parents="319 6758 6831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      (x * (y / z)) / T(y / z,x) = T(x,T(z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,3267,a,b,6836,a)].">
      <j1 rule="hyper" parents="319 3267 6836"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(3818(a,1),6836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3818 6836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,6199,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="130 6199 6838"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,4069,a,b,6838,a)].">
      <j1 rule="hyper" parents="38 4069 6838"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6838(a,1),336(a,1,1))].">
      <j1 rule="para" parents="6838 336"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      K(x,T(y,z)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,y)) / w = u
    ]]></literal>
    <justification jstring="[para(6838(a,1),576(a,1,1))].">
      <j1 rule="para" parents="6838 576"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(6838(a,1),883(a,1,1,1))].">
      <j1 rule="para" parents="6838 883"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(6838(a,1),822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6838 822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      T(x,T(y,z)) * (x \ z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4564,a,6839,a)].">
      <j1 rule="hyper" parents="4564 6839"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),z)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,6446,a,b,6839,a),flip(a)].">
      <j1 rule="hyper" parents="36 6446 6839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(206,a,6839,a(flip),b,6151,a)].">
      <j1 rule="hyper" parents="206 6839 6151"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,T(z,u)),u) = (x * u) / (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(206,a,6839,a(flip),b,520,a),flip(a)].">
      <j1 rule="hyper" parents="206 6839 520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,6839,a(flip),b,4288,a),flip(a)].">
      <j1 rule="hyper" parents="131 6839 4288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,6839,a(flip),b,4037,a)].">
      <j1 rule="hyper" parents="128 6839 4037"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      (x * K(y,z)) \ (K(y,T(z,x)) * (x * u)) = L(u,x,K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(6839(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6839 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(111(a,1),6839(a,1,1,2))].">
      <j1 rule="para" parents="111 6839"/>
    </justification>
  </clause>

  <clause id="6920">
    <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(6839(a,1),4387(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="6839 4387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(6839(a,1),6064(a,1,2,1))].">
      <j1 rule="para" parents="6839 6064"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6839(a,1),6588(a,1,2,2))].">
      <j1 rule="para" parents="6839 6588"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6839(a,1),6650(a,1,1,2))].">
      <j1 rule="para" parents="6839 6650"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6284,a(flip),b,6846,a)].">
      <j1 rule="hyper" parents="64 6284 6846"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(5039,a,6850,a)].">
      <j1 rule="hyper" parents="5039 6850"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6850,a(flip),b,4938,a),flip(a)].">
      <j1 rule="hyper" parents="131 6850 4938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      (x \ y) * K(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,6850,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 6850 4012"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(14(a,2),6850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 6850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      K(x \ y,T(T(z,x),u)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),6850(a,1,2))].">
      <j1 rule="para" parents="23 6850"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(6850(a,1),3446(a,1,2))].">
      <j1 rule="para" parents="6850 3446"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6850(a,1),4916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6850 4916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(4651(a,1),6930(a,1,2))].">
      <j1 rule="para" parents="4651 6930"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      K((x * y) / x,T(z \ 1,u)) = K(y,T(T(z,u) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(6243,a,6852,a)].">
      <j1 rule="hyper" parents="6243 6852"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      L(x * K((y * z) / y,x),u,w) / L(x,u,w) = K(z,T(L(x,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4627,a,b,6852,a)].">
      <j1 rule="hyper" parents="64 4627 6852"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4484,a,b,6852,a)].">
      <j1 rule="hyper" parents="64 4484 6852"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(6852(a,1),4554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6852 4554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      K(((x \ y) * z) / (x \ y),T(x,y)) = K(z,(x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[para(6342(a,1),6852(a,2,2))].">
      <j1 rule="para" parents="6342 6852"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6852(a,1),6216(a,1))].">
      <j1 rule="para" parents="6852 6216"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(5741,a,6853,a)].">
      <j1 rule="hyper" parents="5741 6853"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      x / K(x / y,z) = K(y \ x,z) \ x
    ]]></literal>
    <justification jstring="[hyper(206,a,6853,a(flip),b,5945,a)].">
      <j1 rule="hyper" parents="206 6853 5945"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y)
    ]]></literal>
    <justification jstring="[para(5800(a,1),6853(a,1,2))].">
      <j1 rule="para" parents="5800 6853"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(6853(a,1),6174(a,1,2,2))].">
      <j1 rule="para" parents="6853 6174"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(6248,a,6857,a)].">
      <j1 rule="hyper" parents="6248 6857"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6857,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6857 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5651,a(flip),b,6857,a)].">
      <j1 rule="hyper" parents="64 5651 6857"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(81(a,1),6857(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 6857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      K(x,T((y * x) \ z,y)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6287,a(flip),b,6858,a)].">
      <j1 rule="hyper" parents="64 6287 6858"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(14(a,2),6858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) = K(x,T(L(u,z,y),y * z))
    ]]></literal>
    <justification jstring="[para(18(a,2),6858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      K(x,T(y * z,u) / y) = K(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(3818(a,1),6858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3818 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(828(a,1),6859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="828 6859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4645,a,b,6870,a),flip(a)].">
      <j1 rule="hyper" parents="319 4645 6870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6870(a,1),6242(a,1))].">
      <j1 rule="para" parents="6870 6242"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      T(x,(y * z) / y) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(231(a,1),6872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="231 6872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(4143(a,1),6872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4143 6872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z / x) = (z / x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6289(a,1),6874(a,1,1))].">
      <j1 rule="para" parents="6289 6874"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      K(T(x,x \ y),((x \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(3549(a,1),6876(a,1,1))].">
      <j1 rule="para" parents="3549 6876"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(5989(a,1),6876(a,1,1))].">
      <j1 rule="para" parents="5989 6876"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4210,a,b,6877,a)].">
      <j1 rule="hyper" parents="64 4210 6877"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6884(a,2),6244(a,1))].">
      <j1 rule="para" parents="6884 6244"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,T(x,y)) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(6895(a,1),3633(a,1,2,1))].">
      <j1 rule="para" parents="6895 3633"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(4817(a,1),6895(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4817 6895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      T(x,K(y \ z,y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),6898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 6898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      T(x \ y,K(z,y)) = T(x \ y,K(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),6902(a,1,2,2))].">
      <j1 rule="para" parents="10 6902"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6902(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 6902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6903,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6903 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(6948(a,2),6261(a,1))].">
      <j1 rule="para" parents="6948 6261"/>
    </justification>
  </clause>

  <clause id="6973">
    <literal><![CDATA[
      T(T(x,y / z),K(y,z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6636,a(flip),b,6967,a),flip(a)].">
      <j1 rule="hyper" parents="64 6636 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      T(x / y,K(z,y)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[para(81(a,1),6970(a,1,2,2))].">
      <j1 rule="para" parents="81 6970"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6746(a,2),6732(a,1))].">
      <j1 rule="para" parents="6746 6732"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(6102(a,1),6762(a,1,2))].">
      <j1 rule="para" parents="6102 6762"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6745(a,2),6780(a,1))].">
      <j1 rule="para" parents="6745 6780"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      K(x,K(x \ y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6828(a,2),6780(a,1))].">
      <j1 rule="para" parents="6828 6780"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(6102(a,1),6789(a,1,2))].">
      <j1 rule="para" parents="6102 6789"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4367(a,2),6824(a,1))].">
      <j1 rule="para" parents="4367 6824"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6901(a,2),6824(a,1))].">
      <j1 rule="para" parents="6901 6824"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6967(a,2),6824(a,1))].">
      <j1 rule="para" parents="6967 6824"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(4985(a,1),6908(a,1))].">
      <j1 rule="para" parents="4985 6908"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5928(a,2),6908(a,1))].">
      <j1 rule="para" parents="5928 6908"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6109(a,1),6908(a,1,1))].">
      <j1 rule="para" parents="6109 6908"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6156(a,1),6908(a,1,1))].">
      <j1 rule="para" parents="6156 6908"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6932(a,1),51(a,2))].">
      <j1 rule="para" parents="6932 51"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),6938(a,1,2,1))].">
      <j1 rule="para" parents="111 6938"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6156(a,1),6938(a,1))].">
      <j1 rule="para" parents="6156 6938"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(6159(a,1),6938(a,1))].">
      <j1 rule="para" parents="6159 6938"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      K(x,T(T(y,z),z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,w,x),y) = u
    ]]></literal>
    <justification jstring="[para(6288(a,1),6938(a,1))].">
      <j1 rule="para" parents="6288 6938"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(6327(a,1),6938(a,1))].">
      <j1 rule="para" parents="6327 6938"/>
    </justification>
  </clause>

  <clause id="6994">
    <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),6985(a,1,2))].">
      <j1 rule="para" parents="23 6985"/>
    </justification>
  </clause>

  <clause id="6995">
    <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),6985(a,1,2))].">
      <j1 rule="para" parents="27 6985"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),6985(a,1,2))].">
      <j1 rule="para" parents="111 6985"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(6211(a,1),6710(a,1,1,2))].">
      <j1 rule="para" parents="6211 6710"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,4370,a,b,6713,a)].">
      <j1 rule="hyper" parents="35 4370 6713"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6713(a,1),44(a,1))].">
      <j1 rule="para" parents="6713 44"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(6714(a,1),5187(a,1,1))].">
      <j1 rule="para" parents="6714 5187"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5943(a,1),6717(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5943 6717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5847(a,1),6718(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5847 6718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6718(a,2),6173(a,1))].">
      <j1 rule="para" parents="6718 6173"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6719(a,1),5871(a,1,2))].">
      <j1 rule="para" parents="6719 5871"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6705,a(flip),b,6730,a),flip(a)].">
      <j1 rule="hyper" parents="319 6705 6730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      K(x,K(K(x,y) \ z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6705,a(flip),b,6731,a),flip(a)].">
      <j1 rule="hyper" parents="319 6705 6731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6828,a(flip),b,6733,a),flip(a)].">
      <j1 rule="hyper" parents="319 6828 6733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6762,a,7007,a)].">
      <j1 rule="hyper" parents="6762 7007"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6732,a,7007,a)].">
      <j1 rule="hyper" parents="6732 7007"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6703,a,b,7007,a),flip(a)].">
      <j1 rule="hyper" parents="319 6703 7007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6758,a,b,7008,a),flip(a)].">
      <j1 rule="hyper" parents="319 6758 7008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6703,a,b,7009,a),flip(a)].">
      <j1 rule="hyper" parents="319 6703 7009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6789,a,7010,a)].">
      <j1 rule="hyper" parents="6789 7010"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),7010(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 7010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7011,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7011 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7012(a,2),6732(a,1))].">
      <j1 rule="para" parents="7012 6732"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6758,a,b,7013,a),flip(a)].">
      <j1 rule="hyper" parents="319 6758 7013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,7013,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7013 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(81(a,1),7013(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 7013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7017,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7017 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),7017(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 7017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ x) = T(z \ x,K(x,y))
    ]]></literal>
    <justification jstring="[para(7017(a,1),6755(a,1,1))].">
      <j1 rule="para" parents="7017 6755"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      (K(x \ y,z) * y) \ T(y,K(x,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,7018,a(flip),b,5966,a)].">
      <j1 rule="hyper" parents="127 7018 5966"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      K(x,K(x / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7019(a,2),6789(a,1))].">
      <j1 rule="para" parents="7019 6789"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),7020(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 7020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(7021(a,1),6098(a,1,1))].">
      <j1 rule="para" parents="7021 6098"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(7025(a,1),4658(a,2,1,1))].">
      <j1 rule="para" parents="7025 4658"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7011,a(flip),b,6737,a),flip(a)].">
      <j1 rule="hyper" parents="319 7011 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,7008,a(flip),b,6737,a),flip(a)].">
      <j1 rule="hyper" parents="319 7008 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6780,a,7028,a)].">
      <j1 rule="hyper" parents="6780 7028"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(6762,a,7028,a)].">
      <j1 rule="hyper" parents="6762 7028"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a(flip),b,7028,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7028,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7028 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),7028(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(4491(a,1),7028(a,1,2))].">
      <j1 rule="para" parents="4491 7028"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(4494(a,2),7028(a,1,2))].">
      <j1 rule="para" parents="4494 7028"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(5084(a,1),7028(a,1,2))].">
      <j1 rule="para" parents="5084 7028"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6789,a,7029,a)].">
      <j1 rule="hyper" parents="6789 7029"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,7029,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7029 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(5084(a,1),7029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5084 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7029(a,2),6789(a,1))].">
      <j1 rule="para" parents="7029 6789"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6703,a,b,7030,a),flip(a)].">
      <j1 rule="hyper" parents="319 6703 7030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(4741(a,1),7030(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4741 7030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5003,a,7031,a)].">
      <j1 rule="hyper" parents="5003 7031"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a(flip),b,7031,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 7031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      T(1 / x,K(y,z)) = K(y,K(z,x)) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,7031,a(flip),b,4263,a),flip(a)].">
      <j1 rule="hyper" parents="128 7031 4263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7031(a,2),6732(a,1))].">
      <j1 rule="para" parents="7031 6732"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6394,a,7033,a),flip(a)].">
      <j1 rule="hyper" parents="6394 7033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,7033,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 7033 22"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7038,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7038 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(4723(a,2),7038(a,1,2))].">
      <j1 rule="para" parents="4723 7038"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7039(a,2),6824(a,1))].">
      <j1 rule="para" parents="7039 6824"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4658,a(flip),b,7044,a)].">
      <j1 rule="hyper" parents="64 4658 7044"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7044(a,2),6789(a,1))].">
      <j1 rule="para" parents="7044 6789"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6099,a(flip),b,6740,a)].">
      <j1 rule="hyper" parents="64 6099 6740"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(6102(a,1),6753(a,1,2,2))].">
      <j1 rule="para" parents="6102 6753"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6759(a,2),6173(a,1))].">
      <j1 rule="para" parents="6759 6173"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(u,z \ y)) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6157(a,1),6773(a,1,2,2))].">
      <j1 rule="para" parents="6157 6773"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,4370,a,b,6774,a)].">
      <j1 rule="hyper" parents="35 4370 6774"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6774,a(flip),b,4442,a)].">
      <j1 rule="hyper" parents="131 6774 4442"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,x) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6774(a,1),4299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6774 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,6747,a(flip),b,6776,a),flip(a)].">
      <j1 rule="hyper" parents="64 6747 6776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(T(x,u),y)) = w
    ]]></literal>
    <justification jstring="[para(6776(a,1),6780(a,1))].">
      <j1 rule="para" parents="6776 6780"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,6713,a(flip),b,6781,a)].">
      <j1 rule="hyper" parents="130 6713 6781"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      (x / y) * K(z,K(y,y \ x)) = (y \ x) * K(y,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(6794(a,1),4541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6794 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6798(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6798 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      T(x / T(y,z),K(z,y)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[para(5163(a,1),6800(a,1,1))].">
      <j1 rule="para" parents="5163 6800"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5823(a,1),6800(a,1,1))].">
      <j1 rule="para" parents="5823 6800"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      K(K(x,y),z) * T(u,K(x,y)) = T(K(x,y),z) * (u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,6801,a(flip),b,4100,a)].">
      <j1 rule="hyper" parents="131 6801 4100"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(6824,a,6805,a)].">
      <j1 rule="hyper" parents="6824 6805"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6809(a,1),3801(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6809 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x
    ]]></literal>
    <justification jstring="[para(7020(a,1),6809(a,1,1))].">
      <j1 rule="para" parents="7020 6809"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      T(x * y,K(z,x)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(6824,a,6814,a)].">
      <j1 rule="hyper" parents="6824 6814"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      T(x * y,K(y,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6805,a,b,6833,a)].">
      <j1 rule="hyper" parents="64 6805 6833"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(4401,a,6837,a)].">
      <j1 rule="hyper" parents="4401 6837"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      x \ (y * T(x,T(y,z))) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4913,a(flip),b,6837,a)].">
      <j1 rule="hyper" parents="64 4913 6837"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6013(a,2),6837(a,1,1,2,2))].">
      <j1 rule="para" parents="6013 6837"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(6843(a,1),332(a,1,2))].">
      <j1 rule="para" parents="6843 332"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = x \ T(x * K(x / y,z),x)
    ]]></literal>
    <justification jstring="[para(6843(a,2),5205(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6843 5205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[para(5686(a,1),6843(a,1,1))].">
      <j1 rule="para" parents="5686 6843"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4592,a,6847,a),flip(a)].">
      <j1 rule="hyper" parents="4592 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(206,a,6869,a(flip),b,4031,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 6869 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(142,a,6892,a)].">
      <j1 rule="hyper" parents="142 6892"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6892(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6892 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      K(x,y) * (y * T(x,z)) = T(x,T(z,y)) * y
    ]]></literal>
    <justification jstring="[para(6892(a,1),5498(a,1,2))].">
      <j1 rule="para" parents="6892 5498"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      (T(T(x,y),T(z,y)) * u) / (T(K(x,y),T(x,z)) * u) = R(T(x,z),T(K(x,y),T(x,z)),u)
    ]]></literal>
    <justification jstring="[para(6893(a,2),238(a,1,1,1))].">
      <j1 rule="para" parents="6893 238"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * y) = z * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(6165,a,6897,a)].">
      <j1 rule="hyper" parents="6165 6897"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6897(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6897 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      K(T(x,y),z) * (y * x) = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(6102(a,2),6897(a,1,1))].">
      <j1 rule="para" parents="6102 6897"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6145(a,1),6897(a,1,1))].">
      <j1 rule="para" parents="6145 6897"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6912(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6912 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7095">
    <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(6916(a,2),5580(a,1,2))].">
      <j1 rule="para" parents="6916 5580"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      (x * K(y,z \ (u \ z))) / (y \ x) = T(y,T((u * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(6317(a,1),6917(a,1,1,2))].">
      <j1 rule="para" parents="6317 6917"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u / x)) * y) = R(T(K(z,x \ u),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(6919(a,1),654(a,1,2,1))].">
      <j1 rule="para" parents="6919 654"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      T(x * K(y,z / x),x \ z) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[para(6919(a,1),5973(a,1,1))].">
      <j1 rule="para" parents="6919 5973"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,6921,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 6921 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      K(x,T(y / (z / x),u)) = K(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(5244(a,1),6921(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5244 6921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(5047(a,1),6922(a,1,2,2))].">
      <j1 rule="para" parents="5047 6922"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(5400(a,1),6922(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5400 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,x)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(5487(a,1),6922(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5487 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(5400(a,1),6923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5400 6923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      T(K(x,y \ ((z * u) * (1 / u))),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(417,a,2176,a,b,6944,a)].">
      <j1 rule="hyper" parents="417 2176 6944"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z) = T(K(T(y,x),z),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),6954(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 6954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      T(K(x \ y,z * (y \ x)),x) = K((x / y) \ 1,z * (x / y))
    ]]></literal>
    <justification jstring="[para(6545(a,1),6954(a,1,1))].">
      <j1 rule="para" parents="6545 6954"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(824(a,2),6956(a,1,2))].">
      <j1 rule="para" parents="824 6956"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6078,a,6973,a)].">
      <j1 rule="hyper" parents="6078 6973"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(410,a,6973,a)].">
      <j1 rule="hyper" parents="410 6973"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),6973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 6973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(6973(a,1),6081(a,1,1))].">
      <j1 rule="para" parents="6973 6081"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      K(x,y) \ T(x / z,K(y,z)) = (x / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,6974,a,b,4367,a)].">
      <j1 rule="hyper" parents="127 6974 4367"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4363(a,1),7005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 7005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(7005(a,1),4943(a,1,3))].">
      <j1 rule="para" parents="7005 4943"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(6839(a,1),7005(a,1,1))].">
      <j1 rule="para" parents="6839 7005"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7005(a,2),6744(a,1))].">
      <j1 rule="para" parents="7005 6744"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5538,a,7115,a)].">
      <j1 rule="hyper" parents="5538 7115"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      K(K(x,y) \ z,K(x,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6744,a,7006,a)].">
      <j1 rule="hyper" parents="6744 7006"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(7036(a,2),6789(a,1))].">
      <j1 rule="para" parents="7036 6789"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(5424(a,1),7040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5424 7040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7040(a,1),6789(a,1))].">
      <j1 rule="para" parents="7040 6789"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6725,a(flip),b,7046,a)].">
      <j1 rule="hyper" parents="319 6725 7046"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6394,a,7048,a),flip(a)].">
      <j1 rule="hyper" parents="6394 7048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,7124,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 7124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,y) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6165,a,7060,a)].">
      <j1 rule="hyper" parents="6165 7060"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,y \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6827,a,b,7061,a),flip(a)].">
      <j1 rule="hyper" parents="319 6827 7061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,z)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6392(a,1),7072(a,2,1))].">
      <j1 rule="para" parents="6392 7072"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,3795,a(flip),b,7075,a(flip))].">
      <j1 rule="hyper" parents="35 3795 7075"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),7075(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      T(x * T(y,K(x,z)),y) = T(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7076(a,1),6391(a,1,1))].">
      <j1 rule="para" parents="7076 6391"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),7083(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 7083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(249(a,1),7083(a,1,2,2,1))].">
      <j1 rule="para" parents="249 7083"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      (x * T(y,z \ y)) / T(x,y) = T(y,T(y * (z \ 1),x))
    ]]></literal>
    <justification jstring="[para(1453(a,1),7085(a,1,1,2))].">
      <j1 rule="para" parents="1453 7085"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      K(x,y) \ (R(x,z,u) * y) = R(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5876(a,1),7090(a,1,1))].">
      <j1 rule="para" parents="5876 7090"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      T(x,T(y / (z / x),u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(5244(a,1),7099(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5244 7099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(410,a,7109,a)].">
      <j1 rule="hyper" parents="410 7109"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6802,a,b,7109,a)].">
      <j1 rule="hyper" parents="64 6802 7109"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      K(K(x,y) \ z,T(K(x,u),w)) = K(x,K(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(6099(a,1),7119(a,1,2))].">
      <j1 rule="para" parents="6099 7119"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(5175(a,1),7123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5175 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4105,a,7125,a)].">
      <j1 rule="hyper" parents="4105 7125"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(6346,a,7142,a)].">
      <j1 rule="hyper" parents="6346 7142"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6345,a,7142,a)].">
      <j1 rule="hyper" parents="6345 7142"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6292,a(flip),b,7142,a)].">
      <j1 rule="hyper" parents="64 6292 7142"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6238,a(flip),b,7142,a),flip(a)].">
      <j1 rule="hyper" parents="64 6238 7142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(25(a,2),7142(a,1,2))].">
      <j1 rule="para" parents="25 7142"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),7142(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 7142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(3424(a,1),7142(a,1,2))].">
      <j1 rule="para" parents="3424 7142"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(5058(a,1),7142(a,1,2))].">
      <j1 rule="para" parents="5058 7142"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(7142(a,1),6124(a,1,2))].">
      <j1 rule="para" parents="7142 6124"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6850,a(flip),b,7145,a),flip(a)].">
      <j1 rule="hyper" parents="64 6850 7145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      (x \ y) * K(z,T(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(7145(a,1),6124(a,1,2))].">
      <j1 rule="para" parents="7145 6124"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,7146,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="130 7146 6838"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(7146(a,1),6322(a,1,2))].">
      <j1 rule="para" parents="7146 6322"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(6392(a,1),7129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6392 7129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(((z \ 1) \ 1) \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(4606(a,1),7139(a,1,1,2))].">
      <j1 rule="para" parents="4606 7139"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,7147,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7147 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(183(a,1),7147(a,1,2)),flip(a)].">
      <j1 rule="para" parents="183 7147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7151(a,1),4172(a,1))].">
      <j1 rule="para" parents="7151 4172"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7151(a,1),5741(a,1))].">
      <j1 rule="para" parents="7151 5741"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7151(a,1),6245(a,1))].">
      <j1 rule="para" parents="7151 6245"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(829(a,2),6864(a,1,1))].">
      <j1 rule="para" parents="829 6864"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6883,a(flip),b,6888,a),flip(a)].">
      <j1 rule="hyper" parents="319 6883 6888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(504(a,1),7165(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="504 7165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6882(a,2),6971(a,1))].">
      <j1 rule="para" parents="6882 6971"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6106(a,2),6984(a,1))].">
      <j1 rule="para" parents="6106 6984"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5928(a,2),6987(a,1))].">
      <j1 rule="para" parents="5928 6987"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6954(a,1),6987(a,1))].">
      <j1 rule="para" parents="6954 6987"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),L(y,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * w) / L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(1168(a,1),6989(a,1,2,1))].">
      <j1 rule="para" parents="1168 6989"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(283(a,1),6990(a,1,2))].">
      <j1 rule="para" parents="283 6990"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(T(x,z),u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(6159(a,1),6993(a,1))].">
      <j1 rule="para" parents="6159 6993"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(111(a,1),7004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      K(x / y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6742(a,1),7024(a,1))].">
      <j1 rule="para" parents="6742 7024"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3886(a,2),7041(a,1,2))].">
      <j1 rule="para" parents="3886 7041"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4491(a,1),7041(a,1,2))].">
      <j1 rule="para" parents="4491 7041"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(4494(a,2),7041(a,1,2))].">
      <j1 rule="para" parents="4494 7041"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(5084(a,1),7052(a,1,2))].">
      <j1 rule="para" parents="5084 7052"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5734(a,2),7162(a,1))].">
      <j1 rule="para" parents="5734 7162"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(5911(a,1),7162(a,1))].">
      <j1 rule="para" parents="5911 7162"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,K(w,u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(5197(a,1),7176(a,1,2))].">
      <j1 rule="para" parents="5197 7176"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(3424(a,1),7180(a,1,2))].">
      <j1 rule="para" parents="3424 7180"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(5754(a,1),7180(a,1,2))].">
      <j1 rule="para" parents="5754 7180"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(6328(a,1),7180(a,1,2))].">
      <j1 rule="para" parents="6328 7180"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y * (T(T(y,K(x,z)),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(127,a,4040,a(flip),b,6750,a)].">
      <j1 rule="hyper" parents="127 4040 6750"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5174(a,2),6760(a,1,2))].">
      <j1 rule="para" parents="5174 6760"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(T(z,y),K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(4162(a,1),6767(a,1,1,2))].">
      <j1 rule="para" parents="4162 6767"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y \ (((u * T(y,K(x,z))) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(127,a,4552,a(flip),b,6779,a)].">
      <j1 rule="hyper" parents="127 4552 6779"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4294,a(flip),b,6799,a),flip(a)].">
      <j1 rule="hyper" parents="319 4294 6799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(6799(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6799 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(3387(a,1),6855(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3387 6855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(6855(a,1),5868(a,1,1,1))].">
      <j1 rule="para" parents="6855 5868"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      K(T(x,y),T(z,L(z,u,w) * y)) = K(x,L(z,y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(1443(a,1),6875(a,1,2))].">
      <j1 rule="para" parents="1443 6875"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      K(T(x * K(y \ x,x),x),z) = K(x,T(z,T(y,x) \ x))
    ]]></literal>
    <justification jstring="[para(5000(a,1),6879(a,1,1))].">
      <j1 rule="para" parents="5000 6879"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(6990,a,6880,a)].">
      <j1 rule="hyper" parents="6990 6880"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(6990,a,6881,a)].">
      <j1 rule="hyper" parents="6990 6881"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6893(a,1),6885(a,1,1))].">
      <j1 rule="para" parents="6893 6885"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      T(x,T(T(y * K(z,y \ u),w),T(u / y,z))) = T(x,T(u / T(u / y,z),w))
    ]]></literal>
    <justification jstring="[para(6270(a,1),6896(a,1,2,1,1))].">
      <j1 rule="para" parents="6270 6896"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5163,a(flip),b,6906,a),flip(a)].">
      <j1 rule="hyper" parents="319 5163 6906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(6483,a,7201,a)].">
      <j1 rule="hyper" parents="6483 7201"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(5928(a,2),7201(a,1,1))].">
      <j1 rule="para" parents="5928 7201"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(6117(a,1),7201(a,1,1))].">
      <j1 rule="para" parents="6117 7201"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(6848(a,1),7201(a,1,1))].">
      <j1 rule="para" parents="6848 7201"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      T(x,T(y,z)) \ (x * (z / x)) = z / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4323,a,7203,a)].">
      <j1 rule="hyper" parents="4323 7203"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(3266(a,1),6907(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3266 6907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[para(6939(a,1),6113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6939 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5589,a(flip),b,6945,a),flip(a)].">
      <j1 rule="hyper" parents="319 5589 6945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6945,a(flip),b,6947,a)].">
      <j1 rule="hyper" parents="64 6945 6947"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (x \ y),u)) = w
    ]]></literal>
    <justification jstring="[para(6947(a,2),6189(a,1,1))].">
      <j1 rule="para" parents="6947 6189"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(5591,a,7211,a),flip(a)].">
      <j1 rule="hyper" parents="5591 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7211(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(7211(a,1),5591(a,1))].">
      <j1 rule="para" parents="7211 5591"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(6039,a,7213,a)].">
      <j1 rule="hyper" parents="6039 7213"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7213,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7213 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6039,a,7214,a)].">
      <j1 rule="hyper" parents="6039 7214"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      K(x,(y / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(7216(a,1),6469(a,1))].">
      <j1 rule="para" parents="7216 6469"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6060,a,b,7217,a)].">
      <j1 rule="hyper" parents="64 6060 7217"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      K(x,(K(y,x * z) * (y \ (x * z))) \ x) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(4902(a,1),7218(a,1,2,1))].">
      <j1 rule="para" parents="4902 7218"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),7219(a,1,2,2))].">
      <j1 rule="para" parents="11 7219"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,6727,a(flip),b,7022,a),flip(a)].">
      <j1 rule="hyper" parents="64 6727 7022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(6703(a,1),7026(a,1,1))].">
      <j1 rule="para" parents="6703 7026"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7077(a,2),44(a,1))].">
      <j1 rule="para" parents="7077 44"/>
    </justification>
  </clause>

  <clause id="7227">
    <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(7118(a,2),4381(a,1,1))].">
      <j1 rule="para" parents="7118 4381"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7127(a,2),6982(a,1))].">
      <j1 rule="para" parents="7127 6982"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      K(T(x * y,T(y,z)) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(7131(a,1),4472(a,1,1,1))].">
      <j1 rule="para" parents="7131 4472"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = K(x,y * K(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5311,a(flip),b,7132,a),flip(a)].">
      <j1 rule="hyper" parents="64 5311 7132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      K(x,1) * ((y \ R(y,z,u)) / K(x,R(y,w,v5))) = K(R(y,w,v5),x) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4814(a,1),7187(a,1,1,2))].">
      <j1 rule="para" parents="4814 7187"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      T(T(x,y) * T(z,x),T(x,y)) = T(z * T(x,y),x)
    ]]></literal>
    <justification jstring="[para(7190(a,1),6812(a,1,1))].">
      <j1 rule="para" parents="7190 6812"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6705(a,1),7199(a,2,1))].">
      <j1 rule="para" parents="6705 7199"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      T(T(x,1),y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(7205(a,2),2734(a,2,1,2))].">
      <j1 rule="para" parents="7205 2734"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      x / T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = (x * (1 / T(T(z,1),y))) \ x
    ]]></literal>
    <justification jstring="[para(7205(a,2),5132(a,1,2,1,2))].">
      <j1 rule="para" parents="7205 5132"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      T(x,y) \ (x * (z / x)) = z / T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6854(a,1),7206(a,1,1))].">
      <j1 rule="para" parents="6854 7206"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[para(7210(a,2),6113(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7210 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,7225,a(flip),b,6783,a)].">
      <j1 rule="hyper" parents="131 7225 6783"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z \ y,x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(6748(a,2),7238(a,1,1))].">
      <j1 rule="para" parents="6748 7238"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6758(a,1),7238(a,1,1))].">
      <j1 rule="para" parents="6758 7238"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(6713(a,1),6726(a,1))].">
      <j1 rule="para" parents="6713 6726"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6776(a,2),6726(a,1,2))].">
      <j1 rule="para" parents="6776 6726"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,T(z,u))) = w
    ]]></literal>
    <justification jstring="[para(7063(a,2),6980(a,1))].">
      <j1 rule="para" parents="7063 6980"/>
    </justification>
  </clause>

  <clause id="7244">
    <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(6702(a,1),7003(a,1,2))].">
      <j1 rule="para" parents="6702 7003"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),7112(a,1))].">
      <j1 rule="para" parents="23 7112"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6802(a,2),7112(a,1))].">
      <j1 rule="para" parents="6802 7112"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      K(K(x,y) * (K(y,z) * u),K(y,w)) = K(y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7117,a,7114,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7117 7114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(y \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7161,a,6929,a),flip(a)].">
      <j1 rule="hyper" parents="7161 6929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6850,a(flip),b,7248,a),flip(a)].">
      <j1 rule="hyper" parents="319 6850 7248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      T(x / y,T(z,x \ y)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,7249,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7249 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7146(a,2),7181(a,1))].">
      <j1 rule="para" parents="7146 7181"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6061(a,2),7215(a,1))].">
      <j1 rule="para" parents="6061 7215"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (x \ z)) = w
    ]]></literal>
    <justification jstring="[para(5274(a,2),7220(a,1))].">
      <j1 rule="para" parents="5274 7220"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6055(a,2),7228(a,1))].">
      <j1 rule="para" parents="6055 7228"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(7252,a,6924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7252 6924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      K(x,y) \ (K(x,K(y,z)) \ u) = K(x,T(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(599,a,6720,a),flip(a)].">
      <j1 rule="hyper" parents="599 6720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5172(a,1),6723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(3503,a,6849,a)].">
      <j1 rule="hyper" parents="3503 6849"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,L(K(x,y),z,u)) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(695,a,7259,a)].">
      <j1 rule="hyper" parents="695 7259"/>
    </justification>
  </clause>

  <clause id="7261">
    <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(5997(a,1),6867(a,1,1,1,2))].">
      <j1 rule="para" parents="5997 6867"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(5178(a,1),6900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5178 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      T(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(6904(a,1),3289(a,1))].">
      <j1 rule="para" parents="6904 3289"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3793,a,b,6957,a)].">
      <j1 rule="hyper" parents="64 3793 6957"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6717,a(flip),b,7001,a),flip(a)].">
      <j1 rule="hyper" parents="319 6717 7001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(6050(a,1),7265(a,1,2))].">
      <j1 rule="para" parents="6050 7265"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,6718,a(flip),b,7002,a),flip(a)].">
      <j1 rule="hyper" parents="319 6718 7002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(R(1 / y,y,x),z)) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3358(a,1),7023(a,1,1,1,1))].">
      <j1 rule="para" parents="3358 7023"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5393(a,1),7051(a,2,2))].">
      <j1 rule="para" parents="5393 7051"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,x * u))) = T(K(x,y),T(z,u * x))
    ]]></literal>
    <justification jstring="[para(3327(a,1),7057(a,1,2,2,2))].">
      <j1 rule="para" parents="3327 7057"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6842,a(flip),b,7074,a),flip(a)].">
      <j1 rule="hyper" parents="319 6842 7074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(64,a,6317,a(flip),b,7101,a),flip(a)].">
      <j1 rule="hyper" parents="64 6317 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      K(x,y \ ((z * K(x,u)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(5172(a,1),7103(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5172 7103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7275">
    <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(484(a,1),7104(a,2,1))].">
      <j1 rule="para" parents="484 7104"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      K(x,y) \ T(x / z,K(z,y)) = (x / z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6791(a,1),7113(a,1,2))].">
      <j1 rule="para" parents="6791 7113"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,4589,a(flip),b,7133,a)].">
      <j1 rule="hyper" parents="64 4589 7133"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      K(x,y * z) \ ((x * y) * z) = R(x,y,z) * T(y * z,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),7136(a,1,2))].">
      <j1 rule="para" parents="105 7136"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5676,a,b,7137,a)].">
      <j1 rule="hyper" parents="64 5676 7137"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),7148(a,2,2))].">
      <j1 rule="para" parents="25 7148"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(7160(a,1),4132(a,1,2))].">
      <j1 rule="para" parents="7160 4132"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,K(w,x * R(y,z,u))) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(7160(a,2),6753(a,2,1))].">
      <j1 rule="para" parents="7160 6753"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(6992,a,7196,a(flip))].">
      <j1 rule="hyper" parents="6992 7196"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5728,a,7283,a),flip(a)].">
      <j1 rule="hyper" parents="5728 7283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7284(a,1,1,1,1))].">
      <j1 rule="para" parents="10 7284"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,7082,a(flip),b,7208,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 7082 7208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4589,a(flip),b,7230,a),flip(a)].">
      <j1 rule="hyper" parents="64 4589 7230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      T(T(x,y) * T((x \ z) / x,x),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(6440(a,2),7232(a,2,1))].">
      <j1 rule="para" parents="6440 7232"/>
    </justification>
  </clause>

  <clause id="7289">
    <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(4583(a,1),7258(a,1,1))].">
      <j1 rule="para" parents="4583 7258"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4105,a,7264,a)].">
      <j1 rule="hyper" parents="4105 7264"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(x,K(z,y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(5747(a,1),7290(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5747 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,7267,a(flip),b,7266,a),flip(a)].">
      <j1 rule="hyper" parents="319 7267 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5174(a,1),7292(a,1,2))].">
      <j1 rule="para" parents="5174 7292"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(4297,a,7271,a)].">
      <j1 rule="hyper" parents="4297 7271"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y * z)) * K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(4500(a,2),7295(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4500 7295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6742(a,1),7295(a,1,1))].">
      <j1 rule="para" parents="6742 7295"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(6748(a,2),7295(a,1,1))].">
      <j1 rule="para" parents="6748 7295"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5942,a,7297,a)].">
      <j1 rule="hyper" parents="5942 7297"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) * K(x,((u * z) \ u) \ y) = K(x,y / ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(5083(a,1),7297(a,1,1,2))].">
      <j1 rule="para" parents="5083 7297"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(u / (z * u)) \ y) = K(x,y / (u / (z * u)))
    ]]></literal>
    <justification jstring="[para(7036(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="7036 7297"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6786,a,7298,a)].">
      <j1 rule="hyper" parents="6786 7298"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5185,a,7298,a)].">
      <j1 rule="hyper" parents="5185 7298"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      (K(x,y / z) * K(K(x,z \ y),u)) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u))
    ]]></literal>
    <justification jstring="[para(7298(a,1),4108(a,1,1,1))].">
      <j1 rule="para" parents="7298 4108"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(5627(a,1),7298(a,1,1,2))].">
      <j1 rule="para" parents="5627 7298"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ (y * u))) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5627(a,1),7299(a,1,2,2))].">
      <j1 rule="para" parents="5627 7299"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z / x) = K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(6742(a,1),7302(a,1,1))].">
      <j1 rule="para" parents="6742 7302"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      K(x / y,z) * K(z,K(y,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(4374,a,7303,a)].">
      <j1 rule="hyper" parents="4374 7303"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      K(x,K(y,x / (1 / (1 / z)))) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(2750(a,2),7307(a,2,2))].">
      <j1 rule="para" parents="2750 7307"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      K(x / y,z) * K(x,K(y,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(6703(a,1),7308(a,1,2))].">
      <j1 rule="para" parents="6703 7308"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) * K(x,K(y,z * (x \ y))) = K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6544,a,b,7310,a),flip(a)].">
      <j1 rule="hyper" parents="319 6544 7310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      K(x,y \ (((z / x) * u) * w)) = K(x,y \ (((x \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(6421(a,1),7274(a,1,2,2,1))].">
      <j1 rule="para" parents="6421 7274"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      T(x / y,K(y,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,6806,a,b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="39 6806 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      x / (y * K(K(y,z),y \ x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6271,a,b,7313,a)].">
      <j1 rule="hyper" parents="64 6271 7313"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      K(x,L(T(y / ((z * u) \ z),u),w,v5)) = K(x,L(((z * u) \ z) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(5063(a,1),7280(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5063 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      x / (y * K(y,K(z,y \ x))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6705(a,1),7314(a,1,2,2))].">
      <j1 rule="para" parents="6705 7314"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      x / (y * K(y,K(x,z))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6831(a,1),7316(a,1,2,2))].">
      <j1 rule="para" parents="6831 7316"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6777(a,1),7317(a,1,2))].">
      <j1 rule="para" parents="6777 7317"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,7318,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 7318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      K(x,L(y \ z,u,z / y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3123(a,1),6573(a,2,2))].">
      <j1 rule="para" parents="3123 6573"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,6641,a(flip),b,4299,a),flip(a)].">
      <j1 rule="hyper" parents="127 6641 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,6641,a(flip),b,4036,a),flip(a)].">
      <j1 rule="hyper" parents="127 6641 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7323">
    <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(6641(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6641 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      1 / ((x * (L(x,y,z) \ 1)) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3524,a(flip),b,6670,a),flip(a)].">
      <j1 rule="hyper" parents="64 3524 6670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ x) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1169(a,1),7324(a,1,2,1))].">
      <j1 rule="para" parents="1169 7324"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(199,a,7326,a),flip(a)].">
      <j1 rule="hyper" parents="199 7326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(356,a,7327,a)].">
      <j1 rule="hyper" parents="356 7327"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(5731,a,6688,a)].">
      <j1 rule="hyper" parents="5731 6688"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * z != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,L(y,u,w))) / v6 = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),6909(a,1,1,2))].">
      <j1 rule="para" parents="25 6909"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,7281,a(flip),b,4299,a),flip(a)].">
      <j1 rule="hyper" parents="127 7281 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      T(x,y) * (K(y * R(x,z,u),x) * w) = R(x,y,R(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(7281(a,1),4542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7281 4542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(5422,a,5638,a),flip(a)].">
      <j1 rule="hyper" parents="5422 5638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7337">
    <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(5639(a,1),5187(a,1,1))].">
      <j1 rule="para" parents="5639 5187"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5601,a(flip),b,5654,a)].">
      <j1 rule="hyper" parents="64 5601 5654"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x * y,K(y,x) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7340(a,1,2,1,1))].">
      <j1 rule="para" parents="9 7340"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(4659(a,1),7340(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4659 7340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y * x,z),y * x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(7341(a,1),4130(a,1,1,2))].">
      <j1 rule="para" parents="7341 4130"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5442,a(flip),b,5690,a)].">
      <j1 rule="hyper" parents="64 5442 5690"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(4345,a,7345,a),flip(a)].">
      <j1 rule="hyper" parents="4345 7345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7345(a,1),4345(a,1))].">
      <j1 rule="para" parents="7345 4345"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,7346,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 7346 4012"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(4166(a,1),7346(a,1,1,1))].">
      <j1 rule="para" parents="4166 7346"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(4041(a,1),7351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4041 7351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(4166(a,1),7348(a,1,1,1))].">
      <j1 rule="para" parents="4166 7348"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(4659(a,1),7348(a,1,1))].">
      <j1 rule="para" parents="4659 7348"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(529,a,5791,a)].">
      <j1 rule="hyper" parents="529 5791"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(3999(a,1),5791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3999 5791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * R(y,u,w) = K(y,x) * ((x * z) * R(y,u,w))
    ]]></literal>
    <justification jstring="[para(4437(a,1),5791(a,1,1))].">
      <j1 rule="para" parents="4437 5791"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      (x * (K(x,y) * (z * R(x,u,w)))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(5791(a,1),4296(a,1,1,2))].">
      <j1 rule="para" parents="5791 4296"/>
    </justification>
  </clause>

  <clause id="7359">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5572,a(flip),b,7355,a)].">
      <j1 rule="hyper" parents="64 5572 7355"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5453,a(flip),b,7355,a)].">
      <j1 rule="hyper" parents="64 5453 7355"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      K(x,y) * R(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(130,a,7360,a(flip),b,4061,a)].">
      <j1 rule="hyper" parents="130 7360 4061"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * K(w,R(x,y,R(x,z,u))) = (K(x,w) / R(x,y,R(x,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(7360(a,1),4463(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7360 4463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6624,a(flip),b,5903,a),flip(a)].">
      <j1 rule="hyper" parents="64 6624 5903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,6027,a(flip),b,7363,a),flip(a)].">
      <j1 rule="hyper" parents="319 6027 7363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),7364(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 7364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5874,a(flip),b,7365,a)].">
      <j1 rule="hyper" parents="64 5874 7365"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(7366(a,1),4127(a,2,2,2))].">
      <j1 rule="para" parents="7366 4127"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4127,a,b,7367,a),flip(a)].">
      <j1 rule="hyper" parents="319 4127 7367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,7368,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 7368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4105,a,7369,a)].">
      <j1 rule="hyper" parents="4105 7369"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5877,a,b,7370,a)].">
      <j1 rule="hyper" parents="64 5877 7370"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(5744,a,7371,a)].">
      <j1 rule="hyper" parents="5744 7371"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      T((x \ K(y,x)) \ L((x \ 1) * (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3934(a,1),5967(a,2,1))].">
      <j1 rule="para" parents="3934 5967"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(6038,a,6023,a),flip(a)].">
      <j1 rule="hyper" parents="6038 6023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * (K(y,x) * z)) = (y / T(x,y)) * L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(5206(a,1),6048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5206 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6568,a(flip),b,6219,a),flip(a)].">
      <j1 rule="hyper" parents="319 6568 6219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,5453,a(flip),b,6239,a),flip(a)].">
      <j1 rule="hyper" parents="64 5453 6239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,7379,a,b,4370,a),flip(a)].">
      <j1 rule="hyper" parents="126 7379 4370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      T(K(x,y) * z,T(y,u)) = K(x,y) * T(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(4976,a,6298,a),flip(a)].">
      <j1 rule="hyper" parents="4976 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      K(T(K(x,y) * z,T(y,u)) \ 1,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(z,T(y,u)) \ K(y,x),w) = v5
    ]]></literal>
    <justification jstring="[para(7381(a,2),5248(a,1,1,1))].">
      <j1 rule="para" parents="7381 5248"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = K(T(1 / x,K(x,u) * z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5484(a,1),6427(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5484 6427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4096(a,1),6429(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4096 6429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,7384,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 7384 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      L(K(x,K(y,z \ 1) * (u \ w)),u \ w,u) = K(x,(K(z \ K(z,u),y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(7385(a,2),5324(a,2,2,1))].">
      <j1 rule="para" parents="7385 5324"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(4976,a,6521,a),flip(a)].">
      <j1 rule="hyper" parents="4976 6521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,305,a(flip),b,6540,a),flip(a)].">
      <j1 rule="hyper" parents="319 305 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),6562(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 6562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),6575(a,2,2))].">
      <j1 rule="para" parents="9 6575"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6642(a,2,2,2,1))].">
      <j1 rule="para" parents="9 6642"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,6839,a,b,7392,a)].">
      <j1 rule="hyper" parents="36 6839 7392"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      L(K(x,K(y \ 1,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(7392(a,2),5324(a,2,2,1))].">
      <j1 rule="para" parents="7392 5324"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7393,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7393 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6316,a(flip),b,7395,a),flip(a)].">
      <j1 rule="hyper" parents="64 6316 7395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4406,a(flip),b,7396,a)].">
      <j1 rule="hyper" parents="64 4406 7396"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((x \ T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(5866,a,6645,a),flip(a)].">
      <j1 rule="hyper" parents="5866 6645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(6448(a,1),6671(a,1,1,2))].">
      <j1 rule="para" parents="6448 6671"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(4730(a,1),6721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4730 6721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(6705(a,1),6722(a,1,1))].">
      <j1 rule="para" parents="6705 6722"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(4730(a,1),6761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4730 6761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7400,a,b,7402,a)].">
      <j1 rule="hyper" parents="64 7400 7402"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6742(a,1),7403(a,1,1))].">
      <j1 rule="para" parents="6742 7403"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,((x / y) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),6770(a,1,2,1))].">
      <j1 rule="para" parents="12 6770"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6875,a(flip),b,6886,a),flip(a)].">
      <j1 rule="hyper" parents="319 6875 6886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,5380,a(flip),b,7407,a)].">
      <j1 rule="hyper" parents="64 5380 7407"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(109(a,1),7407(a,1,2))].">
      <j1 rule="para" parents="109 7407"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(228(a,1),7407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="228 7407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(6455,a,7410,a)].">
      <j1 rule="hyper" parents="6455 7410"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,7410,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 7410 18"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="12 7410"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(4036(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="4036 7410"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6113(a,1),7409(a,1,2,2))].">
      <j1 rule="para" parents="6113 7409"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(496,a,7414,a)].">
      <j1 rule="hyper" parents="496 7414"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(6995,a,6887,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6995 6887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7421">
    <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(6887(a,2),6995(a,1))].">
      <j1 rule="para" parents="6887 6995"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),7420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5584,a,b,7422,a)].">
      <j1 rule="hyper" parents="64 5584 7422"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(536,a,7423,a),flip(a)].">
      <j1 rule="hyper" parents="536 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(4429(a,1),7423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4429 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = ((((x \ 1) * (K(y,x) * u)) / ((x \ 1) * u)) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(7426(a,2),1882(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7426 1882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z),u)) = K(x,T(T(y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(6864,a,6933,a)].">
      <j1 rule="hyper" parents="6864 6933"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      K(x,T(T((y / z) \ 1,z),u)) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),7428(a,2,2,1,1))].">
      <j1 rule="para" parents="111 7428"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6891,a(flip),b,6943,a)].">
      <j1 rule="hyper" parents="64 6891 6943"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(6984,a,7430,a),flip(a)].">
      <j1 rule="hyper" parents="6984 7430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(7431(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7431 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,7433,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(4041(a,1),7434(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4041 7434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / u) = K(x,(y * x) / u)
    ]]></literal>
    <justification jstring="[para(6897(a,1),7434(a,1,2,1))].">
      <j1 rule="para" parents="6897 7434"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(5241(a,1),7435(a,2,2,1))].">
      <j1 rule="para" parents="5241 7435"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(7436(a,2),6482(a,1))].">
      <j1 rule="para" parents="7436 6482"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(4016(a,1),6962(a,1,1,1,2))].">
      <j1 rule="para" parents="4016 6962"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6711,a,6997,a),flip(a)].">
      <j1 rule="hyper" parents="6711 6997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),7441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(6851(a,1),7084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6851 7084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(3349(a,1),7108(a,1,2,1))].">
      <j1 rule="para" parents="3349 7108"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      T(x,T(x * (y \ 1),z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7086,a,7134,a),flip(a)].">
      <j1 rule="hyper" parents="7086 7134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(6796(a,1),7188(a,2,1))].">
      <j1 rule="para" parents="6796 7188"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      K(x * T(R(y,z,u),w),T(T(y,v5),K(R(y,z,u),w))) = K(x * R(y,z,u),T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,7193,a(flip),b,7191,a),flip(a)].">
      <j1 rule="hyper" parents="319 7193 7191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,7379,a(flip),b,7192,a),flip(a)].">
      <j1 rule="hyper" parents="319 7379 7192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(106(a,1),7449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 7449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7451">
    <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(5390(a,1),7195(a,1,1,1,2))].">
      <j1 rule="para" parents="5390 7195"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      (K(x,K(y,z)) * T(x,K(u,w))) \ x = K(u,K(w,x)) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6743(a,1),7233(a,2,2))].">
      <j1 rule="para" parents="6743 7233"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      K(x / y,y) * (z * (x / y)) = T(z * (y \ x),K(y,x))
    ]]></literal>
    <justification jstring="[para(4167(a,2),7262(a,1,1))].">
      <j1 rule="para" parents="4167 7262"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,7344,a(flip),b,4913,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 7344 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(4976,a,7350,a),flip(a)].">
      <j1 rule="hyper" parents="4976 7350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(4166(a,1),7455(a,2,1))].">
      <j1 rule="para" parents="4166 7455"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1480(a,2),7356(a,1,2))].">
      <j1 rule="para" parents="1480 7356"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6028,a(flip),b,7359,a),flip(a)].">
      <j1 rule="hyper" parents="319 6028 7359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,R(x,u,w))) = x \ R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(127,a,7361,a(flip),b,4305,a),flip(a)].">
      <j1 rule="hyper" parents="127 7361 4305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (y * R(T(x,y),z,R(x,u,w))) * x
    ]]></literal>
    <justification jstring="[para(7361(a,1),5671(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7361 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(4228,a,7380,a),flip(a)].">
      <j1 rule="hyper" parents="4228 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7028,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="319 7028 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(7028(a,1),7462(a,1,1))].">
      <j1 rule="para" parents="7028 7462"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(7029(a,1),7462(a,1,1))].">
      <j1 rule="para" parents="7029 7462"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(7032(a,1),7462(a,1,1))].">
      <j1 rule="para" parents="7032 7462"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7404,a(flip),b,7464,a)].">
      <j1 rule="hyper" parents="64 7404 7464"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7404,a(flip),b,7465,a)].">
      <j1 rule="hyper" parents="64 7404 7465"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,7468,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7468 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,7469,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7469 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,v5))) = K(x,K(w,(y * v5) / (R(y,z,u) * v5)))
    ]]></literal>
    <justification jstring="[para(5574(a,1),7469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5574 7469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7470,a(flip),b,7471,a)].">
      <j1 rule="hyper" parents="64 7470 7471"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      T(x,K(y,R(z \ 1,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7050,a(flip),b,7473,a),flip(a)].">
      <j1 rule="hyper" parents="319 7050 7473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,7418,a(flip),b,7415,a),flip(a)].">
      <j1 rule="hyper" parents="319 7418 7415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) * z = z * K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7429(a,1),6187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7429 6187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(144,a,7440,a)].">
      <j1 rule="hyper" parents="144 7440"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4516,a(flip),b,7453,a),flip(a)].">
      <j1 rule="hyper" parents="64 4516 7453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(206,a,7478,a(flip),b,4356,a)].">
      <j1 rule="hyper" parents="206 7478 4356"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7478(a,1),4377(a,1,2))].">
      <j1 rule="para" parents="7478 4377"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      ((x * K(y,z)) / x) / ((x * (K(y,z) * K(u,K(y,z)))) / x) = K(y,K(z,T(u,x)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6705,a(flip),b,7480,a),flip(a)].">
      <j1 rule="hyper" parents="319 6705 7480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3883(a,1),5769(a,1))].">
      <j1 rule="para" parents="3883 5769"/>
    </justification>
  </clause>

  <clause id="7484">
    <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(6052(a,1),5977(a,1,2,1))].">
      <j1 rule="para" parents="6052 5977"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(6001(a,1),6019(a,2,2))].">
      <j1 rule="para" parents="6001 6019"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(7487(a,2),4754(a,1))].">
      <j1 rule="para" parents="7487 4754"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(6099(a,2),6105(a,1,1))].">
      <j1 rule="para" parents="6099 6105"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6107,a,b,6134,a),flip(a)].">
      <j1 rule="hyper" parents="319 6107 6134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7493">
    <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(319,a,6102,a(flip),b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5237(a,1),6368(a,1,1,1))].">
      <j1 rule="para" parents="5237 6368"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(6457,a,5541,a),flip(a)].">
      <j1 rule="hyper" parents="6457 5541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(5541(a,1),6457(a,1))].">
      <j1 rule="para" parents="5541 6457"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,7495,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7495 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),7495(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 7495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(7495(a,1),5176(a,1,1,2))].">
      <j1 rule="para" parents="7495 5176"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(6471,a,7498,a)].">
      <j1 rule="hyper" parents="6471 7498"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6579,a(flip),b,7501,a)].">
      <j1 rule="hyper" parents="64 6579 7501"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(7501(a,1),4430(a,1,2,2))].">
      <j1 rule="para" parents="7501 4430"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(7501(a,1),5276(a,1,1))].">
      <j1 rule="para" parents="7501 5276"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(8(a,1),7503(a,2,2,1))].">
      <j1 rule="para" parents="8 7503"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6602,a(flip),b,7506,a),flip(a)].">
      <j1 rule="hyper" parents="319 6602 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5726,a,b,7506,a)].">
      <j1 rule="hyper" parents="64 5726 7506"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(x,(y / (x \ 1)) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7507(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z * u),z,u)) = K(x,a(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(654(a,1),6589(a,1,2))].">
      <j1 rule="para" parents="654 6589"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,4591,a(flip),b,7513,a),flip(a)].">
      <j1 rule="hyper" parents="64 4591 7513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,7514,a)].">
      <j1 rule="hyper" parents="57 7514"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(55,a,7516,a)].">
      <j1 rule="hyper" parents="55 7516"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7516(a,1),5925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7516 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(7517(a,1),5925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7517 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7520">
    <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(6703(a,1),6617(a,1,1))].">
      <j1 rule="para" parents="6703 6617"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(4601(a,1),6620(a,1,2))].">
      <j1 rule="para" parents="4601 6620"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(6678,a,6961,a)].">
      <j1 rule="hyper" parents="6678 6961"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6996,a,7522,a),flip(a)].">
      <j1 rule="hyper" parents="6996 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(88(a,1),7523(a,1,2,2))].">
      <j1 rule="para" parents="88 7523"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(1191(a,1),7523(a,1,2,2))].">
      <j1 rule="para" parents="1191 7523"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(4636(a,1),7523(a,1,2,2))].">
      <j1 rule="para" parents="4636 7523"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      K(x,y / (z * T(u,x))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(4922(a,1),7523(a,1,2,2))].">
      <j1 rule="para" parents="4922 7523"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5172(a,1),7523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5172 7523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(106(a,2),7524(a,2,2)),flip(a)].">
      <j1 rule="para" parents="106 7524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(5487(a,1),7528(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5487 7528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7532">
    <literal><![CDATA[
      K(x,y / ((z / x) * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(6421(a,1),7528(a,1,2,2))].">
      <j1 rule="para" parents="6421 7528"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(3382(a,1),7525(a,1,2,2,1))].">
      <j1 rule="para" parents="3382 7525"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4178,a(flip),b,7530,a)].">
      <j1 rule="hyper" parents="64 4178 7530"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(88(a,1),7531(a,1,2,2,1))].">
      <j1 rule="para" parents="88 7531"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(305(a,1),7531(a,1,2,2,1))].">
      <j1 rule="para" parents="305 7531"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(6141(a,1),7531(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6141 7531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(6113(a,1),6911(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6113 6911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,5637,a,b,7413,a),flip(a)].">
      <j1 rule="hyper" parents="35 5637 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),7539(a,1,2))].">
      <j1 rule="para" parents="25 7539"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(6938,a,7450,a)].">
      <j1 rule="hyper" parents="6938 7450"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(4964,a,7491,a)].">
      <j1 rule="hyper" parents="4964 7491"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,7255,a(flip),b,7544,a),flip(a)].">
      <j1 rule="hyper" parents="319 7255 7544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),7545(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(3349(a,1),7546(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3349 7546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(3204,a,7492,a),flip(a)].">
      <j1 rule="hyper" parents="3204 7492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(7492(a,1),499(a,1))].">
      <j1 rule="para" parents="7492 499"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,7548,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7548 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6570,a,b,7548,a)].">
      <j1 rule="hyper" parents="64 6570 7548"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T((y \ z) \ 1,u)) = K(((y \ z) \ 1) * x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4813,a,b,7548,a)].">
      <j1 rule="hyper" parents="64 4813 7548"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      x * K(y,T((x \ z) \ 1,u)) = K(y,T(x / z,u)) * x
    ]]></literal>
    <justification jstring="[para(7548(a,2),6446(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7548 6446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7548(a,2),6993(a,1))].">
      <j1 rule="para" parents="7548 6993"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ 1) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(6206,a,7550,a)].">
      <j1 rule="hyper" parents="6206 7550"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      T(x,((y \ z) * u) \ u) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(5119,a,7555,a)].">
      <j1 rule="hyper" parents="5119 7555"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      T(x,y \ T(z,z \ y)) = T(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5135(a,1),7556(a,1,2))].">
      <j1 rule="para" parents="5135 7556"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      T(x,y \ T(z,z \ y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6946,a(flip),b,7557,a),flip(a)].">
      <j1 rule="hyper" parents="319 6946 7557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),7554(a,1,2,1,1))].">
      <j1 rule="para" parents="9 7554"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6256(a,1),7554(a,1))].">
      <j1 rule="para" parents="6256 7554"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(7559,a,6282,a)].">
      <j1 rule="hyper" parents="7559 6282"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(7559,a,6256,a)].">
      <j1 rule="hyper" parents="7559 6256"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(3891(a,2),7559(a,1))].">
      <j1 rule="para" parents="3891 7559"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      K((x * y) / x,x / (x * z)) = K(y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(7563,a,6158,a)].">
      <j1 rule="hyper" parents="7563 6158"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * z) / x)) = K(y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(4574,a,7564,a)].">
      <j1 rule="hyper" parents="4574 7564"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(7565(a,1),2357(a,1,2))].">
      <j1 rule="para" parents="7565 2357"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u \ z,y)) = w
    ]]></literal>
    <justification jstring="[para(6282(a,1),7549(a,1))].">
      <j1 rule="para" parents="6282 7549"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7360,a(flip),b,7493,a)].">
      <j1 rule="hyper" parents="64 7360 7493"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7568(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7174,a(flip),b,7570,a)].">
      <j1 rule="hyper" parents="64 7174 7570"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),7571(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(6993,a,7573,a),flip(a)].">
      <j1 rule="hyper" parents="6993 7573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6713,a,b,7573,a),flip(a)].">
      <j1 rule="hyper" parents="319 6713 7573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(6999,a,7575,a)].">
      <j1 rule="hyper" parents="6999 7575"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(7575(a,2),7003(a,1))].">
      <j1 rule="para" parents="7575 7003"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),7576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 7576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(105(a,1),7576(a,1,2,2))].">
      <j1 rule="para" parents="105 7576"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7122,a,7578,a)].">
      <j1 rule="hyper" parents="7122 7578"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(81(a,1),7580(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 7580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7178,a,7581,a),flip(a)].">
      <j1 rule="hyper" parents="7178 7581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(6744,a,7579,a)].">
      <j1 rule="hyper" parents="6744 7579"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(7579(a,1),6775(a,1,1))].">
      <j1 rule="para" parents="7579 6775"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(7058,a,7584,a),flip(a)].">
      <j1 rule="hyper" parents="7058 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),7585(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6248,a,7586,a),flip(a)].">
      <j1 rule="hyper" parents="6248 7586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),7587(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6832(a,1),7520(a,1,1))].">
      <j1 rule="para" parents="6832 7520"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(36,a,6839,a,b,7521,a(flip))].">
      <j1 rule="hyper" parents="36 6839 7521"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6181,a(flip),b,7542,a)].">
      <j1 rule="hyper" parents="319 6181 7542"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),7591(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="81 7591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),7592(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 7592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5580,a(flip),b,7593,a),flip(a)].">
      <j1 rule="hyper" parents="64 5580 7593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,4628,a(flip),b,5689,a),flip(a)].">
      <j1 rule="hyper" parents="319 4628 5689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(503(a,1),7599(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 7599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(7483,a,7600,a),flip(a)].">
      <j1 rule="hyper" parents="7483 7600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3871,a(flip),b,5863,a)].">
      <j1 rule="hyper" parents="64 3871 5863"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,7088,a(flip),b,5909,a),flip(a)].">
      <j1 rule="hyper" parents="36 7088 5909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7603,a)].">
      <j1 rule="hyper" parents="134 7603"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7604(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7604 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,443,a(flip),b,6058,a),flip(a)].">
      <j1 rule="hyper" parents="319 443 6058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(6132(a,2),7243(a,1))].">
      <j1 rule="para" parents="6132 7243"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5203,a(flip),b,6191,a),flip(a)].">
      <j1 rule="hyper" parents="64 5203 6191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(6372(a,1),4747(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6372 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ (((y \ 1) \ 1) \ (T(y,y \ 1) * z))),y \ 1) = K(x * (z / (T(y,y \ 1) * z)),y \ 1)
    ]]></literal>
    <justification jstring="[para(426(a,1),6410(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="426 6410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4133(a,1),6443(a,1,2,2))].">
      <j1 rule="para" parents="4133 6443"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,6563,a,b,6565,a(flip))].">
      <j1 rule="hyper" parents="35 6563 6565"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(7613(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7613 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,7614,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 7614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      K((x * (y \ z)) \ 1,x) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5686,a,b,7616,a)].">
      <j1 rule="hyper" parents="64 5686 7616"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      (x * K(y,z)) * ((u * y) / u) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(4915(a,1),6625(a,1,1))].">
      <j1 rule="para" parents="4915 6625"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,y)) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4150,a(flip),b,7618,a)].">
      <j1 rule="hyper" parents="64 4150 7618"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(z,y)) = x * y
    ]]></literal>
    <justification jstring="[para(4004(a,1),7619(a,2,2))].">
      <j1 rule="para" parents="4004 7619"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(5144(a,1),7620(a,1,1))].">
      <j1 rule="para" parents="5144 7620"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5172(a,1),7620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 7620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      (x * (y * K(z,y))) / y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,7622,a)].">
      <j1 rule="hyper" parents="142 7622"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (y * K(u,y)) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,7622,a(flip),b,7620,a)].">
      <j1 rule="hyper" parents="128 7622 7620"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      a(x,K(y,z),z) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,7622,a(flip),b,2848,a),flip(a)].">
      <j1 rule="hyper" parents="126 7622 2848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(5900(a,2),7622(a,1,1))].">
      <j1 rule="para" parents="5900 7622"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,7625,a)].">
      <j1 rule="hyper" parents="53 7625"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      L((x \ y) \ y,K(z,x),u) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(7627(a,1),316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7627 316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(7627(a,1),438(a,1,2,1))].">
      <j1 rule="para" parents="7627 438"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(7627(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="7627 435"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(7627(a,1),436(a,1,2,1))].">
      <j1 rule="para" parents="7627 436"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(7621(a,1),4329(a,1,1))].">
      <j1 rule="para" parents="7621 4329"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (K(y,z) \ y)
    ]]></literal>
    <justification jstring="[para(4232(a,2),7626(a,2,2))].">
      <j1 rule="para" parents="4232 7626"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,7629,a)].">
      <j1 rule="hyper" parents="529 7629"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(5195,a,7635,a)].">
      <j1 rule="hyper" parents="5195 7635"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,7118,a(flip),b,7635,a)].">
      <j1 rule="hyper" parents="64 7118 7635"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(4295(a,1),7636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4295 7636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,7630,a)].">
      <j1 rule="hyper" parents="529 7630"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(6158(a,1),7639(a,1,2))].">
      <j1 rule="para" parents="6158 7639"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      x \ (((y \ x) * y) * L(T(y,z),u,w)) = K(y \ x,y) * L(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7640(a,1),551(a,1,1))].">
      <j1 rule="para" parents="7640 551"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      R(x,K(y,z),R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,7631,a)].">
      <j1 rule="hyper" parents="529 7631"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(5195,a,7642,a)].">
      <j1 rule="hyper" parents="5195 7642"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),7643(a,1,2))].">
      <j1 rule="para" parents="6365 7643"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(531,a,7633,a),flip(a)].">
      <j1 rule="hyper" parents="531 7633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6763(a,1),7645(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6763 7645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,7118,a(flip),b,7646,a),flip(a)].">
      <j1 rule="hyper" parents="319 7118 7646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7649">
    <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(7294(a,1),7647(a,1,2))].">
      <j1 rule="para" parents="7294 7647"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4674,a(flip),b,6637,a),flip(a)].">
      <j1 rule="hyper" parents="319 4674 6637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,7651,a(flip),b,4036,a)].">
      <j1 rule="hyper" parents="127 7651 4036"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = K(x,y) * (T(z,K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(6838(a,1),6808(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6838 6808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(6850(a,1),6931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6850 6931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(7654(a,1),570(a,1))].">
      <j1 rule="para" parents="7654 570"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(7655,a,4803,a),flip(a)].">
      <j1 rule="hyper" parents="7655 4803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(4181(a,1),7656(a,1,2))].">
      <j1 rule="para" parents="4181 7656"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(4648(a,1),7657(a,2,2))].">
      <j1 rule="para" parents="4648 7657"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      K((x \ y) \ ((x \ y) * z),x) = K(z,(x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[hyper(6358,a,6937,a)].">
      <j1 rule="hyper" parents="6358 6937"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4345,a,7659,a),flip(a)].">
      <j1 rule="hyper" parents="4345 7659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      K(T(x,y),((x \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(6263,a,6960,a)].">
      <j1 rule="hyper" parents="6263 6960"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      K(T(x,T(y,x)),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * T(y,x)))
    ]]></literal>
    <justification jstring="[para(4928(a,2),7662(a,1,2,1))].">
      <j1 rule="para" parents="4928 7662"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x) * (z * K(x,y))) = L(z * K(x,y),K(y,x),z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,3334,a(flip),b,7067,a),flip(a)].">
      <j1 rule="hyper" parents="36 3334 7067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(K(y,x),w) * (K(y,x) * T(z * K(x,y),u))
    ]]></literal>
    <justification jstring="[para(7067(a,1),6222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7067 6222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      T(K(x,y) * T(z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(5964(a,1),7070(a,1,1,2))].">
      <j1 rule="para" parents="5964 7070"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6757(a,1),7071(a,1,1))].">
      <j1 rule="para" parents="6757 7071"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(7421,a,7095,a),flip(a)].">
      <j1 rule="hyper" parents="7421 7095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4004(a,1),7668(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4004 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6113(a,1),7668(a,1,2,2))].">
      <j1 rule="para" parents="6113 7668"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5581,a,b,7670,a)].">
      <j1 rule="hyper" parents="64 5581 7670"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),7672(a,1,2))].">
      <j1 rule="para" parents="10 7672"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(7671(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7671 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(2972(a,1),7673(a,2,2))].">
      <j1 rule="para" parents="2972 7673"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,7674,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 7674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5455,a(flip),b,7676,a)].">
      <j1 rule="hyper" parents="64 5455 7676"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),7676(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 7676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,5454,a(flip),b,7677,a),flip(a)].">
      <j1 rule="hyper" parents="319 5454 7677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4116(a,1),7680(a,1,2))].">
      <j1 rule="para" parents="4116 7680"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(7681(a,1),5567(a,1,1))].">
      <j1 rule="para" parents="7681 5567"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      x * ((y / T(z,y)) * u) != (y / z) * u
    ]]></literal>
    <literal><![CDATA[
      R(K(z,y),z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(7682(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="7682 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      T(x,T((y * z) \ z,u)) = T(x,T(z \ (y \ z),u))
    ]]></literal>
    <justification jstring="[hyper(7094,a,7096,a),flip(a)].">
      <j1 rule="hyper" parents="7094 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K((x / y) \ 1,z * (x / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z * (y \ x)) = u
    ]]></literal>
    <justification jstring="[para(7107(a,1),6987(a,1))].">
      <j1 rule="para" parents="7107 6987"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(7164,a,5688,a)].">
      <j1 rule="hyper" parents="7164 5688"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7009,a(flip),b,7269,a),flip(a)].">
      <j1 rule="hyper" parents="319 7009 7269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),7687(a,1,2,2,1,2))].">
      <j1 rule="para" parents="81 7687"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4601,a(flip),b,7688,a)].">
      <j1 rule="hyper" parents="64 4601 7688"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(7242,a,7270,a),flip(a)].">
      <j1 rule="hyper" parents="7242 7270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6395,a(flip),b,7690,a),flip(a)].">
      <j1 rule="hyper" parents="64 6395 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7329,a(flip),b,7390,a),flip(a)].">
      <j1 rule="hyper" parents="64 7329 7390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(7461(a,1),7445(a,2,2))].">
      <j1 rule="para" parents="7461 7445"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,7108,a,b,7693,a)].">
      <j1 rule="hyper" parents="319 7108 7693"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(4166(a,1),7456(a,1,1,1))].">
      <j1 rule="para" parents="4166 7456"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4858,a(flip),b,7695,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4858 7695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      (x * (y * z)) \ ((y * z) * T(x * K(z,y),y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[para(7696(a,2),236(a,1,2,2))].">
      <j1 rule="para" parents="7696 236"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,7553,a(flip),b,7477,a),flip(a)].">
      <j1 rule="hyper" parents="36 7553 7477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,7701,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7701 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      T(x,T((y / (z * K(y,u))) \ 1,w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(4936(a,1),7702(a,2,2,1))].">
      <j1 rule="para" parents="4936 7702"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(5187,a,7499,a),flip(a)].">
      <j1 rule="hyper" parents="5187 7499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(7499(a,1),5187(a,1))].">
      <j1 rule="para" parents="7499 5187"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6647,a(flip),b,7705,a)].">
      <j1 rule="hyper" parents="64 6647 7705"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      L(x * K((y * z) \ (x \ u),x),w,v5) / L(x,w,v5) = K((y * (z * x)) \ u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(7705(a,1),4627(a,1,1,1,2))].">
      <j1 rule="para" parents="7705 4627"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      K((x * y) \ ((1 / y) \ z),1 / y) = K(x \ z,1 / y)
    ]]></literal>
    <justification jstring="[para(80(a,1),7707(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 7707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      K((x * (y \ z)) \ ((1 / (y \ z)) \ u),1 / (y \ z)) = K(x \ u,z \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5089,a(flip),b,7709,a),flip(a)].">
      <j1 rule="hyper" parents="319 5089 7709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(6647(a,1),7706(a,1))].">
      <j1 rule="para" parents="6647 7706"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,T(y / x,x / y))
    ]]></literal>
    <justification jstring="[para(670(a,1),7601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="670 7601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3877,a(flip),b,7602,a),flip(a)].">
      <j1 rule="hyper" parents="319 3877 7602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7714">
    <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),7606(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 7606"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,4359,a(flip),b,7609,a),flip(a)].">
      <j1 rule="hyper" parents="319 4359 7609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,4819,a(flip),b,7715,a)].">
      <j1 rule="hyper" parents="64 4819 7715"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,7524,a,b,7717,a)].">
      <j1 rule="hyper" parents="64 7524 7717"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),7718(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 7718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(3418(a,1),7718(a,1,2,2,1))].">
      <j1 rule="para" parents="3418 7718"/>
    </justification>
  </clause>

  <clause id="7721">
    <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(6099(a,2),7649(a,1,2))].">
      <j1 rule="para" parents="6099 7649"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,7608,a(flip),b,7652,a),flip(a)].">
      <j1 rule="hyper" parents="319 7608 7652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6056,a,b,7667,a)].">
      <j1 rule="hyper" parents="64 6056 7667"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7442,a(flip),b,7691,a)].">
      <j1 rule="hyper" parents="64 7442 7691"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(6173,a,7724,a)].">
      <j1 rule="hyper" parents="6173 7724"/>
    </justification>
  </clause>

  <clause id="7726">
    <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(4483(a,1),7714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4483 7714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = K(y,T(z,x)) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6483,a,7723,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6483 7723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4630,a(flip),b,6015,a),flip(a)].">
      <j1 rule="hyper" parents="319 4630 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5172(a,1),7728(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5172 7728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      R(K(x,T((y / z) \ x,u)),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[para(6099(a,2),6103(a,1,1))].">
      <j1 rule="para" parents="6099 6103"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(713,a,6360,a),flip(a)].">
      <j1 rule="hyper" parents="713 6360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5860(a,1),6382(a,1,1,1))].">
      <j1 rule="para" parents="5860 6382"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(3991(a,1),7732(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3991 7732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,7733,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 7733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      L(R(T(x,y),z,u),x \ T(w,x),x) = R(L(T(x,y),x \ w,x),z,u)
    ]]></literal>
    <justification jstring="[para(7734(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7734 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(x,(y * T(z,x \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(5520,a,6527,a),flip(a)].">
      <j1 rule="hyper" parents="5520 6527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 7736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,7507,a(flip),b,7737,a),flip(a)].">
      <j1 rule="hyper" parents="319 7507 7737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,7506,a(flip),b,7737,a),flip(a)].">
      <j1 rule="hyper" parents="319 7506 7737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      K(x,L(y,x \ 1,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5775,a(flip),b,7738,a)].">
      <j1 rule="hyper" parents="64 5775 7738"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(x,T((x \ 1) \ y,z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[para(620(a,1),7740(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="620 7740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,7503,a(flip),b,6607,a),flip(a)].">
      <j1 rule="hyper" parents="319 7503 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,5733,a(flip),b,6691,a),flip(a)].">
      <j1 rule="hyper" parents="319 5733 6691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(6099(a,2),6910(a,1,1))].">
      <j1 rule="para" parents="6099 6910"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6146(a,1),6915(a,1,1))].">
      <j1 rule="para" parents="6146 6915"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7337,a,5334,a),flip(a)].">
      <j1 rule="hyper" parents="7337 5334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6455,a,7747,a)].">
      <j1 rule="hyper" parents="6455 7747"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7475,a(flip),b,7747,a)].">
      <j1 rule="hyper" parents="64 7475 7747"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      K(T(x \ (L(y,z,u) * w),L(y,z,u) \ x),y) = K((((L(y,z,u) \ x) \ w) \ w) \ w,y)
    ]]></literal>
    <justification jstring="[para(3363(a,1),7748(a,1,1))].">
      <j1 rule="para" parents="3363 7748"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6424,a(flip),b,7383,a),flip(a)].">
      <j1 rule="hyper" parents="319 6424 7383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      T(K(x,y),K(x,z) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5821,a(flip),b,7751,a),flip(a)].">
      <j1 rule="hyper" parents="64 5821 7751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = z * L(T(K(x,u),K(x,y) * (K(x,y) \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(7751(a,1),715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7751 715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),7752(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 7752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(6123(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="6123 7538"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      K(x,T((y / (x * z)) \ 1,u)) = K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(3238,a,7730,a),flip(a)].">
      <j1 rule="hyper" parents="3238 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6319,a(flip),b,7757,a),flip(a)].">
      <j1 rule="hyper" parents="64 6319 7757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6592,a,b,7759,a),flip(a)].">
      <j1 rule="hyper" parents="319 6592 7759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      K(x,y \ (x * (z \ y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(78(a,1),7759(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="78 7759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[para(7760(a,1),6848(a,1,1))].">
      <j1 rule="para" parents="7760 6848"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      T(x,y \ (x * (z \ y))) = T(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,7761,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7761 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,T(u \ z,y))) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[para(7761(a,1),6332(a,1,2,2))].">
      <j1 rule="para" parents="7761 6332"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7725,a,b,7762,a)].">
      <j1 rule="hyper" parents="64 7725 7762"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      R(K(T(T(x,y),y * z),u),y,z) = ((y * z) \ ((y * K(u,x)) * z)) \ 1
    ]]></literal>
    <justification jstring="[para(7745(a,1),5564(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7745 5564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      L(T(K(x \ y,T(x,z)),z),z,y) = (y * (K(x \ y,x) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(7587(a,1),7756(a,1,1,1))].">
      <j1 rule="para" parents="7587 7756"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(5800(a,1),5813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5800 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4398,a(flip),b,7768,a),flip(a)].">
      <j1 rule="hyper" parents="319 4398 7768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      T(x * K((K(x,y) * z) * R(x,u,w),x),z) = R(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,4400,a(flip),b,7769,a),flip(a)].">
      <j1 rule="hyper" parents="64 4400 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(488,a,5893,a)].">
      <j1 rule="hyper" parents="488 5893"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7744,a(flip),b,7772,a)].">
      <j1 rule="hyper" parents="64 7744 7772"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),7773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 7773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6042(a,1),7773(a,1,2))].">
      <j1 rule="para" parents="6042 7773"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      K(x,T(y,z \ L(y,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7181,a,7775,a)].">
      <j1 rule="hyper" parents="7181 7775"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      T(x,T(y,z \ L(y,u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7777,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 7777 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      T(x / L(y,z,u),T(y,x)) = T(x / L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7250,a(flip),b,7778,a),flip(a)].">
      <j1 rule="hyper" parents="64 7250 7778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),7776(a,1,2,2,2))].">
      <j1 rule="para" parents="10 7776"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      K(x,T(y,z * (u / y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(12(a,1),7776(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6013(a,1),7776(a,1,2))].">
      <j1 rule="para" parents="6013 7776"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5858(a,1),7781(a,1,2))].">
      <j1 rule="para" parents="5858 7781"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6287,a(flip),b,7782,a),flip(a)].">
      <j1 rule="hyper" parents="64 6287 7782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = w / (K(u,T(x,y * z)) * w)
    ]]></literal>
    <justification jstring="[para(7783(a,1),4359(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7783 4359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6299,a,b,7784,a)].">
      <j1 rule="hyper" parents="64 6299 7784"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6287,a(flip),b,7780,a),flip(a)].">
      <j1 rule="hyper" parents="64 6287 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7787(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6444,a(flip),b,7788,a)].">
      <j1 rule="hyper" parents="64 6444 7788"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7547,a(flip),b,7789,a)].">
      <j1 rule="hyper" parents="64 7547 7789"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7218,a(flip),b,7790,a),flip(a)].">
      <j1 rule="hyper" parents="64 7218 7790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(6248,a,7791,a),flip(a)].">
      <j1 rule="hyper" parents="6248 7791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) = K(x,T(w \ x,R(T(x,u),y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7377,a(flip),b,7792,a)].">
      <j1 rule="hyper" parents="64 7377 7792"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = K(T(x,y * z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4359,a(flip),b,7785,a),flip(a)].">
      <j1 rule="hyper" parents="319 4359 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = K(x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a(flip),b,7794,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 7794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(6244,a,7795,a)].">
      <j1 rule="hyper" parents="6244 7795"/>
    </justification>
  </clause>

  <clause id="7797">
    <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(7795(a,1),6996(a,1))].">
      <j1 rule="para" parents="7795 6996"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6304,a,b,7796,a)].">
      <j1 rule="hyper" parents="64 6304 7796"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(5296(a,1),5906(a,1,1))].">
      <j1 rule="para" parents="5296 5906"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(4130(a,1),5978(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4130 5978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4130(a,1),7800(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4130 7800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4097(a,1),7801(a,1,3))].">
      <j1 rule="para" parents="4097 7801"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),(((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u))
    ]]></literal>
    <justification jstring="[para(3994(a,1),6290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3994 6290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = u
    ]]></literal>
    <justification jstring="[para(6431(a,1),6214(a,1))].">
      <j1 rule="para" parents="6431 6214"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(6547(a,2),6660(a,2,2))].">
      <j1 rule="para" parents="6547 6660"/>
    </justification>
  </clause>

  <clause id="7806">
    <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(319,a,6266,a(flip),b,6673,a),flip(a)].">
      <j1 rule="hyper" parents="319 6266 6673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7289,a(flip),b,7806,a)].">
      <j1 rule="hyper" parents="64 7289 7806"/>
    </justification>
  </clause>

  <clause id="7808">
    <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(7807(a,1),7244(a,1))].">
      <j1 rule="para" parents="7807 7244"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(6674(a,1),4465(a,1))].">
      <j1 rule="para" parents="6674 4465"/>
    </justification>
  </clause>

  <clause id="7810">
    <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(319,a,3315,a(flip),b,6683,a),flip(a)].">
      <j1 rule="hyper" parents="319 3315 6683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),K(u,K(y,z))) = K(y,K(z,u)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(6099(a,2),6728(a,1,1,2))].">
      <j1 rule="para" parents="6099 6728"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(6792(a,1),6768(a,1,1))].">
      <j1 rule="para" parents="6792 6768"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = ((T(y,K(x,z)) / u) * u) / y
    ]]></literal>
    <justification jstring="[para(7812(a,1),107(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7812 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      x * (T(y,K(z,u)) / w) != y / w
    ]]></literal>
    <literal><![CDATA[
      K((T(y,u) / w) / (y / w),z) = x
    ]]></literal>
    <justification jstring="[para(7812(a,1),4373(a,1,2))].">
      <j1 rule="para" parents="7812 4373"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6896,a(flip),b,6966,a)].">
      <j1 rule="hyper" parents="64 6896 6966"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3421,a(flip),b,7815,a),flip(a)].">
      <j1 rule="hyper" parents="319 3421 7815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3747,a(flip),b,7816,a),flip(a)].">
      <j1 rule="hyper" parents="319 3747 7816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7391(a,1,2))].">
      <j1 rule="para" parents="9 7391"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7713,a(flip),b,7819,a)].">
      <j1 rule="hyper" parents="64 7713 7819"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7820(a,2),6955(a,1))].">
      <j1 rule="para" parents="7820 6955"/>
    </justification>
  </clause>

  <clause id="7822">
    <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(5686(a,1),7451(a,1,1,1,2))].">
      <j1 rule="para" parents="5686 7451"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      (K(x,K(y,z)) * T(y,K(u,w))) \ y = K(u,K(w,y)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6748(a,1),7452(a,1,1,1))].">
      <j1 rule="para" parents="6748 7452"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(4465,a,7504,a),flip(a)].">
      <j1 rule="hyper" parents="4465 7504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(7809,a,7824,a)].">
      <j1 rule="hyper" parents="7809 7824"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),7825(a,2,1,1))].">
      <j1 rule="para" parents="8 7825"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5404,a,b,7826,a)].">
      <j1 rule="hyper" parents="64 5404 7826"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5389,a,b,7826,a)].">
      <j1 rule="hyper" parents="64 5389 7826"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),7826(a,2,1,2))].">
      <j1 rule="para" parents="7 7826"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(7829(a,1),4734(a,1,2,2))].">
      <j1 rule="para" parents="7829 4734"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(7830(a,1),1572(a,2,2,1))].">
      <j1 rule="para" parents="7830 1572"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(7827(a,2),5392(a,1))].">
      <j1 rule="para" parents="7827 5392"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7525,a(flip),b,7533,a),flip(a)].">
      <j1 rule="hyper" parents="64 7525 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(4083(a,1),7566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4083 7566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(319,a,4044,a(flip),b,7834,a),flip(a)].">
      <j1 rule="hyper" parents="319 4044 7834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,7719,a(flip),b,7720,a),flip(a)].">
      <j1 rule="hyper" parents="319 7719 7720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7534,a,b,7836,a)].">
      <j1 rule="hyper" parents="64 7534 7836"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(81(a,1),7837(a,2,2,2,1))].">
      <j1 rule="para" parents="81 7837"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      L(R(T(x,y),z,u),x \ T(w,x),x) = L(R(T(x,y),z,u),x \ w,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,29,a(flip),b,7735,a),flip(a)].">
      <j1 rule="hyper" parents="319 29 7735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(4251,a,6609,a),flip(a)].">
      <j1 rule="hyper" parents="4251 6609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7841">
    <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(2972(a,2),6928(a,1,1))].">
      <j1 rule="para" parents="2972 6928"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,T(L(x,u,w),z))
    ]]></literal>
    <justification jstring="[para(6852(a,1),6934(a,1,1,1,2))].">
      <j1 rule="para" parents="6852 6934"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),7842(a,2,2))].">
      <j1 rule="para" parents="25 7842"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,x * z),u,w))
    ]]></literal>
    <justification jstring="[para(5698(a,1),7843(a,1,1,1,2))].">
      <j1 rule="para" parents="5698 7843"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      K(x,a(y,z,u)) * K(x,K(a(y,z,u),y * (z * u))) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6713,a,b,6950,a)].">
      <j1 rule="hyper" parents="319 6713 6950"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(3122(a,1),6965(a,1,2,1))].">
      <j1 rule="para" parents="3122 6965"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(7212,a,7237,a)].">
      <j1 rule="hyper" parents="7212 7237"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      K(x,T(y / (x \ z),z)) = K(x,z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,7759,a(flip),b,7847,a),flip(a)].">
      <j1 rule="hyper" parents="319 7759 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      x * K(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(131,a,7847,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 7847 4012"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z / y) \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(7849(a,1),4089(a,1))].">
      <j1 rule="para" parents="7849 4089"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(x,x \ y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7589,a,5500,a)].">
      <j1 rule="hyper" parents="7589 5500"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      R(K(T(x,y),T(z,y * u)),y,u) = ((y * u) \ ((y * K(z,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(6102(a,1),7766(a,1,1))].">
      <j1 rule="para" parents="6102 7766"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(6848(a,1),7767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 7767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,7853,a)].">
      <j1 rule="hyper" parents="144 7853"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(y \ (y * x),y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7854(a,1,1,1,1))].">
      <j1 rule="para" parents="9 7854"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      K(R(K(x,y) \ R(K(x,y),z,u),K(x,y),z * u),((z * u) \ K(y,x)) \ 1) = K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(4380(a,1),7841(a,2,2))].">
      <j1 rule="para" parents="4380 7841"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      K(x,K(y,R(z \ R(z,u,w),z,u * w) \ 1)) = K(x,K(a(z,u,w),T(y,z * (u * w))))
    ]]></literal>
    <justification jstring="[para(7841(a,1),7029(a,2,2))].">
      <j1 rule="para" parents="7841 7029"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      K(x,L(T(y,y * z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7843,a(flip),b,7844,a),flip(a)].">
      <j1 rule="hyper" parents="64 7843 7844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = ((z * u) \ ((z * K(y,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(6153(a,1),7852(a,1,1))].">
      <j1 rule="para" parents="6153 7852"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7745,a(flip),b,7860,a),flip(a)].">
      <j1 rule="hyper" parents="64 7745 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(5489(a,2),7861(a,1,1))].">
      <j1 rule="para" parents="5489 7861"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,((x / u) * y) \ (x * y)) = w
    ]]></literal>
    <justification jstring="[para(7862(a,1),4229(a,1))].">
      <j1 rule="para" parents="7862 4229"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(5787,a,6560,a)].">
      <j1 rule="hyper" parents="5787 6560"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(6839(a,1),7864(a,1,3))].">
      <j1 rule="para" parents="6839 7864"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(5346,a,7865,a)].">
      <j1 rule="hyper" parents="5346 7865"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      L(x \ 1,x,y) * L(L(x \ 1,T(x,z),y) \ 1,u,w) = L((x \ 1) * L((x \ 1) \ 1,u,w),T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7866(a,1),2636(a,1,1))].">
      <j1 rule="para" parents="7866 2636"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      K(x / y,T(z,u)) \ T(x / (K(y \ x,z) \ x),u) = K(K(x / y,z) \ x,T(K(x / y,z),u))
    ]]></literal>
    <justification jstring="[para(6942(a,1),6130(a,1,2,1,2))].">
      <j1 rule="para" parents="6942 6130"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      a((x \ y) * K(x,y / x),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),6269(a,1,1,2,1))].">
      <j1 rule="para" parents="81 6269"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      a(x / y,x / (x / y),z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[para(4044(a,1),7869(a,1,1))].">
      <j1 rule="para" parents="4044 7869"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      a(((x * y) / x) / T(x,y),((x * y) / x) / (((x * y) / x) / T(x,y)),z) = a(x \ y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3126(a,1),7871(a,2,1))].">
      <j1 rule="para" parents="3126 7871"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      T(x,y) * (((x * y) / x) / T(x,y)) = ((x \ T(y,x)) \ y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),6344(a,1,2,1))].">
      <j1 rule="para" parents="3106 6344"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) * (x \ y) = T(x,y) * (y / x)
    ]]></literal>
    <justification jstring="[para(1294(a,1),7873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1294 7873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      (T(x,y) * (y / x)) * K(x \ y,(x \ T(y,x)) \ y) = (x \ y) * ((x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[hyper(130,a,7874,a(flip),b,196,a)].">
      <j1 rule="hyper" parents="130 7874 196"/>
    </justification>
  </clause>

  <clause id="7876">
    <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(4730(a,1),6366(a,1,1,2))].">
      <j1 rule="para" parents="4730 6366"/>
    </justification>
  </clause>

  <clause id="7877">
    <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(7876(a,2),5577(a,1,1))].">
      <j1 rule="para" parents="7876 5577"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(2753(a,1),6542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2753 6542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3876,a,b,7878,a),flip(a)].">
      <j1 rule="hyper" parents="319 3876 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3876,a,b,7879,a)].">
      <j1 rule="hyper" parents="64 3876 7879"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(7880(a,1),4018(a,2,2))].">
      <j1 rule="para" parents="7880 4018"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5095,a(flip),b,6550,a)].">
      <j1 rule="hyper" parents="64 5095 6550"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(7054,a,7027,a)].">
      <j1 rule="hyper" parents="7054 7027"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7053,a(flip),b,7885,a),flip(a)].">
      <j1 rule="hyper" parents="319 7053 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(x,K((1 / (y \ z)) / u,R(u / y,y,y \ z))) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[para(539(a,2),7886(a,1,2,2))].">
      <j1 rule="para" parents="539 7886"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(T(x / (x / y),x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,5326,a,b,7081,a),flip(a)].">
      <j1 rule="hyper" parents="319 5326 7081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5684,a(flip),b,7275,a),flip(a)].">
      <j1 rule="hyper" parents="319 5684 7275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(7711,a,7890,a)].">
      <j1 rule="hyper" parents="7711 7890"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      T(T(x,y) * (x \ (x \ z)),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(111(a,1),7288(a,1,1,2))].">
      <j1 rule="para" parents="111 7288"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      T(x \ (T(x,y) * (x \ z)),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1010(a,2),7893(a,1,1))].">
      <j1 rule="para" parents="1010 7893"/>
    </justification>
  </clause>

  <clause id="7895">
    <literal><![CDATA[
      T(x \ (x \ (T(x,y) * z)),T(x,y)) = T(x \ ((z / x) * T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1010(a,2),7894(a,1,1,2))].">
      <j1 rule="para" parents="1010 7894"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      T(x \ (x \ (T(x,y) * z)),T(x,y)) = x \ (T(z / x,x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6253,a(flip),b,7895,a),flip(a)].">
      <j1 rule="hyper" parents="319 6253 7895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      T(x \ (x \ (T(x,y) * z)),T(x,y)) = x \ ((x \ z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),7896(a,2,2,1))].">
      <j1 rule="para" parents="111 7896"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u * z) \ u) \ y) = K(x,y / ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(7028(a,1),7300(a,1,1))].">
      <j1 rule="para" parents="7028 7300"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(7549,a,7551,a)].">
      <j1 rule="hyper" parents="7549 7551"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      K(x \ y,x) * L(T(x,x \ y),z,u) = y \ ((L(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(1141(a,1),7641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1141 7641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      K(T(x,y),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * T(y,x)))
    ]]></literal>
    <justification jstring="[para(3252(a,1),7663(a,1,1))].">
      <j1 rule="para" parents="3252 7663"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      K(T(x,y),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,7527,a(flip),b,7901,a),flip(a)].">
      <j1 rule="hyper" parents="319 7527 7901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7739,a(flip),b,7902,a)].">
      <j1 rule="hyper" parents="64 7739 7902"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / z) = K(x,y / ((x \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(6996,a,7903,a)].">
      <j1 rule="hyper" parents="6996 7903"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      K(x,y / ((x \ 1) * z)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7439,a,7904,a),flip(a)].">
      <j1 rule="hyper" parents="7439 7904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(x,(((x \ 1) * y) * z) / (x \ z)) = K(T(x,x \ 1),R(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6878,a(flip),b,7905,a),flip(a)].">
      <j1 rule="hyper" parents="64 6878 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      K(x,(((x \ 1) * y) * z) / (x \ z)) = K(x,R(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,2932,a(flip),b,7907,a),flip(a)].">
      <j1 rule="hyper" parents="319 2932 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      K(x,(y / (((x \ 1) * z) * y)) \ x) = K(x,R(z,x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(7215,a,7908,a)].">
      <j1 rule="hyper" parents="7215 7908"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      R(K(x,(x \ 1) \ y),y,z) = K(x,(z / (((x \ 1) * ((x \ 1) \ y)) * z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,7673,a,b,7909,a)].">
      <j1 rule="hyper" parents="319 7673 7909"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),1 / ((y * z) \ y)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7710(a,2,2))].">
      <j1 rule="para" parents="9 7710"/>
    </justification>
  </clause>

  <clause id="7912">
    <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),7810(a,1,1,2,1))].">
      <j1 rule="para" parents="9 7810"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6541(a,1),7881(a,2,2))].">
      <j1 rule="para" parents="6541 7881"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6657(a,1),7913(a,2,2))].">
      <j1 rule="para" parents="6657 7913"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,2194,a(flip),b,7914,a),flip(a)].">
      <j1 rule="hyper" parents="319 2194 7914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(78(a,1),7915(a,1,1))].">
      <j1 rule="para" parents="78 7915"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(78(a,1),7916(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 7916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(4454(a,1),7917(a,1,1))].">
      <j1 rule="para" parents="4454 7917"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(3484(a,1),7888(a,2,1))].">
      <j1 rule="para" parents="3484 7888"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,7919,a(flip),b,7081,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 7919 7081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      T(K(x \ y,x) * L(x,z,u),x \ y) = y \ ((L(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5985,a,b,7900,a)].">
      <j1 rule="hyper" parents="64 5985 7900"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5981,a(flip),b,7921,a)].">
      <j1 rule="hyper" parents="64 5981 7921"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,4627,a(flip),b,5971,a),flip(a)].">
      <j1 rule="hyper" parents="64 4627 5971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(L(x \ y,x,z),L(x,u,w)) = K(z \ (x \ (z * y)),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(96(a,2),7923(a,1,1))].">
      <j1 rule="para" parents="96 7923"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      (x * T(K(y,z),u)) * T(K(z,y),u) = R(x,T(K(y,z),u),T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(6114(a,1),6197(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6114 6197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,y),u)) != w * T(K(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      x * T(K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(7925(a,1),45(a,1))].">
      <j1 rule="para" parents="7925 45"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,4626,a(flip),b,6254,a),flip(a)].">
      <j1 rule="hyper" parents="319 4626 6254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,4628,a(flip),b,6255,a),flip(a)].">
      <j1 rule="hyper" parents="319 4628 6255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4122(a,1),7928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4122 7928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,T(y,T(x,w)),R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5958,a(flip),b,6300,a)].">
      <j1 rule="hyper" parents="64 5958 6300"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,4400,a(flip),b,7930,a),flip(a)].">
      <j1 rule="hyper" parents="64 4400 7930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      R(T(x,y),T(z,x),R(T(x,y),u,w)) = R(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(6854(a,1),7932(a,1,2))].">
      <j1 rule="para" parents="6854 7932"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (K(x * z,y) * x)) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5282,a(flip),b,7222,a)].">
      <j1 rule="hyper" parents="64 5282 7222"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6798(a,1),7227(a,1,1,3))].">
      <j1 rule="para" parents="6798 7227"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4356(a,1),7935(a,2,2))].">
      <j1 rule="para" parents="4356 7935"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ K(y,u),w) = T(K(x \ K(y,u),w),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7382,a,6429,a)].">
      <j1 rule="hyper" parents="7382 6429"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      T(K((x / y) \ K(y,z),u),T(y,x)) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5420,a(flip),b,7937,a),flip(a)].">
      <j1 rule="hyper" parents="64 5420 7937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(41,a,6844,a,b,7938,a)].">
      <j1 rule="hyper" parents="41 6844 7938"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      K(x,K(R(y,z,u),R(z,w,v5) \ z)) = K(x,K(y,(z * u) / (R(z,w,v5) * u)))
    ]]></literal>
    <justification jstring="[hyper(6789,a,7472,a)].">
      <j1 rule="hyper" parents="6789 7472"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7743,a(flip),b,7505,a),flip(a)].">
      <j1 rule="hyper" parents="64 7743 7505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,K(x,w) * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5867(a,1),7771(a,1,1,2))].">
      <j1 rule="para" parents="5867 7771"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,4400,a(flip),b,7942,a),flip(a)].">
      <j1 rule="hyper" parents="64 4400 7942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,155,a(flip),b,7813,a),flip(a)].">
      <j1 rule="hyper" parents="319 155 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4011,a,b,7945,a),flip(a)].">
      <j1 rule="hyper" parents="319 4011 7945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6742,a,b,7946,a),flip(a)].">
      <j1 rule="hyper" parents="319 6742 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7856(a,2,2,1,1))].">
      <j1 rule="para" parents="9 7856"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,7949,a)].">
      <j1 rule="hyper" parents="142 7949"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,7949,a(flip),b,229,a)].">
      <j1 rule="hyper" parents="128 7949 229"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,x * y) = u
    ]]></literal>
    <justification jstring="[para(7949(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7949 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      ((K(x,y) * z) * T(y * x,z)) / (z * T(y * x,z)) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(7454(a,2),7951(a,1,1))].">
      <j1 rule="para" parents="7454 7951"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,(z / (((x \ 1) * ((x \ 1) \ y)) * z)) \ x)
    ]]></literal>
    <justification jstring="[para(5650(a,1),7910(a,1,1))].">
      <j1 rule="para" parents="5650 7910"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,(z / (y * z)) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7955(a,2,2,1,2,1))].">
      <j1 rule="para" parents="10 7955"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = R(K(x,x * y),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4624,a,b,7956,a)].">
      <j1 rule="hyper" parents="319 4624 7956"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * R(K(x,x * y),y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,7957,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 7957 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(R(z,w,v5) \ z,R(y,z,u))) = v6
    ]]></literal>
    <justification jstring="[para(7940(a,1),6789(a,1))].">
      <j1 rule="para" parents="7940 6789"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = u
    ]]></literal>
    <justification jstring="[para(7954(a,1),531(a,1))].">
      <j1 rule="para" parents="7954 531"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) = T(y,x) * K(y \ (x \ z),T(y,x))
    ]]></literal>
    <justification jstring="[hyper(6336,a,3992,a)].">
      <j1 rule="hyper" parents="6336 3992"/>
    </justification>
  </clause>

  <clause id="7963">
    <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(4417(a,1),4142(a,2,1))].">
      <j1 rule="para" parents="4417 4142"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4130(a,1),7963(a,1,1,1))].">
      <j1 rule="para" parents="4130 7963"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(199,a,7964,a)].">
      <j1 rule="hyper" parents="199 7964"/>
    </justification>
  </clause>

  <clause id="7966">
    <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(3290(a,1),7965(a,1,1,2))].">
      <j1 rule="para" parents="3290 7965"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      T(K(x,y),z) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(6114(a,1),4223(a,1,2,1))].">
      <j1 rule="para" parents="6114 4223"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(6483,a,7967,a)].">
      <j1 rule="hyper" parents="6483 7967"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      K(x,T(y,z)) * R(K(y,T(x,z)),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(6099(a,2),7968(a,1,2,1))].">
      <j1 rule="para" parents="6099 7968"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),4391(a,2,2))].">
      <j1 rule="para" parents="4363 4391"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(7970(a,2),332(a,1))].">
      <j1 rule="para" parents="7970 332"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      L(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5790(a,1),7971(a,1))].">
      <j1 rule="para" parents="5790 7971"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      (K(x,y) * R(K(x,y) \ 1,z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(243(a,1),4456(a,1,2)),flip(a)].">
      <j1 rule="para" parents="243 4456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      (K(x,y) * R(K(y,x),z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(4213(a,1),7974(a,1,1,2,1))].">
      <j1 rule="para" parents="4213 7974"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4437(a,1),4531(a,1,2))].">
      <j1 rule="para" parents="4437 4531"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(1 / x,x) \ (R(1 / L(x,y,z),L(x,y,z),K(1 / x,x)) * ((u * (1 / (1 / L(x,y,z)))) / u)) = K(u,1 / (K(1 / x,x) \ R(1 / L(x,y,z),L(x,y,z),K(1 / x,x))))
    ]]></literal>
    <justification jstring="[para(5408(a,1),4768(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5408 4768"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      T(K(x * R(1 / y,y,z),y \ 1) / y,x) = R(1 / y,x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(3895(a,1),4778(a,1,1))].">
      <j1 rule="para" parents="3895 4778"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,1787,a(flip),b,4812,a),flip(a)].">
      <j1 rule="hyper" parents="319 1787 4812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,3415,a(flip),b,7979,a),flip(a)].">
      <j1 rule="hyper" parents="319 3415 7979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(6333(a,1),7980(a,1,2))].">
      <j1 rule="para" parents="6333 7980"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      T(((T(x,y) \ y) * ((x \ y) \ y)) / (T(x,y) \ y),x * (y / T(x,y))) = L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(7981(a,1),617(a,1,2))].">
      <j1 rule="para" parents="7981 617"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      K(x,y / (K(z * u,u \ 1) \ z)) = K(x,y / ((u \ 1) * (z / (1 / u))))
    ]]></literal>
    <justification jstring="[para(6539(a,1),4854(a,1,2,2,1))].">
      <j1 rule="para" parents="6539 4854"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,839,a(flip),b,5530,a)].">
      <j1 rule="hyper" parents="64 839 5530"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = K(y \ x,z \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7285(a,1),6422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7285 6422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = T(x / y,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6213,a(flip),b,7985,a),flip(a)].">
      <j1 rule="hyper" parents="319 6213 7985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[para(3119(a,1),7986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3119 7986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7804,a,7987,a)].">
      <j1 rule="hyper" parents="7804 7987"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) * K(z,x) = (T(x,y) \ 1) \ K(z,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,9,a(flip),b,6432,a)].">
      <j1 rule="hyper" parents="131 9 6432"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) / ((T(x,y) \ 1) \ K(z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7989(a,1),5531(a,1,2))].">
      <j1 rule="para" parents="7989 5531"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      T(T((x \ 1) * y,x \ y),K(z,u)) = T((x \ 1) * y,K(z,T(u,x \ y)))
    ]]></literal>
    <justification jstring="[hyper(133,a,6633,a),flip(a)].">
      <j1 rule="hyper" parents="133 6633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3763(a,1),7992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3763 7992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,x \ L((x \ 1) \ 1,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4847,a,7993,a)].">
      <j1 rule="hyper" parents="4847 7993"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3771,a(flip),b,7158,a)].">
      <j1 rule="hyper" parents="64 3771 7158"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(7246,a,7995,a),flip(a)].">
      <j1 rule="hyper" parents="7246 7995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) / y) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,7186,a(flip),b,7189,a),flip(a)].">
      <j1 rule="hyper" parents="64 7186 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(453(a,1),7997(a,1,2,1))].">
      <j1 rule="para" parents="453 7997"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      K(x,y) * (K(y,T(K(z,u),x)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,6936,a(flip),b,7998,a)].">
      <j1 rule="hyper" parents="64 6936 7998"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      K(x,y) * (K(y,K(z,T(u,x))) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(6099(a,2),7999(a,1,2,1,2))].">
      <j1 rule="para" parents="6099 7999"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,7290,a(flip),b,7291,a),flip(a)].">
      <j1 rule="hyper" parents="319 7290 7291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      K(T(x,((y \ 1) / (y \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),8001(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="78 8001"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6403,a(flip),b,8002,a)].">
      <j1 rule="hyper" parents="64 6403 8002"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7167,a,8003,a)].">
      <j1 rule="hyper" parents="7167 8003"/>
    </justification>
  </clause>

  <clause id="8005">
    <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(319,a,6229,a(flip),b,7323,a),flip(a)].">
      <j1 rule="hyper" parents="319 6229 7323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (R(x,z,R(x,u,w)) * y) * x
    ]]></literal>
    <justification jstring="[para(243(a,1),7460(a,2,1))].">
      <j1 rule="para" parents="243 7460"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7457,a(flip),b,8007,a),flip(a)].">
      <j1 rule="hyper" parents="64 7457 8007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      K(x,T(y,z)) / ((z * (K(x,y) * K(u,K(x,y)))) / z) = K(x,K(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6838(a,1),7482(a,1,1))].">
      <j1 rule="para" parents="6838 7482"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      K(x,T(y,z)) / ((z * K(x,T(y,u))) / z) = K(x,K(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6794(a,1),8009(a,1,2,1,2))].">
      <j1 rule="para" parents="6794 8009"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      K(x,T(y,z)) / K(x,T(T(y,u),z)) = K(x,K(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6838(a,1),8010(a,1,2))].">
      <j1 rule="para" parents="6838 8010"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(7549,a,7552,a),flip(a)].">
      <j1 rule="hyper" parents="7549 7552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,u)) = K((y \ z) \ x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7899,a(flip),b,8012,a),flip(a)].">
      <j1 rule="hyper" parents="64 7899 8012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6858,a(flip),b,8013,a),flip(a)].">
      <j1 rule="hyper" parents="319 6858 8013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6989,a,8014,a)].">
      <j1 rule="hyper" parents="6989 8014"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1271,a(flip),b,7726,a)].">
      <j1 rule="hyper" parents="64 1271 7726"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(6651(a,2),8016(a,1,1))].">
      <j1 rule="para" parents="6651 8016"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(81(a,1),8017(a,1,1,2,1))].">
      <j1 rule="para" parents="81 8017"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,8018,a)].">
      <j1 rule="hyper" parents="488 8018"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,8018,a),flip(a)].">
      <j1 rule="hyper" parents="417 8018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      L(x,K(y,z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,4412,a,b,8018,a)].">
      <j1 rule="hyper" parents="35 4412 8018"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(u,y),x) = w
    ]]></literal>
    <justification jstring="[para(8018(a,1),335(a,1,2))].">
      <j1 rule="para" parents="8018 335"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2099(a,1),8018(a,1,1))].">
      <j1 rule="para" parents="2099 8018"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4775,a(flip),b,8019,a)].">
      <j1 rule="hyper" parents="64 4775 8019"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      L(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(4831(a,1),8019(a,1,2))].">
      <j1 rule="para" parents="4831 8019"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(6102(a,1),8019(a,1,2))].">
      <j1 rule="para" parents="6102 8019"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1143,a,8027,a),flip(a)].">
      <j1 rule="hyper" parents="1143 8027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      (K(x,y) * L(K(z,x),u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1143,a,8026,a),flip(a)].">
      <j1 rule="hyper" parents="1143 8026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2099(a,1),8025(a,1,1))].">
      <j1 rule="para" parents="2099 8025"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = (K(y,x) * K(z,y)) * u
    ]]></literal>
    <justification jstring="[hyper(319,a,8018,a,b,8030,a),flip(a)].">
      <j1 rule="hyper" parents="319 8018 8030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(x,z) * u) = (K(x,z) * u) \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),8020(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4363 8020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8034">
    <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(5861(a,1),7822(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5861 7822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x * K(u \ z,x),y)
    ]]></literal>
    <justification jstring="[para(1929(a,1),8034(a,2,1))].">
      <j1 rule="para" parents="1929 8034"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6883,a(flip),b,8035,a),flip(a)].">
      <j1 rule="hyper" parents="319 6883 8035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      K(x,T(y,(z \ (x * u)) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6417,a(flip),b,8036,a)].">
      <j1 rule="hyper" parents="64 6417 8036"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7251,a,8037,a)].">
      <j1 rule="hyper" parents="7251 8037"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8038(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[para(3784(a,1),8038(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3784 8038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6713,a,b,8039,a)].">
      <j1 rule="hyper" parents="319 6713 8039"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7166,a(flip),b,8039,a)].">
      <j1 rule="hyper" parents="64 7166 8039"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8039(a,1),5741(a,1))].">
      <j1 rule="para" parents="8039 5741"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      K(x,T(y,z \ (x \ u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8042(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(7162,a,8044,a),flip(a)].">
      <j1 rule="hyper" parents="7162 8044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(35,a,6713,a,b,8041,a)].">
      <j1 rule="hyper" parents="35 6713 8041"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(7122,a,8046,a)].">
      <j1 rule="hyper" parents="7122 8046"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7037,a,b,8047,a),flip(a)].">
      <j1 rule="hyper" parents="319 7037 8047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      K(x,K(y,z \ (x * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),8048(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5263(a,1),7831(a,1,1,1))].">
      <j1 rule="para" parents="5263 7831"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,6697,a(flip),b,8050,a(flip))].">
      <j1 rule="hyper" parents="128 6697 8050"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) \ T(y,x) = K(T(y,x),y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(7962(a,2),4201(a,1,1))].">
      <j1 rule="para" parents="7962 4201"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(L(x,y,u),u * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(801,a,7976,a)].">
      <j1 rule="hyper" parents="801 7976"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4122(a,1),7976(a,1,1))].">
      <j1 rule="para" parents="4122 7976"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(4081(a,1),8054(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4081 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,236,a(flip),b,8055,a),flip(a)].">
      <j1 rule="hyper" parents="319 236 8055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),z) = u
    ]]></literal>
    <justification jstring="[para(8055(a,2),799(a,1))].">
      <j1 rule="para" parents="8055 799"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,K(x,z) * u,R(x,w,v5)) = x \ (y \ ((R(x,u,R(x,w,v5)) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[para(7943(a,1),7984(a,2,2,2,1,1))].">
      <j1 rule="para" parents="7943 7984"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K((R(x,y,z) \ 1) \ 1,u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3594(a,1),4811(a,1,2,1,1))].">
      <j1 rule="para" parents="3594 4811"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2920(a,1),8060(a,1,2))].">
      <j1 rule="para" parents="2920 8060"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5571,a(flip),b,5469,a),flip(a)].">
      <j1 rule="hyper" parents="64 5571 5469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      (x / (x / (x / y))) * z = (((y * (x / y)) / y) * z) * a(u,K(w \ 1,w),v5)
    ]]></literal>
    <justification jstring="[para(4540(a,2),5507(a,2,1))].">
      <j1 rule="para" parents="4540 5507"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      ((x / (x * x)) * y) * a(z,K(u \ 1,u),w) = (1 / (1 / (1 / x))) * y
    ]]></literal>
    <justification jstring="[para(644(a,1),8063(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="644 8063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      (x * ((x * x) \ y)) * a(z,K(u \ 1,u),w) = (1 / (1 / (1 / x))) * y
    ]]></literal>
    <justification jstring="[para(689(a,1),8064(a,1,1))].">
      <j1 rule="para" parents="689 8064"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      (x * ((x * x) \ y)) * a(z,K(u,u \ 1),w) = (1 / (1 / (1 / x))) * y
    ]]></literal>
    <justification jstring="[para(1639(a,1),8065(a,1,2,2))].">
      <j1 rule="para" parents="1639 8065"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      K(x \ ((y / z) \ u),L(z,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((z \ y) \ u),L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(6680(a,1),4251(a,1))].">
      <j1 rule="para" parents="6680 4251"/>
    </justification>
  </clause>

  <clause id="8068">
    <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(6102(a,1),6920(a,2,1,2))].">
      <j1 rule="para" parents="6102 6920"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,K(x,y),y \ x) = (x / y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(4681,a,7375,a),flip(a)].">
      <j1 rule="hyper" parents="4681 7375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(T(y,v5),K(R(y,u,w),z))) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(27(a,2),7448(a,1,1,2))].">
      <j1 rule="para" parents="27 7448"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) = T(K(y,z) * x,T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(4367(a,1),7664(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4367 7664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * x,x) = u
    ]]></literal>
    <justification jstring="[para(8071(a,2),5756(a,1))].">
      <j1 rule="para" parents="8071 5756"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ x) = v5
    ]]></literal>
    <justification jstring="[para(7793(a,2),6991(a,1))].">
      <j1 rule="para" parents="7793 6991"/>
    </justification>
  </clause>

  <clause id="8074">
    <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(7721(a,1),8068(a,2,1))].">
      <j1 rule="para" parents="7721 8068"/>
    </justification>
  </clause>

  <clause id="8075">
    <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(319,a,7936,a(flip),b,8074,a),flip(a)].">
      <j1 rule="hyper" parents="319 7936 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8076">
    <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(6102(a,1),8075(a,1,1,2))].">
      <j1 rule="para" parents="6102 8075"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6839(a,1),8076(a,1,2))].">
      <j1 rule="para" parents="6839 8076"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      (K(x,T(y,z)) * a(K(x,u),w,v5)) * (z * K(y,x)) = (a(K(x,u),w,v5) * K(x,y)) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(7518(a,2),8077(a,1,1))].">
      <j1 rule="para" parents="7518 8077"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(T(y,v5),K(z,R(y,u,w)))) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(6791(a,1),8070(a,1,2))].">
      <j1 rule="para" parents="6791 8070"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(y,v5)) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(2843(a,1),8079(a,1,2))].">
      <j1 rule="para" parents="2843 8079"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      T(T(x,y) * K(z * R(x,u,w),T(x,y)),z) = R(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(8080(a,1),4400(a,1,1,2))].">
      <j1 rule="para" parents="8080 4400"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(T(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(4398(a,1),8082(a,1,1))].">
      <j1 rule="para" parents="4398 8082"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      R(T(x,y),z,R(T(x,y),u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,5606,a(flip),b,8083,a),flip(a)].">
      <j1 rule="hyper" parents="64 5606 8083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      T(T(x,y),z) * (K(z * R(T(x,y),u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(8084(a,1),7335(a,2,1))].">
      <j1 rule="para" parents="8084 7335"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(3837(a,1),3848(a,2,1))].">
      <j1 rule="para" parents="3837 3848"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5144(a,1),5155(a,2,1))].">
      <j1 rule="para" parents="5144 5155"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,8087,a),flip(a)].">
      <j1 rule="hyper" parents="319 20 8087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      R(R(x,y,(z \ u) \ u),y * T(z,z \ u),K(z \ u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(110(a,1),8088(a,1,1,3))].">
      <j1 rule="para" parents="110 8088"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      R(R(x,y \ z,T(y,y \ z)),z,K(y \ z,y)) = R(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(228(a,1),8088(a,1,2))].">
      <j1 rule="para" parents="228 8088"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(5435(a,1),8091(a,1,1))].">
      <j1 rule="para" parents="5435 8091"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3725,a,8090,a)].">
      <j1 rule="hyper" parents="3725 8090"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(130,a,8093,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 8093 20"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(8094(a,1),45(a,1))].">
      <j1 rule="para" parents="8094 45"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      (((x * y) \ x) * z) / T((x * y) \ x,u) = z * (K(y \ 1,z) * K(u,y \ 1))
    ]]></literal>
    <justification jstring="[para(5083(a,1),5236(a,2,2,2))].">
      <j1 rule="para" parents="5083 5236"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      (((x * y) \ x) * z) / T((x * y) \ x,u) = ((y \ 1) * z) / T(y \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5201,a(flip),b,8096,a),flip(a)].">
      <j1 rule="hyper" parents="319 5201 8096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,3792,a(flip),b,5547,a),flip(a)].">
      <j1 rule="hyper" parents="36 3792 5547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R((x \ y) * K(x,x \ y),z,x \ y)
    ]]></literal>
    <justification jstring="[para(2969(a,1),6364(a,1,1))].">
      <j1 rule="para" parents="2969 6364"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      1 * ((x \ R(x,y,z)) / K(u,R(x,w,v5))) = K(R(x,w,v5),u) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(209(a,1),7231(a,1,1))].">
      <j1 rule="para" parents="209 7231"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      1 * ((x \ R(x,y,z)) * K(R(x,u,w),v5)) = K(R(x,u,w),v5) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(5174(a,1),8101(a,1,2))].">
      <j1 rule="para" parents="5174 8101"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = 1 * (x \ R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(8061(a,1),8103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8061 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,7,a(flip),b,8104,a),flip(a)].">
      <j1 rule="hyper" parents="319 7 8104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(4374,a,8105,a)].">
      <j1 rule="hyper" parents="4374 8105"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K(x * y,R(T(y,z),x,y)) * (T(y,z) \ T(T(y,z),x)) = T(y,z) \ R(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[para(3512(a,1),8106(a,1,2,2))].">
      <j1 rule="para" parents="3512 8106"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(z,y) \ R(T(K(z,y),x),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7469(a,1),8106(a,1,1))].">
      <j1 rule="para" parents="7469 8106"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7941,a(flip),b,7273,a),flip(a)].">
      <j1 rule="hyper" parents="64 7941 7273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y)) * K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(6830(a,1),7296(a,2,1))].">
      <j1 rule="para" parents="6830 7296"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y)) * K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(7562(a,2),8110(a,2,2))].">
      <j1 rule="para" parents="7562 8110"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5114,a,b,8111,a)].">
      <j1 rule="hyper" parents="64 5114 8111"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      K(x,1 / (1 / (y \ (y / z)))) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(4573,a,8112,a)].">
      <j1 rule="hyper" parents="4573 8112"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      (T(x,y) * (y / x)) * K(x \ y,x) = (x \ y) * ((x \ T(y,x)) \ y)
    ]]></literal>
    <justification jstring="[para(7660(a,1),7875(a,1,2))].">
      <j1 rule="para" parents="7660 7875"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      (x \ y) * ((x \ T(y,x)) \ y) = (y / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(6176,a,8115,a),flip(a)].">
      <j1 rule="hyper" parents="6176 8115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      (x \ y) * ((x \ T(y,x)) \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,1290,a(flip),b,8116,a),flip(a)].">
      <j1 rule="hyper" parents="319 1290 8116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),y \ (y * z)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[hyper(5256,a,7911,a)].">
      <j1 rule="hyper" parents="5256 7911"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8119(a,1,2))].">
      <j1 rule="para" parents="9 8119"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ ((1 / ((x * y) \ x)) \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(6486,a,8120,a)].">
      <j1 rule="hyper" parents="6486 8120"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(81(a,1),8086(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="81 8086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4097(a,1),8100(a,2,1))].">
      <j1 rule="para" parents="4097 8100"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      K(x * y,T(y,z)) * (T(y,z) \ T(T(y,z),x)) = T(y,z) \ R(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[para(5979(a,1),8107(a,1,1))].">
      <j1 rule="para" parents="5979 8107"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      K(x * y,T(y,z)) * K(T(y,z),x) = T(y,z) \ R(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[para(4012(a,2),8124(a,1,2))].">
      <j1 rule="para" parents="4012 8124"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(T(x,z),y) = T(x,z) \ R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(4813(a,1),8125(a,1,1))].">
      <j1 rule="para" parents="4813 8125"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(T(x,z),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5782,a(flip),b,8127,a),flip(a)].">
      <j1 rule="hyper" parents="319 5782 8127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      K(T(x,y),z) * K(x * z,T(x,y)) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(2104,a,8128,a)].">
      <j1 rule="hyper" parents="2104 8128"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(6283,a,8109,a),flip(a)].">
      <j1 rule="hyper" parents="6283 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7798,a(flip),b,8131,a),flip(a)].">
      <j1 rule="hyper" parents="319 7798 8131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      K(x,T((y / (z * u)) \ 1,z * u)) = K(x,y \ ((z * (x \ u)) * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),8132(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 8132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(6441,a,8133,a),flip(a)].">
      <j1 rule="hyper" parents="6441 8133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * u)) = w
    ]]></literal>
    <justification jstring="[para(8133(a,1),6441(a,1))].">
      <j1 rule="para" parents="8133 6441"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(4254,a,8134,a),flip(a)].">
      <j1 rule="hyper" parents="4254 8134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6606,a(flip),b,8134,a),flip(a)].">
      <j1 rule="hyper" parents="64 6606 8134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(8134(a,1),4254(a,1))].">
      <j1 rule="para" parents="8134 4254"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8136(a,2,2,2))].">
      <j1 rule="para" parents="9 8136"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(8136(a,1),5176(a,1,1,2))].">
      <j1 rule="para" parents="8136 5176"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8137(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7102,a,b,8139,a)].">
      <j1 rule="hyper" parents="64 7102 8139"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8141(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(72(a,1),8142(a,1,2,2))].">
      <j1 rule="para" parents="72 8142"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),8142(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 8142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,K(y,z * (u * y))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(8142(a,1),6736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8142 6736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      x * K(y,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,8145,a,b,4242,a)].">
      <j1 rule="hyper" parents="131 8145 4242"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(5731,a,8143,a)].">
      <j1 rule="hyper" parents="5731 8143"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(8143(a,1),5731(a,1))].">
      <j1 rule="para" parents="8143 5731"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(78(a,1),8147(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="78 8147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(4595(a,1),8147(a,1,2))].">
      <j1 rule="para" parents="4595 8147"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6471,a,8148,a),flip(a)].">
      <j1 rule="hyper" parents="6471 8148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      T(x,y \ (x \ z)) = T(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8148,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 8148 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(127,a,8148,a(flip),b,6564,a)].">
      <j1 rule="hyper" parents="127 8148 6564"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8148(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8148(a,2,2,2))].">
      <j1 rule="para" parents="9 8148"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8153(a,1),6736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8153 6736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8154(a,2,2,2))].">
      <j1 rule="para" parents="9 8154"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8156(a,1),6736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8156 6736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4173,a(flip),b,8157,a),flip(a)].">
      <j1 rule="hyper" parents="319 4173 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(8157(a,1),6672(a,1,2))].">
      <j1 rule="para" parents="8157 6672"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6693,a,8162,a)].">
      <j1 rule="hyper" parents="6693 8162"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8164,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 8164 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7412,a,b,8164,a)].">
      <j1 rule="hyper" parents="64 7412 8164"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7411,a(flip),b,8164,a)].">
      <j1 rule="hyper" parents="64 7411 8164"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      T(x,L(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,8164,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 8164 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(8164(a,1),5400(a,1,2))].">
      <j1 rule="para" parents="8164 5400"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,8168,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 8168 22"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      T(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = T(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(513(a,1),8168(a,1,2))].">
      <j1 rule="para" parents="513 8168"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(8168(a,1),5543(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8168 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,8164,a,b,8169,a),flip(a)].">
      <j1 rule="hyper" parents="319 8164 8169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(302(a,1),8169(a,1,1))].">
      <j1 rule="para" parents="302 8169"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(504(a,1),8169(a,1,1)),flip(a)].">
      <j1 rule="para" parents="504 8169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(8169(a,1),7475(a,1,1))].">
      <j1 rule="para" parents="8169 7475"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(8171(a,2),4089(a,1))].">
      <j1 rule="para" parents="8171 4089"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8178(a,1),5728(a,1))].">
      <j1 rule="para" parents="8178 5728"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      K(x,T((y * x) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ (y \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(565(a,1),8184(a,1,2))].">
      <j1 rule="para" parents="565 8184"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(7411(a,1),8184(a,1))].">
      <j1 rule="para" parents="7411 8184"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(8170(a,1),493(a,1,2))].">
      <j1 rule="para" parents="8170 493"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(324,a,8172,a),flip(a)].">
      <j1 rule="hyper" parents="324 8172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = K(y,z) * (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(131,a,8172,a(flip),b,6806,a),flip(a)].">
      <j1 rule="hyper" parents="131 8172 6806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,533,a,b,8172,a(flip))].">
      <j1 rule="hyper" parents="36 533 8172"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(8172(a,1),6021(a,1,1))].">
      <j1 rule="para" parents="8172 6021"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5538,a,8191,a)].">
      <j1 rule="hyper" parents="5538 8191"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),8191(a,1,2))].">
      <j1 rule="para" parents="10 8191"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(8191(a,1),52(a,2))].">
      <j1 rule="para" parents="8191 52"/>
    </justification>
  </clause>

  <clause id="8198">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8092,a(flip),b,8196,a),flip(a)].">
      <j1 rule="hyper" parents="64 8092 8196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      ((x * x) * ((y * z) * T(u,z))) / (u * z) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1156,a,b,8195,a)].">
      <j1 rule="hyper" parents="64 1156 8195"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      R(x,y,z) = ((x * y) * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,239,a,b,8195,a),flip(a)].">
      <j1 rule="hyper" parents="64 239 8195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,542,a(flip),b,8195,a)].">
      <j1 rule="hyper" parents="64 542 8195"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,8195,a(flip),b,239,a)].">
      <j1 rule="hyper" parents="130 8195 239"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(111(a,1),8195(a,1,3)),flip(a)].">
      <j1 rule="para" parents="111 8195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6099(a,2),8195(a,1,3))].">
      <j1 rule="para" parents="6099 8195"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      R(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5537(a,1),8197(a,1))].">
      <j1 rule="para" parents="5537 8197"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5571,a(flip),b,8198,a),flip(a)].">
      <j1 rule="hyper" parents="64 5571 8198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,540,a(flip),b,8198,a),flip(a)].">
      <j1 rule="hyper" parents="64 540 8198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,8198,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="130 8198 107"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(3171(a,1),8207(a,1))].">
      <j1 rule="para" parents="3171 8207"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      ((x * T(y,x)) * L(x,y,z)) \ (x * (y * L(x,y,z))) = K(L(x,y,z),x * T(y,x))
    ]]></literal>
    <justification jstring="[para(8175(a,1),1171(a,1,2,2))].">
      <j1 rule="para" parents="8175 1171"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6485,a,8179,a)].">
      <j1 rule="hyper" parents="6485 8179"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6479,a,8179,a),flip(a)].">
      <j1 rule="hyper" parents="6479 8179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(8179(a,1),6843(a,1,1))].">
      <j1 rule="para" parents="8179 6843"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      (x / ((y \ z) * y)) * z = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(331,a,8189,a)].">
      <j1 rule="hyper" parents="331 8189"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5144,a(flip),b,8189,a),flip(a)].">
      <j1 rule="hyper" parents="128 5144 8189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      x * K(y \ (z \ u),z) = x * K(z \ (y \ u),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,8216,a,b,9,a)].">
      <j1 rule="hyper" parents="131 8216 9"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5899,a(flip),b,8216,a),flip(a)].">
      <j1 rule="hyper" parents="64 5899 8216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      K(x \ (((x \ y) * z) \ y),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(8216(a,1),5033(a,1))].">
      <j1 rule="para" parents="8216 5033"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,y) \ u,x) = K(x \ (((x \ 1) * ((y * (x \ 1)) \ z)) \ u),x)
    ]]></literal>
    <justification jstring="[para(1064(a,1),8222(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1064 8222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(5711(a,1),8202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5711 8202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      K((x * y) * T(z,y),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K((z * y) * R(x,y,z),z * y) = u
    ]]></literal>
    <justification jstring="[para(8203(a,1),4282(a,1,1))].">
      <j1 rule="para" parents="8203 4282"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      R(x / (y / (y * K(z,u))),K(u,z),y * K(z,u)) = (x * (y * K(z,u))) / y
    ]]></literal>
    <justification jstring="[para(5176(a,1),8210(a,1,2))].">
      <j1 rule="para" parents="5176 8210"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      R(x * K(y,z),z \ (z * y),z) = ((x * y) * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(5298(a,1),8210(a,1,1))].">
      <j1 rule="para" parents="5298 8210"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(6068(a,1),8146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6068 8146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = K(x,K(y,z \ R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(1119(a,1),8159(a,1,2,2))].">
      <j1 rule="para" parents="1119 8159"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(8161(a,1),7305(a,1,1))].">
      <j1 rule="para" parents="8161 7305"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8161(a,1),7306(a,1,2))].">
      <j1 rule="para" parents="8161 7306"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,y \ x) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(628,a,8163,a)].">
      <j1 rule="hyper" parents="628 8163"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      (1 / x) * (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(217,a,8163,a),flip(a)].">
      <j1 rule="hyper" parents="217 8163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,x \ y) * K(y \ 1,y) = (y \ 1) * (x * (y / x))
    ]]></literal>
    <justification jstring="[para(8234(a,1),2363(a,1,1))].">
      <j1 rule="para" parents="8234 2363"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      (x * K(y \ z,y)) / ((y \ z) * y) = x / z
    ]]></literal>
    <justification jstring="[hyper(630,a,8188,a)].">
      <j1 rule="hyper" parents="630 8188"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3979,a,b,8188,a),flip(a)].">
      <j1 rule="hyper" parents="64 3979 8188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      (x / (x / y)) / ((y \ x) * y) = y / x
    ]]></literal>
    <justification jstring="[para(3979(a,2),8237(a,1,1))].">
      <j1 rule="para" parents="3979 8237"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      (x / y) \ (y / (y / x)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(199,a,8240,a)].">
      <j1 rule="hyper" parents="199 8240"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (x \ (u \ y))) = z
    ]]></literal>
    <justification jstring="[para(10(a,1),8138(a,1,2,2))].">
      <j1 rule="para" parents="10 8138"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ (y * z))) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),8150(a,1,2,2))].">
      <j1 rule="para" parents="22 8150"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,18,a,b,8177,a)].">
      <j1 rule="hyper" parents="319 18 8177"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      (x * T(y,K(z,u))) \ (x * (K(z,u) * y)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(6809(a,1),8177(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6809 8177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),8244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(6099(a,2),8244(a,1,2))].">
      <j1 rule="para" parents="6099 8244"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,98,a(flip),b,8247,a),flip(a)].">
      <j1 rule="hyper" parents="64 98 8247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      (x * y) / L(z,z \ y,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,8247,a(flip),b,98,a(flip))].">
      <j1 rule="hyper" parents="206 8247 98"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(8247(a,1),5367(a,1,1))].">
      <j1 rule="para" parents="8247 5367"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(8247(a,1),5401(a,1,1))].">
      <j1 rule="para" parents="8247 5401"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8251(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = L(K(x,u),K(y,x),z)
    ]]></literal>
    <justification jstring="[para(4024(a,2),8251(a,1,1,2))].">
      <j1 rule="para" parents="4024 8251"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4982,a,8253,a),flip(a)].">
      <j1 rule="hyper" parents="4982 8253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5275,a(flip),b,8253,a),flip(a)].">
      <j1 rule="hyper" parents="64 5275 8253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8257">
    <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(6851(a,1),8253(a,1,1))].">
      <j1 rule="para" parents="6851 8253"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(8249(a,2),6857(a,1,2,1))].">
      <j1 rule="para" parents="8249 6857"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) * (u * (z / y)) = (u * (z / y)) * K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(8249(a,2),6919(a,1,1,2))].">
      <j1 rule="para" parents="8249 6919"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      T(x * (y / z),L(z,z \ y,x)) = L(z,z \ y,x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(8250(a,1),111(a,1,1))].">
      <j1 rule="para" parents="8250 111"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(5187,a,8140,a),flip(a)].">
      <j1 rule="hyper" parents="5187 8140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8261(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      (x \ 1) * ((y / x) / (x \ 1)) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),8151(a,2,2,2))].">
      <j1 rule="para" parents="12 8151"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(x \ (y * z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(6043,a,8180,a)].">
      <j1 rule="hyper" parents="6043 8180"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(8264(a,1),7172(a,1))].">
      <j1 rule="para" parents="8264 7172"/>
    </justification>
  </clause>

  <clause id="8266">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7475,a(flip),b,8181,a),flip(a)].">
      <j1 rule="hyper" parents="64 7475 8181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) = K(y \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7924,a(flip),b,8266,a)].">
      <j1 rule="hyper" parents="64 7924 8266"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(909(a,1),8266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="909 8266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(7213(a,1),8209(a,1,1))].">
      <j1 rule="para" parents="7213 8209"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      x / (K(y \ x,y) * ((x \ 1) \ 1)) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4386,a,b,8233,a)].">
      <j1 rule="hyper" parents="64 4386 8233"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6856,a(flip),b,8257,a),flip(a)].">
      <j1 rule="hyper" parents="319 6856 8257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,494,a(flip),b,8273,a),flip(a)].">
      <j1 rule="hyper" parents="319 494 8273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8276">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8254,a(flip),b,8274,a)].">
      <j1 rule="hyper" parents="64 8254 8274"/>
    </justification>
  </clause>

  <clause id="8278">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,8276,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 8276 18"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8276(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8276 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8280">
    <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(8276(a,1),436(a,1,2,1))].">
      <j1 rule="para" parents="8276 436"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(v5,y),v6) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(206,a,8279,a,b,5330,a)].">
      <j1 rule="hyper" parents="206 8279 5330"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5185,a,8278,a)].">
      <j1 rule="hyper" parents="5185 8278"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,8278,a)].">
      <j1 rule="hyper" parents="529 8278"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5491,a,b,8278,a)].">
      <j1 rule="hyper" parents="64 5491 8278"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,6623,a(flip),b,8278,a),flip(a)].">
      <j1 rule="hyper" parents="64 6623 8278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2099(a,2),8278(a,2,2))].">
      <j1 rule="para" parents="2099 8278"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1800(a,1),8283(a,1,2))].">
      <j1 rule="para" parents="1800 8283"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      (x * R(R(x,K(y,z),K(z,u)) \ (x * K(y,z)),w,v5)) * K(z,u) = R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(8283(a,1),2579(a,1,1,1))].">
      <j1 rule="para" parents="8283 2579"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(4831(a,1),8283(a,1,2))].">
      <j1 rule="para" parents="4831 8283"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8283(a,1),4953(a,1,1))].">
      <j1 rule="para" parents="8283 4953"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(5560(a,1),8283(a,1,3))].">
      <j1 rule="para" parents="5560 8283"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(4586(a,1),8287(a,1,3))].">
      <j1 rule="para" parents="4586 8287"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (L(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(130,a,8289,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 8289 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,w)) = L(K(z,u),y,x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(8289(a,1),552(a,1,1))].">
      <j1 rule="para" parents="8289 552"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(8291(a,1),52(a,2))].">
      <j1 rule="para" parents="8291 52"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),K(x,y) * z) = z \ (K(y,u) * (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(8292(a,1),882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8292 882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(8292(a,1),7926(a,1)),flip(a)].">
      <j1 rule="para" parents="8292 7926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      (x * (y * R(x,z,u))) \ ((y * R(x,z,u)) * T(x,y)) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7334,a(flip),b,8290,a),flip(a)].">
      <j1 rule="hyper" parents="319 7334 8290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      (x * (y * L(x,z,u))) \ ((y * L(x,z,u)) * T(x,y)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7321,a(flip),b,8290,a),flip(a)].">
      <j1 rule="hyper" parents="319 7321 8290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3385,a(flip),b,8290,a),flip(a)].">
      <j1 rule="hyper" parents="64 3385 8290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * L(T(x,w),y,z)) = K(u,L(x,y,z)) * K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),8290(a,1,2,2))].">
      <j1 rule="para" parents="25 8290"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8290(a,2),2104(a,1))].">
      <j1 rule="para" parents="8290 2104"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4582,a,b,8300,a)].">
      <j1 rule="hyper" parents="64 4582 8300"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8300(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="8300 5176"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(8300(a,1),5181(a,1,1))].">
      <j1 rule="para" parents="8300 5181"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8304(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),8307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 8307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(3405(a,1),8308(a,1,2))].">
      <j1 rule="para" parents="3405 8308"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7488,a,8309,a),flip(a)].">
      <j1 rule="hyper" parents="7488 8309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4581,a,8309,a)].">
      <j1 rule="hyper" parents="4581 8309"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,8309,a)].">
      <j1 rule="hyper" parents="145 8309"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5512,a,b,8309,a)].">
      <j1 rule="hyper" parents="64 5512 8309"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4578,a,b,8309,a)].">
      <j1 rule="hyper" parents="64 4578 8309"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4569,a,b,8309,a)].">
      <j1 rule="hyper" parents="64 4569 8309"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2969,a,b,8309,a)].">
      <j1 rule="hyper" parents="64 2969 8309"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4582,a(flip),b,8309,a)].">
      <j1 rule="hyper" parents="64 4582 8309"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,8309,a(flip),b,5782,a)].">
      <j1 rule="hyper" parents="131 8309 5782"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,8309,a(flip),b,2969,a)].">
      <j1 rule="hyper" parents="130 8309 2969"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      a(x,y,x) != x \ z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8309(a,1),48(a,1))].">
      <j1 rule="para" parents="8309 48"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      L(x \ a(y,z,y),x,y) = (y * x) \ R(y,z,y)
    ]]></literal>
    <justification jstring="[para(8309(a,1),302(a,1,1,2))].">
      <j1 rule="para" parents="8309 302"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(8309(a,1),4581(a,1))].">
      <j1 rule="para" parents="8309 4581"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8309(a,1),5269(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8309 5269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(8309(a,1),8123(a,1,1))].">
      <j1 rule="para" parents="8309 8123"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8312(a,1),330(a,1,2))].">
      <j1 rule="para" parents="8312 330"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(8316(a,1),8225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8316 8225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5185,a,8311,a)].">
      <j1 rule="hyper" parents="5185 8311"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8311(a,1),4370(a,1,2))].">
      <j1 rule="para" parents="8311 4370"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8311(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="8311 5176"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      K(x,y) \ K(x * y,y) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(4393,a,8314,a)].">
      <j1 rule="hyper" parents="4393 8314"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(4374,a,8314,a)].">
      <j1 rule="hyper" parents="4374 8314"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5185,a,8315,a)].">
      <j1 rule="hyper" parents="5185 8315"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(8315(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="8315 5176"/>
    </justification>
  </clause>

  <clause id="8334">
    <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(64,a,1511,a,b,8323,a)].">
      <j1 rule="hyper" parents="64 1511 8323"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),8323(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(8323(a,1),111(a,1,1))].">
      <j1 rule="para" parents="8323 111"/>
    </justification>
  </clause>

  <clause id="8337">
    <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(8323(a,2),483(a,1,2,2))].">
      <j1 rule="para" parents="8323 483"/>
    </justification>
  </clause>

  <clause id="8338">
    <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(8323(a,2),801(a,1,2,2,2))].">
      <j1 rule="para" parents="8323 801"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4568(a,2),8325(a,1))].">
      <j1 rule="para" parents="4568 8325"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      a(x,x \ y,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8327(a,1,2,2))].">
      <j1 rule="para" parents="10 8327"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8328(a,1,1,2))].">
      <j1 rule="para" parents="10 8328"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = (z * K(x,x * y)) \ (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8328(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="8328 18"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4281,a,b,8332,a),flip(a)].">
      <j1 rule="hyper" parents="319 4281 8332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,5396,a(flip),b,8332,a)].">
      <j1 rule="hyper" parents="127 5396 8332"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      a(1 / ((x * y) \ x),T(z,y),1 / ((x * y) \ x)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(5074(a,1),8332(a,2,1))].">
      <j1 rule="para" parents="5074 8332"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      a(T(x,y * z),z,T(x,y * z)) * K(z,T(x,y)) = K(T(x,y * z) * z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(6287(a,1),8332(a,1,2))].">
      <j1 rule="para" parents="6287 8332"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a(flip),b,8310,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 8310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(8310(a,2),8325(a,1))].">
      <j1 rule="para" parents="8310 8325"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      a(x,y \ T(z,x),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(5271(a,1),8348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5271 8348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(127,a,3375,a(flip),b,8318,a),flip(a)].">
      <j1 rule="hyper" parents="127 3375 8318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      T(x,y) \ T(x,x \ y) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,3329,a(flip),b,8318,a)].">
      <j1 rule="hyper" parents="127 3329 8318"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(7731(a,1),8349(a,1))].">
      <j1 rule="para" parents="7731 8349"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5336,a,8282,a)].">
      <j1 rule="hyper" parents="5336 8282"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2099(a,2),8282(a,1,1,2))].">
      <j1 rule="para" parents="2099 8282"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,8354,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 8354 18"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2099(a,2),8284(a,2,2))].">
      <j1 rule="para" parents="2099 8284"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      T(L(x,K(y,z),K(z,u)) * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(244,a,8286,a,b,646,a)].">
      <j1 rule="hyper" parents="244 8286 646"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5163(a,1),8286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5163 8286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,8282,a,b,8356,a(flip))].">
      <j1 rule="hyper" parents="36 8282 8356"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      (x * K(y,z)) * (K(u,y) * K(z,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(5493,a,8357,a),flip(a)].">
      <j1 rule="hyper" parents="5493 8357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * K(y,u)) = K(y,u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(5490,a,8358,a)].">
      <j1 rule="hyper" parents="5490 8358"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      ((K(x,y) \ z) * ((K(x,y) \ 1) \ 1)) * K(u,x) = ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[para(2685(a,1),8358(a,1,1))].">
      <j1 rule="para" parents="2685 8358"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      L((K(x,y) * K(z,x)) \ 1,K(x,y) * K(z,x),u) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(399,a,8361,a)].">
      <j1 rule="hyper" parents="399 8361"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * w != x
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * K(y,u) = w
    ]]></literal>
    <justification jstring="[para(8361(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8361 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,y) * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(8361(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8361 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * K(x,u)) = K(x,u) * K(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(6113(a,1),8363(a,1,1))].">
      <j1 rule="para" parents="6113 8363"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(4656(a,1),8285(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4656 8285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6374,a,8369,a)].">
      <j1 rule="hyper" parents="6374 8369"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      x / R(x,y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,8369,a(flip),b,1481,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 8369 1481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,8370,a(flip),b,1123,a)].">
      <j1 rule="hyper" parents="127 8370 1123"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      (x * ((y \ L(y,z,y)) \ 1)) * T(y / R(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(8371(a,1),2705(a,1,1,2,1))].">
      <j1 rule="para" parents="8371 2705"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(8372(a,1),3971(a,2,2))].">
      <j1 rule="para" parents="8372 3971"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      (x \ 1) \ ((y \ (y / x)) * y) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,4735,a,b,8263,a)].">
      <j1 rule="hyper" parents="127 4735 8263"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      (x / (y \ x)) / ((y \ x) \ 1) = ((y \ x) \ 1) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(78(a,1),8375(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 8375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6369,a,b,8324,a)].">
      <j1 rule="hyper" parents="319 6369 8324"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,7638,a(flip),b,8360,a),flip(a)].">
      <j1 rule="hyper" parents="319 7638 8360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(8311(a,1),8379(a,1,2))].">
      <j1 rule="para" parents="8311 8379"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      (x / y) \ (x / L(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,8380,a)].">
      <j1 rule="hyper" parents="134 8380"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),8380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1535,a,8382,a)].">
      <j1 rule="hyper" parents="1535 8382"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(199,a,8382,a)].">
      <j1 rule="hyper" parents="199 8382"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5725,a(flip),b,8383,a)].">
      <j1 rule="hyper" parents="64 5725 8383"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      L(x,y,x) * a(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,179,a(flip),b,8383,a),flip(a)].">
      <j1 rule="hyper" parents="64 179 8383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      x / a(x,y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,179,a(flip),b,8383,a(flip))].">
      <j1 rule="hyper" parents="128 179 8383"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,179,a(flip),b,8383,a(flip))].">
      <j1 rule="hyper" parents="127 179 8383"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),8383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      x / a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8386(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8386 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      L(x \ a(y,z,y),x,L(y,z,y)) = (L(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(8386(a,1),96(a,2,2))].">
      <j1 rule="para" parents="8386 96"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      L(x,y,x) \ x = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a,b,8388,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 8388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8388(a,1),3946(a,1,1))].">
      <j1 rule="para" parents="8388 3946"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      ((x * y) * a(T(y,x),z,T(y,x))) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(859(a,1),8384(a,1,2))].">
      <j1 rule="para" parents="859 8384"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8323(a,2),8384(a,1,1))].">
      <j1 rule="para" parents="8323 8384"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      (L(x,y,x) * z) * a(x,y,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(586,a,8385,a),flip(a)].">
      <j1 rule="hyper" parents="586 8385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6566,a,b,8385,a)].">
      <j1 rule="hyper" parents="64 6566 8385"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6475,a,b,8385,a)].">
      <j1 rule="hyper" parents="64 6475 8385"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      L(x,y,x) * (z * a(x,y,x)) = x * z
    ]]></literal>
    <justification jstring="[hyper(131,a,8385,a(flip),b,1168,a)].">
      <j1 rule="hyper" parents="131 8385 1168"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,8396,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 8396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,8399,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 8399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,8400,a(flip),b,5901,a(flip))].">
      <j1 rule="hyper" parents="127 8400 5901"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      (T(x * K(y \ x,z),x) / x) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(6843(a,1),8395(a,1,2))].">
      <j1 rule="para" parents="6843 8395"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(4374,a,8398,a)].">
      <j1 rule="hyper" parents="4374 8398"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,8397,a(flip),b,4308,a)].">
      <j1 rule="hyper" parents="131 8397 4308"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * K(x,u)) = K(x,u) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6142,a(flip),b,8368,a),flip(a)].">
      <j1 rule="hyper" parents="319 6142 8368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,u) * z) = K(x,T(u,z)) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6113(a,1),8406(a,1,2))].">
      <j1 rule="para" parents="6113 8406"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),8135(a,1,2,2,1))].">
      <j1 rule="para" parents="10 8135"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ (z \ y),z)) = u
    ]]></literal>
    <justification jstring="[para(6949(a,1),8185(a,1))].">
      <j1 rule="para" parents="6949 8185"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      R(x * K(K(y,T(z,x)),u),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(6113(a,1),8410(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6113 8410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,5330,a,b,8245,a)].">
      <j1 rule="hyper" parents="40 5330 8245"/>
    </justification>
  </clause>

  <clause id="8413">
    <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(484(a,1),8256(a,2,2))].">
      <j1 rule="para" parents="484 8256"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(z,u),w,v5))) * K(y,z) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(856,a,8281,a)].">
      <j1 rule="hyper" parents="856 8281"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),L(K(z,y),u,x)) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x)
    ]]></literal>
    <justification jstring="[para(8412(a,1),4794(a,1,1,2))].">
      <j1 rule="para" parents="8412 4794"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(8230(a,2),7122(a,1))].">
      <j1 rule="para" parents="8230 7122"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      x / T((y \ x) * y,x \ 1) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(4845(a,1),8270(a,1,2))].">
      <j1 rule="para" parents="4845 8270"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      T((x \ y) * x,y \ 1) \ y = (y \ 1) * (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(6478,a,8417,a)].">
      <j1 rule="hyper" parents="6478 8417"/>
    </justification>
  </clause>

  <clause id="8419">
    <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(8323(a,1),8334(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8323 8334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,1972,a(flip),b,8374,a),flip(a)].">
      <j1 rule="hyper" parents="319 1972 8374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8421">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4306(a,1),8420(a,1,2))].">
      <j1 rule="para" parents="4306 8420"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(5777(a,1),8421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5777 8421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5719,a,b,8422,a)].">
      <j1 rule="hyper" parents="64 5719 8422"/>
    </justification>
  </clause>

  <clause id="8424">
    <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(8423(a,1),5753(a,1,1,2,1))].">
      <j1 rule="para" parents="8423 5753"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      ((x \ y) \ 1) \ ((y \ x) * y) = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(78(a,1),8376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 8376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      x / ((x \ L(x,y,z)) \ 1) = ((x \ L(x,y,z)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3939(a,1),8425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3939 8425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      (x * x) * (((y * z) * T(u,z)) / (u * z)) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,719,a(flip),b,8200,a)].">
      <j1 rule="hyper" parents="64 719 8200"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      K(x,L(T(y,z * u),y \ u,z)) = K(x,(z * u) / (z * (u / y)))
    ]]></literal>
    <justification jstring="[para(25(a,2),8258(a,1,2))].">
      <j1 rule="para" parents="25 8258"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      R((x * x) * y,z,u) = (x * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(8201(a,2),8427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8201 8427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      R((x * x) * ((x * x) \ y),z,u) = R(y,(x * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,1570,a(flip),b,8429,a),flip(a)].">
      <j1 rule="hyper" parents="319 1570 8429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      R(x,(y * y) \ z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(275(a,1),8431(a,1,2))].">
      <j1 rule="para" parents="275 8431"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      R(x,K(y,z),u) = R(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(5176(a,1),8431(a,1,2))].">
      <j1 rule="para" parents="5176 8431"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      R(x,y \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),8432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 8432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,8432,a,b,8434,a)].">
      <j1 rule="hyper" parents="319 8432 8434"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,6167,a(flip),b,8434,a),flip(a)].">
      <j1 rule="hyper" parents="319 6167 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,5044,a(flip),b,8434,a),flip(a)].">
      <j1 rule="hyper" parents="319 5044 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,5044,a(flip),b,8434,a),flip(a)].">
      <j1 rule="hyper" parents="64 5044 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4107,a,8438,a)].">
      <j1 rule="hyper" parents="4107 8438"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(130,a,8438,a(flip),b,2855,a),flip(a)].">
      <j1 rule="hyper" parents="130 8438 2855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(130,a,8439,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 8439 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(5084(a,1),8439(a,1,3))].">
      <j1 rule="para" parents="5084 8439"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(4130(a,1),8437(a,1,3,2))].">
      <j1 rule="para" parents="4130 8437"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(8443(a,1),519(a,1,1))].">
      <j1 rule="para" parents="8443 519"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,7637,a(flip),b,8433,a),flip(a)].">
      <j1 rule="hyper" parents="319 7637 8433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,7424,a(flip),b,8433,a),flip(a)].">
      <j1 rule="hyper" parents="319 7424 8433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5158,a,b,8446,a),flip(a)].">
      <j1 rule="hyper" parents="319 5158 8446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(130,a,8447,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 8447 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(R(K(x,y),K(y,w),v5) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8447(a,1),3590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8447 3590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8435(a,1),5451(a,1,1))].">
      <j1 rule="para" parents="8435 5451"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8435(a,1),5452(a,1))].">
      <j1 rule="para" parents="8435 5452"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(4224(a,1),8444(a,1,2))].">
      <j1 rule="para" parents="4224 8444"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5209,a(flip),b,8457,a)].">
      <j1 rule="hyper" parents="64 5209 8457"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(4017(a,1),8440(a,1,2))].">
      <j1 rule="para" parents="4017 8440"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(199,a,8459,a)].">
      <j1 rule="hyper" parents="199 8459"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5423,a,b,8460,a)].">
      <j1 rule="hyper" parents="64 5423 8460"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(8461(a,1),3457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8461 3457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5473,a,b,8441,a)].">
      <j1 rule="hyper" parents="64 5473 8441"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5475,a(flip),b,8441,a),flip(a)].">
      <j1 rule="hyper" parents="64 5475 8441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(4019(a,2),8458(a,1,1))].">
      <j1 rule="para" parents="4019 8458"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,8466,a,b,156,a)].">
      <j1 rule="hyper" parents="129 8466 156"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(127,a,8466,a(flip),b,3056,a(flip))].">
      <j1 rule="hyper" parents="127 8466 3056"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      (T(x / y,y) / (y \ 1)) \ (x / y) = y \ K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4175(a,1),8467(a,2,2))].">
      <j1 rule="para" parents="4175 8467"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(8467(a,1),5517(a,1,1))].">
      <j1 rule="para" parents="8467 5517"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,1819,a,b,8470,a),flip(a)].">
      <j1 rule="hyper" parents="319 1819 8470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3052,a(flip),b,8470,a),flip(a)].">
      <j1 rule="hyper" parents="319 3052 8470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(127,a,8470,a,b,3052,a(flip))].">
      <j1 rule="hyper" parents="127 8470 3052"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(81(a,1),8462(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 8462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(4024(a,2),8463(a,2,2))].">
      <j1 rule="para" parents="4024 8463"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(4404(a,1),8468(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4404 8468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(207,a,8474,a)].">
      <j1 rule="hyper" parents="207 8474"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(127,a,4989,a(flip),b,8475,a(flip))].">
      <j1 rule="hyper" parents="127 4989 8475"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5172(a,1),8475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 8475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5449,a,b,8477,a),flip(a)].">
      <j1 rule="hyper" parents="64 5449 8477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(81(a,1),8477(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="81 8477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,312,a(flip),b,8478,a),flip(a)].">
      <j1 rule="hyper" parents="319 312 8478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,8479,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 8479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(8480(a,1),2312(a,1,1))].">
      <j1 rule="para" parents="8480 2312"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,8482,a(flip),b,3797,a),flip(a)].">
      <j1 rule="hyper" parents="130 8482 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4737,a,b,8483,a)].">
      <j1 rule="hyper" parents="64 4737 8483"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8152,a(flip),b,8483,a),flip(a)].">
      <j1 rule="hyper" parents="64 8152 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      (((x \ y) * x) \ x) \ 1 = T((y \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5135(a,2),8484(a,1,1))].">
      <j1 rule="para" parents="5135 8484"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,3232,a(flip),b,8485,a)].">
      <j1 rule="hyper" parents="64 3232 8485"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(4024(a,1),8487(a,1,2))].">
      <j1 rule="para" parents="4024 8487"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((y * x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),8488(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(127,a,8490,a,b,xx)].">
      <j1 rule="hyper" parents="127 8490"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      L(x \ 1,x,y) \ K(x,y) = ((x * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(972,a,8491,a)].">
      <j1 rule="hyper" parents="972 8491"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(569,a,8464,a)].">
      <j1 rule="hyper" parents="569 8464"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      L((K(x,y) * K(z,x)) \ 1,K(x,y) * K(z,x),u) \ K(K(x,y) * K(z,x),u) = (((K(y,x) * K(x,z)) \ u) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(8031(a,2),8493(a,2,1,1))].">
      <j1 rule="para" parents="8031 8493"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(8442(a,1),6310(a,1,2))].">
      <j1 rule="para" parents="8442 6310"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,8445,a(flip),b,4823,a)].">
      <j1 rule="hyper" parents="131 8445 4823"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,8452,a)].">
      <j1 rule="hyper" parents="488 8452"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8024,a(flip),b,8452,a)].">
      <j1 rule="hyper" parents="64 8024 8452"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) = u * K(K(x,y) * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(128,a,8452,a(flip),b,4095,a)].">
      <j1 rule="hyper" parents="128 8452 4095"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2099(a,2),8452(a,1,1))].">
      <j1 rule="para" parents="2099 8452"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(8315(a,1),8452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8315 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(8498(a,1),300(a,1,2))].">
      <j1 rule="para" parents="8498 300"/>
    </justification>
  </clause>

  <clause id="8505">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(8498(a,1),4412(a,1,2))].">
      <j1 rule="para" parents="8498 4412"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(4374,a,8503,a)].">
      <j1 rule="hyper" parents="4374 8503"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8398,a(flip),b,8503,a),flip(a)].">
      <j1 rule="hyper" parents="64 8398 8503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(244,a,8398,a(flip),b,8503,a(flip))].">
      <j1 rule="hyper" parents="244 8398 8503"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(244,a,8503,a(flip),b,8398,a(flip))].">
      <j1 rule="hyper" parents="244 8503 8398"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(4281(a,2),8503(a,1,1))].">
      <j1 rule="para" parents="4281 8503"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(6413,a,8508,a),flip(a)].">
      <j1 rule="hyper" parents="6413 8508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(2177,a,8508,a)].">
      <j1 rule="hyper" parents="2177 8508"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,8508,a)].">
      <j1 rule="hyper" parents="56 8508"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ z = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,3324,a(flip),b,8508,a(flip))].">
      <j1 rule="hyper" parents="40 3324 8508"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a,b,8509,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 8509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(8509(a,1),291(a,1,2))].">
      <j1 rule="para" parents="8509 291"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      L(a(x,y,x),z,u) * w = w * L(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8509(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8509 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8509(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8509 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <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(319,a,8419,a(flip),b,8507,a),flip(a)].">
      <j1 rule="hyper" parents="319 8419 8507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(319,a,8396,a(flip),b,8507,a),flip(a)].">
      <j1 rule="hyper" parents="319 8396 8507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8318,a(flip),b,8507,a),flip(a)].">
      <j1 rule="hyper" parents="319 8318 8507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,8396,a(flip),b,8507,a)].">
      <j1 rule="hyper" parents="127 8396 8507"/>
    </justification>
  </clause>

  <clause id="8524">
    <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(127,a,8507,a,b,653,a)].">
      <j1 rule="hyper" parents="127 8507 653"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(8507(a,1),261(a,1))].">
      <j1 rule="para" parents="8507 261"/>
    </justification>
  </clause>

  <clause id="8526">
    <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(8507(a,1),743(a,1,1))].">
      <j1 rule="para" parents="8507 743"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(L(w,y,a(z,u,z)),a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(8507(a,1),484(a,1,1,2))].">
      <j1 rule="para" parents="8507 484"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ ((x * a(z,u,z)) * (L(y,a(z,u,z),x) * w)) = L(w,L(y,a(z,u,z),x),x * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(8507(a,1),483(a,1,1,2))].">
      <j1 rule="para" parents="8507 483"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(8511(a,1),8402(a,1,2))].">
      <j1 rule="para" parents="8511 8402"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(8512(a,1),8399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8512 8399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[para(8512(a,1),8404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8512 8404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      T(a(x / y,z,x / y),u) = (x / y) \ R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(5762(a,1),8515(a,2,2))].">
      <j1 rule="para" parents="5762 8515"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6072(a,1),8522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6072 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      (x / y) * L(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,8529,a)].">
      <j1 rule="hyper" parents="145 8529"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(127,a,3298,a,b,8531,a),flip(a)].">
      <j1 rule="hyper" parents="127 3298 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,8,a(flip),b,8531,a),flip(a)].">
      <j1 rule="hyper" parents="127 8 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      a(x,x \ y,x) \ y = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,738,a,b,8531,a),flip(a)].">
      <j1 rule="hyper" parents="35 738 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * (L(y,z,u) * x)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4801,a(flip),b,8506,a),flip(a)].">
      <j1 rule="hyper" parents="319 4801 8506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4437(a,1),8510(a,1,2))].">
      <j1 rule="para" parents="4437 8510"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,8476,a,b,xx)].">
      <j1 rule="hyper" parents="131 8476"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(81(a,1),8489(a,2,1,1,1))].">
      <j1 rule="para" parents="81 8489"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      T(x,y) \ (x * (K(x,z) * u)) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4312,a,b,8499,a)].">
      <j1 rule="hyper" parents="319 4312 8499"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(319,a,153,a(flip),b,8499,a),flip(a)].">
      <j1 rule="hyper" parents="319 153 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8025,a,b,8499,a)].">
      <j1 rule="hyper" parents="64 8025 8499"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(4363(a,1),8499(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(4363(a,1),8499(a,2,2))].">
      <j1 rule="para" parents="4363 8499"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      K(L(x,y / x,z),u) * (K(u,w) * v5) = K(u,w) * (L(K(x,u),y,z) * v5)
    ]]></literal>
    <justification jstring="[para(5367(a,1),8499(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5367 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(6998(a,1),8502(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6998 8502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6713(a,1),8505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6713 8505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,94,a(flip),b,8517,a)].">
      <j1 rule="hyper" parents="128 94 8517"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,8518,a)].">
      <j1 rule="hyper" parents="247 8518"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,3236,a(flip),b,8544,a)].">
      <j1 rule="hyper" parents="64 3236 8544"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      T(x,T(((y / z) \ 1) * y,y)) = T(x,((z \ y) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(8544(a,1),5738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8544 5738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(u,w)),K(u,w)) = K(y,v5) * (K(x,y) * (K(y,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6797,a,b,8546,a)].">
      <j1 rule="hyper" parents="319 6797 8546"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,8503,a(flip),b,8548,a)].">
      <j1 rule="hyper" parents="64 8503 8548"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,8548,a(flip),b,4356,a)].">
      <j1 rule="hyper" parents="206 8548 4356"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,8548,a(flip),b,8452,a)].">
      <j1 rule="hyper" parents="128 8548 8452"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(4374,a,8549,a)].">
      <j1 rule="hyper" parents="4374 8549"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) = K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w)
    ]]></literal>
    <justification jstring="[para(8552(a,1),3818(a,1,1,2,1))].">
      <j1 rule="para" parents="8552 3818"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,y * (z / y),(z / y) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(8555(a,1),5285(a,2,2,1))].">
      <j1 rule="para" parents="8555 5285"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(130,a,6748,a,b,8559,a)].">
      <j1 rule="hyper" parents="130 6748 8559"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(3985(a,1),8560(a,1,1))].">
      <j1 rule="para" parents="3985 8560"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      (((K(x,y) * (K(z,y) * u)) / (K(z,y) * u)) * K(z,y)) * u = K(z,y) * (R(K(x,y),K(z,y),u) * u)
    ]]></literal>
    <justification jstring="[para(8561(a,1),1882(a,1,1,1,1))].">
      <j1 rule="para" parents="8561 1882"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ (y / x) = x \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),8469(a,1,1,1))].">
      <j1 rule="para" parents="111 8469"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      (x \ K(x,x \ y)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(8567(a,1),5519(a,1,1))].">
      <j1 rule="para" parents="8567 5519"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      (x \ K(x,(x \ 1) * y)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5679(a,2),8568(a,1,1,2))].">
      <j1 rule="para" parents="5679 8568"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(4036(a,1),8545(a,1,2))].">
      <j1 rule="para" parents="4036 8545"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      x \ (T(x,y) * (K(z,x) * u)) = T(x,z) \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4288,a,b,8570,a)].">
      <j1 rule="hyper" parents="319 4288 8570"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      (R(x,y,z) \ K(R(x,y,z),R(x,y,z) \ 1)) \ (K(x,u) / R(x,y,z)) = (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u))
    ]]></literal>
    <justification jstring="[para(7728(a,1),8569(a,1,1,2))].">
      <j1 rule="para" parents="7728 8569"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * (K(y,x) * u) = w
    ]]></literal>
    <justification jstring="[para(8571(a,1),4298(a,1))].">
      <j1 rule="para" parents="8571 4298"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * (K(x,y) * u) = w
    ]]></literal>
    <justification jstring="[para(8024(a,1),8504(a,1))].">
      <j1 rule="para" parents="8024 8504"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * (K(x,z) * u) = w
    ]]></literal>
    <justification jstring="[para(8025(a,2),8574(a,1))].">
      <j1 rule="para" parents="8025 8574"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(6748(a,2),8564(a,2,2,1))].">
      <j1 rule="para" parents="6748 8564"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(331,a,8576,a),flip(a)].">
      <j1 rule="hyper" parents="331 8576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(6748(a,2),8577(a,1,2,1))].">
      <j1 rule="para" parents="6748 8577"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,5986,a(flip),b,8268,a),flip(a)].">
      <j1 rule="hyper" parents="319 5986 8268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,u),w,v5) = x * (R(K(z,u),w,v5) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2105(a,2),8280(a,2,2))].">
      <j1 rule="para" parents="2105 8280"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * R(K(y,u),w,v5)) = x * R(K(y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5172(a,1),8280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 8280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2101(a,1),8293(a,2,2))].">
      <j1 rule="para" parents="2101 8293"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = K(x,y) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8363,a(flip),b,8342,a),flip(a)].">
      <j1 rule="hyper" parents="319 8363 8342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8311,a(flip),b,8583,a),flip(a)].">
      <j1 rule="hyper" parents="319 8311 8583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = u
    ]]></literal>
    <justification jstring="[para(8585(a,1),856(a,1,2))].">
      <j1 rule="para" parents="8585 856"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(4566,a,8497,a),flip(a)].">
      <j1 rule="hyper" parents="4566 8497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,8587,a)].">
      <j1 rule="hyper" parents="55 8587"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),8589(a,1,2,1))].">
      <j1 rule="para" parents="9 8589"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,8591,a)].">
      <j1 rule="hyper" parents="56 8591"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      K(x,y * L(y \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[para(224(a,2),8593(a,1,2,2))].">
      <j1 rule="para" parents="224 8593"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(36,a,8378,a(flip),b,8535,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 8378 8535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8596">
    <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(223(a,2),8565(a,1,2,2,2))].">
      <j1 rule="para" parents="223 8565"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,683,a(flip),b,8579,a),flip(a)].">
      <j1 rule="hyper" parents="319 683 8579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6355,a,8597,a)].">
      <j1 rule="hyper" parents="6355 8597"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(8067,a,8598,a)].">
      <j1 rule="hyper" parents="8067 8598"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * (R(K(x,y),u,w) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7261,a,b,8580,a)].">
      <j1 rule="hyper" parents="64 7261 8580"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      x / (K(y,z) * R(K(z,u),w,v5)) = (x * R(K(u,z),w,v5)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5579,a(flip),b,8581,a)].">
      <j1 rule="hyper" parents="128 5579 8581"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      (x * (K(y,z) * L(K(u,y),w,v5))) * K(z,y) = x * L(K(u,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(5185,a,8582,a)].">
      <j1 rule="hyper" parents="5185 8582"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(5190,a,8294,a)].">
      <j1 rule="hyper" parents="5190 8294"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,2101,a(flip),b,8604,a),flip(a)].">
      <j1 rule="hyper" parents="319 2101 8604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5172(a,1),8605(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5172 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5356(a,1),8606(a,1,2))].">
      <j1 rule="para" parents="5356 8606"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(8606(a,1),5804(a,1,2))].">
      <j1 rule="para" parents="8606 5804"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(w,z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,z) * a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(8608(a,1),6124(a,1,2,2))].">
      <j1 rule="para" parents="8608 6124"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(5333,a,8607,a)].">
      <j1 rule="hyper" parents="5333 8607"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(4374,a,8607,a)].">
      <j1 rule="hyper" parents="4374 8607"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2103,a,8607,a)].">
      <j1 rule="hyper" parents="2103 8607"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(4712(a,1),8607(a,1,2))].">
      <j1 rule="para" parents="4712 8607"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(5363(a,1),8607(a,1,2))].">
      <j1 rule="para" parents="5363 8607"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(7828(a,1),8607(a,1,2))].">
      <j1 rule="para" parents="7828 8607"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(8607(a,1),8029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8607 8029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(8607(a,1),8414(a,1,1,2))].">
      <j1 rule="para" parents="8607 8414"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(8607(a,1),8603(a,1,1,2))].">
      <j1 rule="para" parents="8607 8603"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4840,a,8612,a)].">
      <j1 rule="hyper" parents="4840 8612"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(5379(a,1),8612(a,1,1))].">
      <j1 rule="para" parents="5379 8612"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      K(a(x,y,z),u) * a(x * y,z,K(L(z,y,x) \ z,u)) = K(L(z,y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5375(a,1),8619(a,1,1))].">
      <j1 rule="para" parents="5375 8619"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,8614,a(flip),b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="131 8614 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(4839(a,1),8616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4839 8616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,8617,a,b,8618,a)].">
      <j1 rule="hyper" parents="36 8617 8618"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(387,a,8624,a)].">
      <j1 rule="hyper" parents="387 8624"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * a(y,z,K(w,u)) = x
    ]]></literal>
    <justification jstring="[para(8624(a,1),144(a,1))].">
      <j1 rule="para" parents="8624 144"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(8624(a,1),333(a,1,1))].">
      <j1 rule="para" parents="8624 333"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(8625(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8625 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(311(a,1),8627(a,1))].">
      <j1 rule="para" parents="311 8627"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(127,a,4363,a(flip),b,8623,a),flip(a)].">
      <j1 rule="hyper" parents="127 4363 8623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,L(L(x \ 1,z,u),w,v5) \ 1) = a(v5,w,K(L(x \ 1,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(4831(a,1),8613(a,1,1))].">
      <j1 rule="para" parents="4831 8613"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(8615(a,1),4370(a,1,2))].">
      <j1 rule="para" parents="8615 4370"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(36,a,8619,a,b,8632,a)].">
      <j1 rule="hyper" parents="36 8619 8632"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(4394(a,2),8633(a,1,1))].">
      <j1 rule="para" parents="4394 8633"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(L(x,y,z),y * x)
    ]]></literal>
    <justification jstring="[para(301(a,1),8634(a,2,2))].">
      <j1 rule="para" parents="301 8634"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5368,a(flip),b,8635,a),flip(a)].">
      <j1 rule="hyper" parents="319 5368 8635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7755(a,1),8296(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7755 8296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),z) = T(K(y,u) * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8022,a,8638,a),flip(a)].">
      <j1 rule="hyper" parents="8022 8638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,w) * v5) = K(y,w) * (L(K(x,y),z,u) * v5)
    ]]></literal>
    <justification jstring="[para(5367(a,1),8550(a,1,1))].">
      <j1 rule="para" parents="5367 8550"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(319,a,8616,a(flip),b,8641,a),flip(a)].">
      <j1 rule="hyper" parents="319 8616 8641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,8630,a(flip),b,8642,a)].">
      <j1 rule="hyper" parents="64 8630 8642"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(206,a,8642,a(flip),b,8630,a(flip))].">
      <j1 rule="hyper" parents="206 8642 8630"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(8609,a,8643,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8609 8643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,7666,a,b,8557,a),flip(a)].">
      <j1 rule="hyper" parents="41 7666 8557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4858,a(flip),b,8646,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4858 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(x * K(y,u),K(y,z)) = K(y,u)
    ]]></literal>
    <justification jstring="[hyper(762,a,8647,a)].">
      <j1 rule="hyper" parents="762 8647"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5172(a,1),8649(a,1,2,1))].">
      <j1 rule="para" parents="5172 8649"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,5176,a,b,8650,a),flip(a)].">
      <j1 rule="hyper" parents="40 5176 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,4880,a(flip),b,8651,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 4880 8651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      T(x * K(L(y \ 1,z,u) \ 1,w),K(w,v5)) = T(x,K(w,v5)) * L(K(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(4831(a,1),8651(a,2,2))].">
      <j1 rule="para" parents="4831 8651"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(x,u)) = T(T(y,K(x,z)),K(x,u))
    ]]></literal>
    <justification jstring="[para(6751(a,1),8652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6751 8652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,R(u,w,v5))) = K(x,y) * T(z,K(u,R(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(7473(a,1),8652(a,2,2))].">
      <j1 rule="para" parents="7473 8652"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(y,K(u,x)) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8654(a,1),7823(a,1,1))].">
      <j1 rule="para" parents="8654 7823"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6748(a,1),8656(a,2,1))].">
      <j1 rule="para" parents="6748 8656"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6742(a,1),8657(a,2,2))].">
      <j1 rule="para" parents="6742 8657"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      x / T(x / y,T(L(y,z,u),y)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(6220,a,8622,a)].">
      <j1 rule="hyper" parents="6220 8622"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(187(a,1),8659(a,1,2,2))].">
      <j1 rule="para" parents="187 8659"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      L(T(x,(y * (z * x)) \ ((y * z) * u)),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,8176,a)].">
      <j1 rule="hyper" parents="64 25 8176"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,z),u * K(z,y)) = (x * (u * K(z,y))) / u
    ]]></literal>
    <justification jstring="[para(6914(a,1),8227(a,1,1,2))].">
      <j1 rule="para" parents="6914 8227"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[para(6146(a,1),8662(a,1,1))].">
      <j1 rule="para" parents="6146 8662"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      (x \ T(K(y \ x,z) * x,x)) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(7073(a,1),8403(a,1,1))].">
      <j1 rule="para" parents="7073 8403"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(8586,a,8511,a)].">
      <j1 rule="hyper" parents="8586 8511"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      (x / K(y,z)) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(8328(a,1),8665(a,1,1,2))].">
      <j1 rule="para" parents="8328 8665"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = a(z,y,z) \ x
    ]]></literal>
    <justification jstring="[para(5174(a,1),8666(a,1,1))].">
      <j1 rule="para" parents="5174 8666"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(127,a,8393,a(flip),b,8667,a)].">
      <j1 rule="hyper" parents="127 8393 8667"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,6623,a(flip),b,8667,a)].">
      <j1 rule="hyper" parents="64 6623 8667"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,8511,a,b,8669,a),flip(a)].">
      <j1 rule="hyper" parents="319 8511 8669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      a(x,x \ y,x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(8669(a,1),4899(a,1))].">
      <j1 rule="para" parents="8669 4899"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      (x * a(y,z,y)) / R(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,11,a(flip),b,8670,a),flip(a)].">
      <j1 rule="hyper" parents="128 11 8670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8369,a(flip),b,8670,a)].">
      <j1 rule="hyper" parents="64 8369 8670"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,8672,a)].">
      <j1 rule="hyper" parents="144 8672"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,11,a(flip),b,8672,a),flip(a)].">
      <j1 rule="hyper" parents="130 11 8672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      x / (y \ L(y,z,y)) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,11,a(flip),b,8673,a)].">
      <j1 rule="hyper" parents="128 11 8673"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      x * (a(y,z,y) \ 1) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[para(8538(a,2),8673(a,1,2))].">
      <j1 rule="para" parents="8538 8673"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5904,a,b,8674,a)].">
      <j1 rule="hyper" parents="64 5904 8674"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(3341(a,1),8674(a,1,2))].">
      <j1 rule="para" parents="3341 8674"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(8674(a,2),8405(a,1,2))].">
      <j1 rule="para" parents="8674 8405"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8516,a,8675,a)].">
      <j1 rule="hyper" parents="8516 8675"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3322,a(flip),b,8675,a),flip(a)].">
      <j1 rule="hyper" parents="319 3322 8675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,8675,a(flip),b,8507,a)].">
      <j1 rule="hyper" parents="128 8675 8507"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(8675(a,1),8553(a,1,1,2))].">
      <j1 rule="para" parents="8675 8553"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(8516,a,8682,a)].">
      <j1 rule="hyper" parents="8516 8682"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      (x * y) \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(8682(a,1),330(a,1,2))].">
      <j1 rule="para" parents="8682 330"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      R(T(x,T(x * y,x)),y * x,a(x,y,x)) = ((y * x) * a(x,y,x)) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(8682(a,1),894(a,1,1,2))].">
      <j1 rule="para" parents="8682 894"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      x / (a(y,z,y) \ 1) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(8538(a,2),8676(a,1,2))].">
      <j1 rule="para" parents="8538 8676"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      (((x * y) / a(z,u,z)) * w) / ((y * (a(z,u,z) \ 1)) * w) = R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(8677(a,1),527(a,1,1,1))].">
      <j1 rule="para" parents="8677 527"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(586,a,8678,a),flip(a)].">
      <j1 rule="hyper" parents="586 8678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6266,a(flip),b,8678,a)].">
      <j1 rule="hyper" parents="64 6266 8678"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,8678,a(flip),b,1119,a)].">
      <j1 rule="hyper" parents="131 8678 1119"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,8681,a(flip),b,153,a(flip))].">
      <j1 rule="hyper" parents="128 8681 153"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * R(x,y,x)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8681(a,1),8541(a,1,2))].">
      <j1 rule="para" parents="8681 8541"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8326,a(flip),b,8683,a)].">
      <j1 rule="hyper" parents="64 8326 8683"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      ((x * y) * R(L(z,y,x),u,L(z,y,x))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(94(a,1),8683(a,1,2))].">
      <j1 rule="para" parents="94 8683"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      ((a(R(x,y,z),u,R(x,y,z)) * R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,528,a,b,8697,a)].">
      <j1 rule="hyper" parents="64 528 8697"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      R(x,a(y,z,y),a(y,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(608,a,8688,a)].">
      <j1 rule="hyper" parents="608 8688"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      R(x,a(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(8538(a,1),8701(a,1,3))].">
      <j1 rule="para" parents="8538 8701"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      R(x,y \ R(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(8309(a,2),8702(a,1,2))].">
      <j1 rule="para" parents="8309 8702"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(8516,a,8690,a)].">
      <j1 rule="hyper" parents="8516 8690"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(244,a,8211,a(flip),b,8692,a),flip(a)].">
      <j1 rule="hyper" parents="244 8211 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(8507(a,2),8692(a,1,2))].">
      <j1 rule="para" parents="8507 8692"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      ((R(x,y,x) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(8704(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="8704 531"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,8706,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      x * a(y,y \ x,y) = y * (T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3795,a(flip),b,8705,a),flip(a)].">
      <j1 rule="hyper" parents="319 3795 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      x \ (y * (T(x,y) / y)) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,3795,a(flip),b,8705,a)].">
      <j1 rule="hyper" parents="127 3795 8705"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      a(x,x \ y,x) * y = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(8516,a,8709,a)].">
      <j1 rule="hyper" parents="8516 8709"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      x \ (y * (T(x,y) / y)) != z
    ]]></literal>
    <literal><![CDATA[
      a(y,y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(8709(a,1),330(a,1,2))].">
      <j1 rule="para" parents="8709 330"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      L(x,y,z) \ (u * (L(T(x,u),y,z) / u)) = a(u,u \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),8710(a,1,2,2,1))].">
      <j1 rule="para" parents="25 8710"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7808,a,8691,a),flip(a)].">
      <j1 rule="hyper" parents="7808 8691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(8714(a,1),8384(a,1,1))].">
      <j1 rule="para" parents="8714 8384"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2841(a,1),8715(a,1,2))].">
      <j1 rule="para" parents="2841 8715"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6166,a,8716,a)].">
      <j1 rule="hyper" parents="6166 8716"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(3825(a,1),8717(a,1,1))].">
      <j1 rule="para" parents="3825 8717"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      L(x,y,z) \ L(u * (T(x,u) / u),y,z) = a(u,u \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3937(a,2),8713(a,1,2))].">
      <j1 rule="para" parents="3937 8713"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      L(T(x,(y * z) \ (x \ ((y * z) * u))),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7497(a,1),8661(a,1,1))].">
      <j1 rule="para" parents="7497 8661"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      (x \ T(x * K(x / y,z),x)) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(6843(a,1),8664(a,1,1,2,1))].">
      <j1 rule="para" parents="6843 8664"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(8160(a,1),8720(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8160 8720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,8722,a(flip))].">
      <j1 rule="hyper" parents="42 25 8722"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,x \ w),y,z) \ u) = K(L(x,y,z),L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(8722(a,1),4360(a,1,2,1))].">
      <j1 rule="para" parents="8722 4360"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      (x * (y * R(x,z,u))) \ ((x * y) * R(x,z,u)) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(1494(a,1),8298(a,1,2))].">
      <j1 rule="para" parents="1494 8298"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(713,a,8729,a),flip(a)].">
      <j1 rule="hyper" parents="713 8729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(8729(a,1),713(a,1))].">
      <j1 rule="para" parents="8729 713"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7334,a,b,8730,a)].">
      <j1 rule="hyper" parents="64 7334 8730"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      x \ R(T(x,y),z,R(x,u,w)) = K(x,y) * a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(8730(a,1),7459(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8730 7459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(7933(a,2),8730(a,1,2))].">
      <j1 rule="para" parents="7933 8730"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8732(a,1),5181(a,1,1))].">
      <j1 rule="para" parents="8732 5181"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,T(x,R(y,w,v5))) = a(y,T(x,R(y,w,v5)),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5875(a,1),8732(a,1,1))].">
      <j1 rule="para" parents="5875 8732"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = a(y,x,R(y,z,u)) * T(K(x,y),w)
    ]]></literal>
    <justification jstring="[para(8732(a,1),7258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8732 7258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      a(x,y / R(x,z,u),R(x,z,u)) * K(x,y) = K(x,y / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),8735(a,1,2,2))].">
      <j1 rule="para" parents="12 8735"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(4431,a,8733,a)].">
      <j1 rule="hyper" parents="4431 8733"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,839,a(flip),b,8739,a)].">
      <j1 rule="hyper" parents="64 839 8739"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      (x * (y * L(x,z,u))) \ ((x * y) * L(x,z,u)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(1540(a,1),8299(a,1,2))].">
      <j1 rule="para" parents="1540 8299"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(713,a,8741,a),flip(a)].">
      <j1 rule="hyper" parents="713 8741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7322,a,b,8742,a)].">
      <j1 rule="hyper" parents="64 7322 8742"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = x \ R(x,y,T(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(5434(a,1),8742(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5434 8742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(8195(a,1),8744(a,2,2))].">
      <j1 rule="para" parents="8195 8744"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,8742,a(flip),b,8745,a),flip(a)].">
      <j1 rule="hyper" parents="319 8742 8745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      a(x,y,T(L(x,z,u),y)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(5509,a,8746,a)].">
      <j1 rule="hyper" parents="5509 8746"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      a(x,y,L(T(x,y),z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),8747(a,1,3))].">
      <j1 rule="para" parents="25 8747"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * L(T(x,x \ u),y,z)) = a(x,x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2269,a(flip),b,8748,a)].">
      <j1 rule="hyper" parents="64 2269 8748"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(L(y,z,u),y \ x) = a(y,y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8749,a(flip),b,8301,a),flip(a)].">
      <j1 rule="hyper" parents="64 8749 8301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) = u * K(K(x,y) * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8367,a,8501,a)].">
      <j1 rule="hyper" parents="8367 8501"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,v5)) = T(x,K(z,v5)) * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4831(a,1),8653(a,1,1,2))].">
      <j1 rule="para" parents="4831 8653"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(y,v5)) = L(K(x,y),z,u) \ T(w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(36,a,3813,a(flip),b,8752,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3813 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(y,x),z,u) \ T(w,K(x,v5))
    ]]></literal>
    <justification jstring="[para(4838(a,1),8753(a,1,1))].">
      <j1 rule="para" parents="4838 8753"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(x,y),z,u) * T(w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,4838,a(flip),b,8754,a),flip(a)].">
      <j1 rule="hyper" parents="319 4838 8754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * T(w,L(K(x,y),z,u)),K(x,v5)) = T(w,K(x,v5)) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,241,a(flip),b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="319 241 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4457,a(flip),b,8724,a),flip(a)].">
      <j1 rule="hyper" parents="64 4457 8724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) = K(u,L(x,y,z)) * K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(8757(a,1),8317(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8757 8317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      a(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(8731,a,8734,a)].">
      <j1 rule="hyper" parents="8731 8734"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      a(T(x,y),T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3654,a(flip),b,8759,a),flip(a)].">
      <j1 rule="hyper" parents="64 3654 8759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(3649,a,8760,a)].">
      <j1 rule="hyper" parents="3649 8760"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      ((x * y) * L(y,x,z)) \ (y * (x * L(y,x,z))) = K(L(y,x,z),y * T(x,y))
    ]]></literal>
    <justification jstring="[para(109(a,1),8215(a,1,1,1))].">
      <j1 rule="para" parents="109 8215"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1532,a,8762,a),flip(a)].">
      <j1 rule="hyper" parents="1532 8762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8763(a,1,2))].">
      <j1 rule="para" parents="109 8763"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5369,a,8764,a),flip(a)].">
      <j1 rule="hyper" parents="5369 8764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(8765(a,1),5363(a,1,1))].">
      <j1 rule="para" parents="8765 5363"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(6455,a,8767,a),flip(a)].">
      <j1 rule="hyper" parents="6455 8767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8768(a,1),8636(a,1,1))].">
      <j1 rule="para" parents="8768 8636"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8255(a,1),8769(a,1,1))].">
      <j1 rule="para" parents="8255 8769"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7508,a(flip),b,8770,a)].">
      <j1 rule="hyper" parents="64 7508 8770"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      a(x,y,K(z * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,8770,a(flip),b,8611,a),flip(a)].">
      <j1 rule="hyper" parents="126 8770 8611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(53,a,8774,a)].">
      <j1 rule="hyper" parents="53 8774"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[para(4281(a,2),8774(a,1,3))].">
      <j1 rule="para" parents="4281 8774"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,8777,a)].">
      <j1 rule="hyper" parents="53 8777"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(7832,a,8776,a)].">
      <j1 rule="hyper" parents="7832 8776"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7827,a(flip),b,8776,a)].">
      <j1 rule="hyper" parents="64 7827 8776"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,8778,a(flip),b,8611,a),flip(a)].">
      <j1 rule="hyper" parents="126 8778 8611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      K(x,y \ (x * z)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8408,a,8773,a)].">
      <j1 rule="hyper" parents="8408 8773"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(5290,a,8773,a)].">
      <j1 rule="hyper" parents="5290 8773"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,8770,a,b,8773,a)].">
      <j1 rule="hyper" parents="319 8770 8773"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1168(a,1),8773(a,1,2))].">
      <j1 rule="para" parents="1168 8773"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6479,a,8780,a),flip(a)].">
      <j1 rule="hyper" parents="6479 8780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6054,a(flip),b,8780,a),flip(a)].">
      <j1 rule="hyper" parents="64 6054 8780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(8780(a,1),8313(a,1,2))].">
      <j1 rule="para" parents="8780 8313"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      T(x,y \ (x * z)) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8782,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 8782 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(2967(a,2),8783(a,1,2,1))].">
      <j1 rule="para" parents="2967 8783"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      K(x \ (y * z),y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8788(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      T(x,x * (y \ (z \ y))) = T(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7763,a(flip),b,8790,a),flip(a)].">
      <j1 rule="hyper" parents="64 7763 8790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(x \ (y \ x),z) * T(z,T(y \ z,x)) = L(z,x \ (y \ x),z)
    ]]></literal>
    <justification jstring="[para(8794(a,1),4295(a,1,2))].">
      <j1 rule="para" parents="8794 4295"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8784(a,1),499(a,1))].">
      <j1 rule="para" parents="8784 499"/>
    </justification>
  </clause>

  <clause id="8798">
    <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(1168(a,1),8797(a,1,2))].">
      <j1 rule="para" parents="1168 8797"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ x)) = T(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(129,a,8785,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 8785 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      K(x,T(y \ (R(y,z,u) * x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7765,a,b,8791,a)].">
      <j1 rule="hyper" parents="64 7765 8791"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(8789(a,1),8339(a,1))].">
      <j1 rule="para" parents="8789 8339"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1119(a,1),8800(a,1,2,1))].">
      <j1 rule="para" parents="1119 8800"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(183(a,1),8802(a,1,2,2))].">
      <j1 rule="para" parents="183 8802"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u) * K(x,y)) = T(z * K(x,y),K(y,u))
    ]]></literal>
    <justification jstring="[para(8019(a,1),8359(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8019 8359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      K(x,y) * T(z,K(x,y) * K(y,u)) = T(z * K(x,y),K(y,u))
    ]]></literal>
    <justification jstring="[para(2099(a,1),8804(a,1,2,2))].">
      <j1 rule="para" parents="2099 8804"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      T((K(x,y) \ z) * K(x,y),K(y,u)) \ z = K(K(x,y) * K(y,u),K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(8805(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="8805 5151"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = T(T(u,K(x,y)),K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(5964(a,1),8806(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5964 8806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8808">
    <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(8524(a,1),8526(a,1))].">
      <j1 rule="para" parents="8524 8526"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      ((x * y) * a(y,x,y)) \ ((y * x) * y) = R(T(y,y * x),x * y,a(y,x,y))
    ]]></literal>
    <justification jstring="[para(3252(a,1),8687(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3252 8687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      a(x,T(y,R(x,z,u)),R(x,w,v5)) = K(y * R(x,w,v5),x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5876(a,1),8736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5876 8736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      a(x,T(y,R(x,z,u)),R(x,w,v5)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,8732,a(flip),b,8810,a),flip(a)].">
      <j1 rule="hyper" parents="319 8732 8810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      a(x,y / R(x,z,u),R(x,w,v5)) = a(x,R(x,z,u) \ y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(111(a,1),8811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 8811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(365(a,1),8811(a,1,2,2))].">
      <j1 rule="para" parents="365 8811"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,u / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8813(a,1),8738(a,1,1))].">
      <j1 rule="para" parents="8813 8738"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5879,a(flip),b,8815,a),flip(a)].">
      <j1 rule="hyper" parents="319 5879 8815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      (x * (y * R(z,u,L(z,y,x)))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(436(a,1),8698(a,1,1))].">
      <j1 rule="para" parents="436 8698"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) = a(x,x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,8750,a(flip),b,8758,a),flip(a)].">
      <j1 rule="hyper" parents="319 8750 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),T(u,x))
    ]]></literal>
    <justification jstring="[para(22(a,2),8758(a,2,2,2))].">
      <j1 rule="para" parents="22 8758"/>
    </justification>
  </clause>

  <clause id="8820">
    <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(2369(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="2369 3865"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3685(a,1),3914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3685 3914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,18,a,b,8821,a),flip(a)].">
      <j1 rule="hyper" parents="319 18 8821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1090(a,1),8822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1090 8822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      L(x,y / ((z \ 1) \ 1),u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[para(2700(a,1),8822(a,1,2))].">
      <j1 rule="para" parents="2700 8822"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      (x * (1 / y)) * L(z,y \ 1,x) = x * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,8824,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 8824 18"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * L(z,y,x) = x * ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),8827(a,1,2,2))].">
      <j1 rule="para" parents="81 8827"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * z != x * ((1 / (1 / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(8828(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8828 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x,x * y),z,u) * T(x,y)) = L(K(x * y,x),z,u) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4838,a,b,4478,a),flip(a)].">
      <j1 rule="hyper" parents="319 4838 4478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(((x * (y * z)) / z) \ 1,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4501,a,4731,a),flip(a)].">
      <j1 rule="hyper" parents="4501 4731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4645,a(flip),b,8831,a),flip(a)].">
      <j1 rule="hyper" parents="319 4645 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4501,a,8833,a)].">
      <j1 rule="hyper" parents="4501 8833"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(7170,a,8834,a)].">
      <j1 rule="hyper" parents="7170 8834"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6351,a,8835,a)].">
      <j1 rule="hyper" parents="6351 8835"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3908,a(flip),b,8837,a)].">
      <j1 rule="hyper" parents="64 3908 8837"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),8837(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 8837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,6655,a(flip),b,8839,a),flip(a)].">
      <j1 rule="hyper" parents="319 6655 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x / ((z \ 1) * x)),z) = u
    ]]></literal>
    <justification jstring="[para(8839(a,2),5740(a,1))].">
      <j1 rule="para" parents="8839 5740"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3732,a,5196,a)].">
      <j1 rule="hyper" parents="3732 5196"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(5408(a,1),8842(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5408 8842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      (x * y) \ (R(T(z * K(x,z),u),x,y) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(27(a,2),6313(a,1,2,1))].">
      <j1 rule="para" parents="27 6313"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,y \ T(y * L(y \ z,u,w),x))
    ]]></literal>
    <justification jstring="[para(22(a,2),6465(a,2,2,2))].">
      <j1 rule="para" parents="22 6465"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,5851,a(flip),b,8846,a),flip(a)].">
      <j1 rule="hyper" parents="319 5851 8846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      K(x,L((y * x) \ (z * x),u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(567(a,1),8847(a,1,2))].">
      <j1 rule="para" parents="567 8847"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      K(x,L((y / x) \ z,u,w)) = K(x,L(y \ (z * x),u,w))
    ]]></literal>
    <justification jstring="[para(12(a,1),8849(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 8849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      K(x,L(y \ (((y / x) * z) * x),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),8850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      L(K(x,y \ (((y / x) * z) * x)),((y / x) * z) * x,u) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5277,a,b,8851,a)].">
      <j1 rule="hyper" parents="64 5277 8851"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      L(K(x,y \ (((x \ y) * z) * x)),((y / x) * z) * x,u) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(7312(a,1),8852(a,1,1))].">
      <j1 rule="para" parents="7312 8852"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      L(K(x,y),((z / x) * y) * x,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6606(a,1),8853(a,1,1))].">
      <j1 rule="para" parents="6606 8853"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      K(L(x,(y / x) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(6455,a,8854,a)].">
      <j1 rule="hyper" parents="6455 8854"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,8593,a(flip),b,8855,a),flip(a)].">
      <j1 rule="hyper" parents="64 8593 8855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) = 1
    ]]></literal>
    <justification jstring="[para(8855(a,1),4967(a,1,3))].">
      <j1 rule="para" parents="8855 4967"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5327,a(flip),b,8857,a)].">
      <j1 rule="hyper" parents="64 5327 8857"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,8859,a)].">
      <j1 rule="hyper" parents="57 8859"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      R(T(x,y),T(K(x,z),T(x,y)),u) = (T(T(x,z),T(y,z)) * u) / (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(2934(a,1),7089(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2934 7089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      (T(T(x,y),T(z,y)) * u) / (K(x,y) * u) = R(T(x,z),K(x,y),u)
    ]]></literal>
    <justification jstring="[para(2934(a,1),8862(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2934 8862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = R(R(T(x,u),K(x,y),z),w,v5) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(8863(a,1),656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8863 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,K(w,x)) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(7582(a,1),7282(a,1,2))].">
      <j1 rule="para" parents="7582 7282"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(6748(a,1),8867(a,1,2))].">
      <j1 rule="para" parents="6748 8867"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),y),w)
    ]]></literal>
    <justification jstring="[para(7160(a,1),8868(a,2,1))].">
      <j1 rule="para" parents="7160 8868"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * T(K(y,x),w) = T(K(y * R(x,z,u),x),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,8737,a(flip),b,8870,a)].">
      <j1 rule="hyper" parents="64 8737 8870"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      T(K(x * R(y,z,u),y),w) * T(K(y,x),w) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8297,a,8871,a)].">
      <j1 rule="hyper" parents="8297 8871"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      T(K(x,y) * K(y * R(x,z,u),x),w) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8639,a(flip),b,8872,a)].">
      <j1 rule="hyper" parents="64 8639 8872"/>
    </justification>
  </clause>

  <clause id="8874">
    <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(6296(a,1),7484(a,1,2))].">
      <j1 rule="para" parents="6296 7484"/>
    </justification>
  </clause>

  <clause id="8875">
    <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(319,a,7056,a(flip),b,8874,a),flip(a)].">
      <j1 rule="hyper" parents="319 7056 8874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * K(z,y)) * (y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7697(a,1,2))].">
      <j1 rule="para" parents="109 7697"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      K(x,((y / z) * (z * x)) \ (y * (z * x))) = L(K(x,z),T(y,z * x),z * x)
    ]]></literal>
    <justification jstring="[hyper(7863,a,8877,a)].">
      <j1 rule="hyper" parents="7863 8877"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(x,((y / z) * z) \ (x \ (y * (z * x)))) = L(K(x,z),T(y,z * x),z * x)
    ]]></literal>
    <justification jstring="[hyper(7496,a,8878,a)].">
      <j1 rule="hyper" parents="7496 8878"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,z \ (x \ (z * (y * x))))
    ]]></literal>
    <justification jstring="[para(12(a,1),8879(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 8879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6692,a(flip),b,8880,a),flip(a)].">
      <j1 rule="hyper" parents="319 6692 8880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,8881,a(flip),b,7697,a)].">
      <j1 rule="hyper" parents="131 8881 7697"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(231(a,1),8881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 8881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8184,a,8883,a),flip(a)].">
      <j1 rule="hyper" parents="8184 8883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,8884,a(flip),b,7950,a)].">
      <j1 rule="hyper" parents="130 8884 7950"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = (z * y) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(127,a,5400,a(flip),b,8882,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 5400 8882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8890">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,8889,a)].">
      <j1 rule="hyper" parents="253 8889"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(392,a,8890,a),flip(a)].">
      <j1 rule="hyper" parents="392 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      ((x / y) * (z * y)) / (y * z) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,5163,a(flip),b,8890,a),flip(a)].">
      <j1 rule="hyper" parents="319 5163 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(130,a,4346,a(flip),b,8890,a),flip(a)].">
      <j1 rule="hyper" parents="130 4346 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      (x * K(y \ z,y)) * z = x * ((y \ z) * y)
    ]]></literal>
    <justification jstring="[para(8890(a,1),321(a,1,1))].">
      <j1 rule="para" parents="8890 321"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(8890(a,1),326(a,1,1))].">
      <j1 rule="para" parents="8890 326"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8189(a,1),8890(a,1,1))].">
      <j1 rule="para" parents="8189 8890"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,8891,a(flip),b,7623,a),flip(a)].">
      <j1 rule="hyper" parents="130 8891 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),8891(a,1,1,2))].">
      <j1 rule="para" parents="12 8891"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),y) = u
    ]]></literal>
    <justification jstring="[para(8891(a,1),6021(a,1,1))].">
      <j1 rule="para" parents="8891 6021"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(8891(a,1),6025(a,1,2))].">
      <j1 rule="para" parents="8891 6025"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      K(x / (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(8891(a,1),6062(a,1,1))].">
      <j1 rule="para" parents="8891 6062"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      (x / T(y,z)) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(8893(a,1),254(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8893 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,T(z,u) \ 1)) = K(x,((T(z,u) \ 1) * y) \ ((z \ 1) * (u * z)))
    ]]></literal>
    <justification jstring="[para(8894(a,1),5285(a,2,2,2))].">
      <j1 rule="para" parents="8894 5285"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7658,a,b,8899,a)].">
      <j1 rule="hyper" parents="64 7658 8899"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(4167(a,1),8899(a,1,2))].">
      <j1 rule="para" parents="4167 8899"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(199,a,8905,a),flip(a)].">
      <j1 rule="hyper" parents="199 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(8907(a,2),2416(a,2,1))].">
      <j1 rule="para" parents="8907 2416"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8896,a,94,a(flip))].">
      <j1 rule="hyper" parents="8896 94"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(7622(a,1),8909(a,1,1))].">
      <j1 rule="para" parents="7622 8909"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      ((x * ((K(y,x / y) / (x \ y)) \ 1)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(7918(a,2),8908(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7918 8908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      K((x * (y * z)) \ u,L(z,w,v5)) = K((x * y) \ (z \ u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,4627,a(flip),b,7708,a),flip(a)].">
      <j1 rule="hyper" parents="64 4627 7708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      L(K(L(x,y,z) \ u,L(x,w,v5)),u,z * y) = K((z * y) \ (x \ ((z * y) * u)),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(5409,a,8912,a)].">
      <j1 rule="hyper" parents="5409 8912"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3890,a(flip),b,7712,a),flip(a)].">
      <j1 rule="hyper" parents="319 3890 7712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(670(a,1),8914(a,1,2))].">
      <j1 rule="para" parents="670 8914"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3890,a(flip),b,8915,a),flip(a)].">
      <j1 rule="hyper" parents="64 3890 8915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,6546,a(flip),b,8916,a),flip(a)].">
      <j1 rule="hyper" parents="319 6546 8916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K(u \ (L(x,y,z) * w),T(x,L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(6244,a,7750,a),flip(a)].">
      <j1 rule="hyper" parents="6244 7750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      K(x,R(K(y,R(z,u,w) \ z),z,u * w)) = K(x,K(a(z,u,w),T(y,z * (u * w))))
    ]]></literal>
    <justification jstring="[para(5563(a,1),7858(a,1,2))].">
      <j1 rule="para" parents="5563 7858"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,z * u))) = K(x,K(a(y,z,u),T(w,y * (z * u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,7469,a(flip),b,8919,a)].">
      <j1 rule="hyper" parents="64 7469 8919"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      T(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(8080(a,1),8085(a,1,2,1))].">
      <j1 rule="para" parents="8080 8085"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      T(T(x,y),z) * (T(T(x,y),z * R(x,u,w)) \ v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5)
    ]]></literal>
    <justification jstring="[para(4314(a,1),8921(a,1,2))].">
      <j1 rule="para" parents="4314 8921"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(z,y) \ R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(6099(a,2),8108(a,1,2,2,1))].">
      <j1 rule="para" parents="6099 8108"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,y) \ 1,x) = K(((y * (x \ 1)) \ z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(8223,a,8224,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8223 8224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,y) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (y * (x \ 1)),x) = u
    ]]></literal>
    <justification jstring="[para(8925(a,2),5247(a,1))].">
      <j1 rule="para" parents="8925 5247"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      R(x * K(y,K(T(z,x),u)),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(6705(a,1),8411(a,1,1,2))].">
      <j1 rule="para" parents="6705 8411"/>
    </justification>
  </clause>

  <clause id="8928">
    <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),8413(a,1,2,1))].">
      <j1 rule="para" parents="9 8413"/>
    </justification>
  </clause>

  <clause id="8930">
    <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),8928(a,1,2))].">
      <j1 rule="para" parents="18 8928"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(6481,a,8930,a)].">
      <j1 rule="hyper" parents="6481 8930"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,5649,a(flip),b,8931,a),flip(a)].">
      <j1 rule="hyper" parents="319 5649 8931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8932(a,2,2,2))].">
      <j1 rule="para" parents="10 8932"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      K(x,L(y,x * (z / y),u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12(a,1),8932(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8936">
    <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(3322(a,1),8934(a,1,1,2))].">
      <j1 rule="para" parents="3322 8934"/>
    </justification>
  </clause>

  <clause id="8937">
    <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(5720,a,8936,a)].">
      <j1 rule="hyper" parents="5720 8936"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(y,v5)) = T(x,K(y,v5)) * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(109(a,1),8756(a,1,1))].">
      <j1 rule="para" parents="109 8756"/>
    </justification>
  </clause>

  <clause id="8940">
    <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(3787,a,8820,a)].">
      <j1 rule="hyper" parents="3787 8820"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * u) * K(z,(y * u) \ ((y * x) * u))
    ]]></literal>
    <justification jstring="[hyper(145,a,8845,a),flip(a)].">
      <j1 rule="hyper" parents="145 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ ((x * u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(u * K(x,u),z),x,y) \ ((x * u) * y) = w
    ]]></literal>
    <justification jstring="[para(8845(a,1),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8845 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K(u \ (L(x,y,z) * w),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7775,a(flip),b,8918,a),flip(a)].">
      <j1 rule="hyper" parents="319 7775 8918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,6850,a(flip),b,8943,a),flip(a)].">
      <j1 rule="hyper" parents="319 6850 8943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(y,z) * R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(4356(a,1),8924(a,1,2))].">
      <j1 rule="para" parents="4356 8924"/>
    </justification>
  </clause>

  <clause id="8947">
    <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(1779(a,1),8940(a,1,2))].">
      <j1 rule="para" parents="1779 8940"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2538,a(flip),b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="64 2538 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      R(x,((y \ 1) \ 1) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(2362(a,1),8948(a,1,2))].">
      <j1 rule="para" parents="2362 8948"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      x * T(L(x \ y,z,u),(x \ 1) * x) = (x \ 1) \ L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1722(a,1),3929(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1722 3929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2336(a,1),8951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2336 8951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = K(x,y) * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(8952(a,1),4750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8952 4750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = T(x,y) * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,4081,a(flip),b,8954,a),flip(a)].">
      <j1 rule="hyper" parents="319 4081 8954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) / K(y,z)
    ]]></literal>
    <justification jstring="[para(7631(a,1),5895(a,2,1))].">
      <j1 rule="para" parents="7631 5895"/>
    </justification>
  </clause>

  <clause id="8957">
    <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(3290(a,1),7966(a,1,2))].">
      <j1 rule="para" parents="3290 7966"/>
    </justification>
  </clause>

  <clause id="8958">
    <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(319,a,4502,a(flip),b,8957,a),flip(a)].">
      <j1 rule="hyper" parents="319 4502 8957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(5658(a,1),8958(a,1,1,1,1))].">
      <j1 rule="para" parents="5658 8958"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[para(4720(a,1),8959(a,1,1))].">
      <j1 rule="para" parents="4720 8959"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(8422(a,1),8960(a,1,1))].">
      <j1 rule="para" parents="8422 8960"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      K((x * y) \ (z \ ((x * y) * u)),L(z,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(z,y,x) \ u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(8913(a,1),8186(a,1))].">
      <j1 rule="para" parents="8913 8186"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(8963,a,8267,a)].">
      <j1 rule="hyper" parents="8963 8267"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5174,a(flip),b,8956,a),flip(a)].">
      <j1 rule="hyper" parents="319 5174 8956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      ((x * (K(y,z) * R(z,u,w))) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(7631(a,1),8965(a,1,1,1))].">
      <j1 rule="para" parents="7631 8965"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      R((x * (K(y,z) * z)) / (x * K(y,z)),u,w) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(1879(a,2),8966(a,1,1))].">
      <j1 rule="para" parents="1879 8966"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      R((x * (y * K(z,y))) / (x * K(z,y)),u,w) * x = (x * (K(z,y) * R(y,u,w))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2826(a,1),8967(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2826 8967"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = (x * (K(w,y) * R(y,z,u))) * K(y,w)
    ]]></literal>
    <justification jstring="[para(7611(a,1),8968(a,1,1,1))].">
      <j1 rule="para" parents="7611 8968"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      (x * (K(y,z) * R(z,u,w))) * K(z,y) = x * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(850,a,8969,a),flip(a)].">
      <j1 rule="hyper" parents="850 8969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      (x * (R(y,z,u) * K(w,y))) * K(y,w) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2835(a,2),8970(a,1,1,2))].">
      <j1 rule="para" parents="2835 8970"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5336,a,8972,a)].">
      <j1 rule="hyper" parents="5336 8972"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,8973,a,b,8619,a),flip(a)].">
      <j1 rule="hyper" parents="126 8973 8619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      K(x,(y \ 1) * R(x,z,u)) = K(x,y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5293,a(flip),b,8973,a)].">
      <j1 rule="hyper" parents="64 5293 8973"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5275,a(flip),b,8973,a),flip(a)].">
      <j1 rule="hyper" parents="64 5275 8973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5877,a,b,8975,a)].">
      <j1 rule="hyper" parents="64 5877 8975"/>
    </justification>
  </clause>

  <clause id="8978">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1669(a,1),3713(a,1,1,2))].">
      <j1 rule="para" parents="1669 3713"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,z,K(y,y \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3693(a,2),3915(a,1,1,1,2))].">
      <j1 rule="para" parents="3693 3915"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z
    ]]></literal>
    <justification jstring="[para(438(a,1),4523(a,1,2))].">
      <j1 rule="para" parents="438 4523"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (T(u,x) * (u \ z))) = y * z
    ]]></literal>
    <justification jstring="[para(241(a,1),8980(a,1,2,2))].">
      <j1 rule="para" parents="241 8980"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(4037(a,1),8981(a,1,2,2))].">
      <j1 rule="para" parents="4037 8981"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(206,a,8982,a(flip),b,4356,a),flip(a)].">
      <j1 rule="hyper" parents="206 8982 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1121(a,1),8982(a,1,1,2))].">
      <j1 rule="para" parents="1121 8982"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(8982(a,1),6583(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8982 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(8982(a,1),6588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8982 6588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(8982(a,1),7537(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8982 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8988">
    <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(484(a,1),8986(a,1,2))].">
      <j1 rule="para" parents="484 8986"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      R(x,y,z) * (K(x,u) * w) = K(x,u) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(4374,a,8984,a),flip(a)].">
      <j1 rule="hyper" parents="4374 8984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),8984(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4363 8984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      K(x,y) * (R(T(y,z),u,w) * (K(T(y,z),T(x,z)) * v5)) = R(T(y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(6851(a,1),8984(a,1,1))].">
      <j1 rule="para" parents="6851 8984"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,72,a(flip),b,8989,a),flip(a)].">
      <j1 rule="hyper" parents="127 72 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      (1 / (K(x,y) \ R(x,z,u))) \ (K(x,y) * (R(x,z,u) \ 1)) = (R(x,z,u) \ K(x,y)) * (K(x,y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,8992,a,b,1401,a)].">
      <j1 rule="hyper" parents="127 8992 1401"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4822,a,8990,a)].">
      <j1 rule="hyper" parents="4822 8990"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      R(x,y,x) * (K(z,x) * (x \ u)) = K(z,x) * ((u / x) * R(x,y,x))
    ]]></literal>
    <justification jstring="[para(5904(a,1),8990(a,2,2))].">
      <j1 rule="para" parents="5904 8990"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(8994(a,1),5577(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8994 5577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(8996(a,2),5187(a,1))].">
      <j1 rule="para" parents="8996 5187"/>
    </justification>
  </clause>

  <clause id="8998">
    <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(5572(a,1),8997(a,1))].">
      <j1 rule="para" parents="5572 8997"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,7538,a,b,8983,a)].">
      <j1 rule="hyper" parents="319 7538 8983"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) = K((z * u) / (z * (x \ u)),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),8999(a,1,1,2))].">
      <j1 rule="para" parents="23 8999"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K((z * y) / (z * (u \ y)),x) \ w
    ]]></literal>
    <justification jstring="[para(8999(a,1),4838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8999 4838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(4314(a,1),8995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4314 8995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8680,a(flip),b,9002,a),flip(a)].">
      <j1 rule="hyper" parents="64 8680 9002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      K(x,y) * (x * (L(T(x,z),u,x) \ w)) = R(T(x,y),u,x) * (T(x,z) \ w)
    ]]></literal>
    <justification jstring="[para(9003(a,1),5666(a,1,2))].">
      <j1 rule="para" parents="9003 5666"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      R(T(x,y),z,x) * (T(x,u) \ w) = T(x,y) * (L(T(x,u),z,x) \ w)
    ]]></literal>
    <justification jstring="[hyper(4310,a,9005,a),flip(a)].">
      <j1 rule="hyper" parents="4310 9005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K(x,(z * y) / (z * (u \ y))) * w
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a(flip),b,9001,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 9001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) * w = K(x,(z * u) / (z * (y \ u))) * w
    ]]></literal>
    <justification jstring="[para(6137(a,1),9008(a,1,1,1))].">
      <j1 rule="para" parents="6137 9008"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) * w = K(z,(x * y) / (x * (u \ y))) * w
    ]]></literal>
    <justification jstring="[para(9000(a,1),9009(a,1,1))].">
      <j1 rule="para" parents="9000 9009"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(45,a,9010,a)].">
      <j1 rule="hyper" parents="45 9010"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8983,a(flip),b,9011,a),flip(a)].">
      <j1 rule="hyper" parents="64 8983 9011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * z) = y * (K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,9011,a(flip),b,8983,a(flip))].">
      <j1 rule="hyper" parents="130 9011 8983"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      K(x,((y * x) * z) / ((y * x) * (y \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,y * x) = u
    ]]></literal>
    <justification jstring="[para(9012(a,2),7952(a,1))].">
      <j1 rule="para" parents="9012 7952"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      K(x,T(y,z)) * (y * u) = y * (K(x,T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1015(a,1),9013(a,1,1,2))].">
      <j1 rule="para" parents="1015 9013"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(x,y * (K(x \ 1,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9013(a,1),6510(a,1,2))].">
      <j1 rule="para" parents="9013 6510"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      K(x,y * (z / T(u,x \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(7202(a,1),9016(a,1,2,2))].">
      <j1 rule="para" parents="7202 9016"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      K(T(x,y),z * (y / (x * y))) = K(T(x,y),z * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(5107(a,1),9017(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5107 9017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5)) = R(T(y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(6851(a,1),8991(a,1,2,2,1))].">
      <j1 rule="para" parents="6851 8991"/>
    </justification>
  </clause>

  <clause id="9021">
    <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(64,a,5828,a(flip),b,8988,a),flip(a)].">
      <j1 rule="hyper" parents="64 5828 8988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8985,a(flip),b,9021,a),flip(a)].">
      <j1 rule="hyper" parents="64 8985 9021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),9023(a,2,2))].">
      <j1 rule="para" parents="18 9023"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4363(a,1),9025(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4363 9025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(9026(a,1),4430(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9026 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4430,a(flip),b,9027,a),flip(a)].">
      <j1 rule="hyper" parents="319 4430 9027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(4021(a,1),9028(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4021 9028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8937,a(flip),b,9029,a)].">
      <j1 rule="hyper" parents="64 8937 9029"/>
    </justification>
  </clause>

  <clause id="9031">
    <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(6748(a,1),5226(a,1,2,2))].">
      <j1 rule="para" parents="6748 5226"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,R(y \ 1,y,x) * z) = K((x / (y * x)) \ 1,z * (x / (y * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8144,a(flip),b,5730,a),flip(a)].">
      <j1 rule="hyper" parents="64 8144 5730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z * (x / (y * x))) = K(y,R(y \ 1,y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4650,a(flip),b,9032,a),flip(a)].">
      <j1 rule="hyper" parents="64 4650 9032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      T(K(T(x,y),z * (y / (x * y))),y) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7106,a(flip),b,9033,a)].">
      <j1 rule="hyper" parents="64 7106 9033"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,z * (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,4650,a(flip),b,9033,a),flip(a)].">
      <j1 rule="hyper" parents="64 4650 9033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      T(K(T(x,y),z * ((x * y) \ y)),y) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[para(9018(a,1),9035(a,1,1))].">
      <j1 rule="para" parents="9018 9035"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      K(T(x,y),T(z * ((x * y) \ y),y)) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(6173,a,9038,a)].">
      <j1 rule="hyper" parents="6173 9038"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,z * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(6985,a,9039,a),flip(a)].">
      <j1 rule="hyper" parents="6985 9039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = a(v5,w,K(L(x \ 1,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(4719(a,1),8631(a,1,2))].">
      <j1 rule="para" parents="4719 8631"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = a(v5,w,L(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(4831(a,1),9042(a,2,3))].">
      <j1 rule="para" parents="4831 9042"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      K(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(4565,a,8922,a)].">
      <j1 rule="hyper" parents="4565 8922"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ (K(y,y \ 1) * ((x * z) * u)) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1669(a,1),8978(a,1,2))].">
      <j1 rule="para" parents="1669 8978"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3774(a,1),8979(a,1,1))].">
      <j1 rule="para" parents="3774 8979"/>
    </justification>
  </clause>

  <clause id="9047">
    <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(5938(a,1),9031(a,2,1))].">
      <j1 rule="para" parents="5938 9031"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,8276,a(flip),b,9047,a),flip(a)].">
      <j1 rule="hyper" parents="319 8276 9047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9050">
    <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(5482(a,2),9048(a,1,1))].">
      <j1 rule="para" parents="5482 9048"/>
    </justification>
  </clause>

  <clause id="9051">
    <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(6016(a,1),9050(a,1,2,2))].">
      <j1 rule="para" parents="6016 9050"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(337,a,9051,a)].">
      <j1 rule="hyper" parents="337 9051"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(4384,a,9052,a)].">
      <j1 rule="hyper" parents="4384 9052"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(5483(a,1),9053(a,1,1))].">
      <j1 rule="para" parents="5483 9053"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6092,a(flip),b,9054,a),flip(a)].">
      <j1 rule="hyper" parents="319 6092 9054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5553,a(flip),b,9055,a)].">
      <j1 rule="hyper" parents="64 5553 9055"/>
    </justification>
  </clause>

  <clause id="9057">
    <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(9056(a,1),4707(a,1,1,1,2))].">
      <j1 rule="para" parents="9056 4707"/>
    </justification>
  </clause>

  <clause id="9058">
    <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(4019(a,2),9057(a,1,1,1))].">
      <j1 rule="para" parents="4019 9057"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6082,a,9058,a)].">
      <j1 rule="hyper" parents="6082 9058"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9059(a,1),8875(a,1,1))].">
      <j1 rule="para" parents="9059 8875"/>
    </justification>
  </clause>

  <clause id="9061">
    <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(7825(a,1),9060(a,1,1,2,2))].">
      <j1 rule="para" parents="7825 9060"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y * R(x,u,w),T(x,z)) * v5) = R(T(x,z),y,R(x,u,w)) * (T(x,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(6473,a,9044,a)].">
      <j1 rule="hyper" parents="6473 9044"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3781,a(flip),b,9045,a)].">
      <j1 rule="hyper" parents="64 3781 9045"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),9046(a,1,1,1))].">
      <j1 rule="para" parents="14 9046"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(5193,a,9064,a)].">
      <j1 rule="hyper" parents="5193 9064"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3915,a,b,9065,a)].">
      <j1 rule="hyper" parents="64 3915 9065"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1637(a,1),9065(a,1,3))].">
      <j1 rule="para" parents="1637 9065"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1647(a,1),9065(a,1,3))].">
      <j1 rule="para" parents="1647 9065"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2325(a,1),9067(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2325 9067"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3774(a,1),9063(a,1,1))].">
      <j1 rule="para" parents="3774 9063"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),9072(a,1,1,1))].">
      <j1 rule="para" parents="14 9072"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(5193,a,9073,a)].">
      <j1 rule="hyper" parents="5193 9073"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1637(a,1),9074(a,1,2))].">
      <j1 rule="para" parents="1637 9074"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2325(a,1),9074(a,1,2))].">
      <j1 rule="para" parents="2325 9074"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5270,a,8051,a)].">
      <j1 rule="hyper" parents="5270 8051"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(8309(a,1),9078(a,1,3))].">
      <j1 rule="para" parents="8309 9078"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(9079(a,1),402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9079 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(9080(a,1),8336(a,1,1))].">
      <j1 rule="para" parents="9080 8336"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R(T(x \ a(y,x \ 1,y),y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9081(a,1),1978(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9081 1978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x * K(y,x \ z),u),T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(5171(a,1),6309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5171 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(K(y,x \ z) * x,x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,6452,a(flip),b,9083,a),flip(a)].">
      <j1 rule="hyper" parents="319 6452 9083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x \ z,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(5973(a,1),9084(a,2,1))].">
      <j1 rule="para" parents="5973 9084"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(9085(a,1),7200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9085 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ (y / (y / x))) * z)
    ]]></literal>
    <justification jstring="[hyper(4345,a,6658,a),flip(a)].">
      <j1 rule="hyper" parents="4345 6658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ ((y / x) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6384,a(flip),b,9087,a),flip(a)].">
      <j1 rule="hyper" parents="319 6384 9087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),9089(a,2,2,1,2))].">
      <j1 rule="para" parents="81 9089"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      K(x / y,z * ((y * (x / y)) \ y)) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(4345,a,9090,a)].">
      <j1 rule="hyper" parents="4345 9090"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K((y * (x / y)) \ y,(x / y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K((x / y) \ 1,(x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4995,a(flip),b,9093,a),flip(a)].">
      <j1 rule="hyper" parents="319 4995 9093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(y / x,(x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4645,a(flip),b,9094,a),flip(a)].">
      <j1 rule="hyper" parents="319 4645 9094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(R(y \ 1,y,x),z)) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3902(a,1),7268(a,1,2,2))].">
      <j1 rule="para" parents="3902 7268"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(4614(a,1),7309(a,1,1,2))].">
      <j1 rule="para" parents="4614 7309"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(7021(a,1),9099(a,1,1))].">
      <j1 rule="para" parents="7021 9099"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(35,a,8113,a(flip),b,9100,a),flip(a)].">
      <j1 rule="hyper" parents="35 8113 9100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,3898,a(flip),b,9101,a)].">
      <j1 rule="hyper" parents="64 3898 9101"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      (T(x,y) * (z * R(x,u,w))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4036(a,1),7358(a,1,1))].">
      <j1 rule="para" parents="4036 7358"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) = a(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(713,a,9105,a),flip(a)].">
      <j1 rule="hyper" parents="713 9105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9105(a,1),713(a,1))].">
      <j1 rule="para" parents="9105 713"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      a(T(x,y),T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4292(a,1),9106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 9106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      T(T(x,y) * L(x \ (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8955(a,1),7373(a,1,1))].">
      <j1 rule="para" parents="8955 7373"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      x * (L(x \ (y / (x \ 1)),z,u) * K(x,w)) = (L(y,z,u) / (x \ 1)) * K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,6489,a(flip),b,9109,a)].">
      <j1 rule="hyper" parents="64 6489 9109"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = (L(x,z,u) / (y \ 1)) * K(y,w)
    ]]></literal>
    <justification jstring="[hyper(5634,a,9110,a)].">
      <j1 rule="hyper" parents="5634 9110"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,8483,a(flip),b,9111,a),flip(a)].">
      <j1 rule="hyper" parents="319 8483 9111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(x / y,T(z,u)) \ T(K(y \ x,z),u)
    ]]></literal>
    <justification jstring="[para(78(a,1),7868(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 7868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(x / y,T(z,u)) \ K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6099(a,2),9113(a,2,2))].">
      <j1 rule="para" parents="6099 9113"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(z,T(x / y,u)) * K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6151,a(flip),b,9115,a),flip(a)].">
      <j1 rule="hyper" parents="319 6151 9115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(y / z,K(y,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7140,a(flip),b,9116,a),flip(a)].">
      <j1 rule="hyper" parents="64 7140 9116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(x,u))) = w
    ]]></literal>
    <justification jstring="[para(9117(a,2),7175(a,1))].">
      <j1 rule="para" parents="9117 7175"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      a(x / y,((y * x) / y) / (((y * x) / y) / T(y,x)),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(1294(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="1294 7872"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      a(x / y,((y * x) / y) / (x / y),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(1294(a,1),9120(a,1,2,2))].">
      <j1 rule="para" parents="1294 9120"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(81(a,1),8122(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="81 8122"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(587,a,9122,a)].">
      <j1 rule="hyper" parents="587 9122"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(9123(a,1),8062(a,1,1))].">
      <j1 rule="para" parents="9123 8062"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5468,a(flip),b,9124,a)].">
      <j1 rule="hyper" parents="64 5468 9124"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(8901,a,9125,a),flip(a)].">
      <j1 rule="hyper" parents="8901 9125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      K(x,R(y / (z * u),z * u,x)) = K(x,(y * x) / ((z * x) * u))
    ]]></literal>
    <justification jstring="[para(106(a,2),9125(a,1,2))].">
      <j1 rule="para" parents="106 9125"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(9014,a,9126,a),flip(a)].">
      <j1 rule="hyper" parents="9014 9126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7535,a(flip),b,9126,a)].">
      <j1 rule="hyper" parents="64 7535 9126"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(131,a,9129,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 9129 4012"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y / (x * (z * u)))) = K(y / ((x * z) * u),x)
    ]]></literal>
    <justification jstring="[para(9129(a,1),4430(a,1,2,2))].">
      <j1 rule="para" parents="9129 4430"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(9127(a,1),5745(a,1))].">
      <j1 rule="para" parents="9127 5745"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),9128(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),9133(a,2,2))].">
      <j1 rule="para" parents="20 9133"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(7961,a,9134,a)].">
      <j1 rule="hyper" parents="7961 9134"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8884,a(flip),b,9134,a),flip(a)].">
      <j1 rule="hyper" parents="64 8884 9134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(4256,a,9137,a)].">
      <j1 rule="hyper" parents="4256 9137"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,9137,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 9137 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7595,a,b,9137,a)].">
      <j1 rule="hyper" parents="64 7595 9137"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7838,a(flip),b,9137,a)].">
      <j1 rule="hyper" parents="64 7838 9137"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(31(a,1),9137(a,1,2))].">
      <j1 rule="para" parents="31 9137"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(537(a,1),9137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="537 9137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      T(R(x,y,z),(u * (y * z)) / ((x * y) * z)) = T(R(x,y,z),u / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(547(a,1),9140(a,1,2))].">
      <j1 rule="para" parents="547 9140"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,9141,a(flip),b,4849,a)].">
      <j1 rule="hyper" parents="130 9141 4849"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9138(a,2),4172(a,1))].">
      <j1 rule="para" parents="9138 4172"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      K(R(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7595(a,2),9149(a,1))].">
      <j1 rule="para" parents="7595 9149"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7692(a,2),9149(a,1))].">
      <j1 rule="para" parents="7692 9149"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(8901,a,9142,a)].">
      <j1 rule="hyper" parents="8901 9142"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      K(x,T(x \ (y \ z),y)) = K(x,x \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(8409,a,9142,a)].">
      <j1 rule="hyper" parents="8409 9142"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7223,a,b,9142,a)].">
      <j1 rule="hyper" parents="64 7223 9142"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9125,a(flip),b,9142,a)].">
      <j1 rule="hyper" parents="64 9125 9142"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(9152(a,1),9130(a,1,2))].">
      <j1 rule="para" parents="9152 9130"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9155(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(3555(a,1),9158(a,1,2,2))].">
      <j1 rule="para" parents="3555 9158"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5582,a,b,9143,a)].">
      <j1 rule="hyper" parents="64 5582 9143"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,9136,a(flip),b,239,a)].">
      <j1 rule="hyper" parents="130 9136 239"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,9144,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="131 9144 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(9144(a,1),7287(a,1,2,2))].">
      <j1 rule="para" parents="9144 7287"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,9147,a(flip),b,4039,a),flip(a)].">
      <j1 rule="hyper" parents="127 9147 4039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      K(T(x,y),x \ (y \ z)) = K(x,x \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(6261,a,9153,a)].">
      <j1 rule="hyper" parents="6261 9153"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(T(x,y),x \ (y \ z)) = (u * K(x \ (z / y),x)) \ u
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a,b,9165,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 9165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7536,a(flip),b,9156,a),flip(a)].">
      <j1 rule="hyper" parents="64 7536 9156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(5027(a,1),9162(a,2,2))].">
      <j1 rule="para" parents="5027 9162"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9158,a(flip),b,9167,a),flip(a)].">
      <j1 rule="hyper" parents="64 9158 9167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(9169(a,1),5591(a,1))].">
      <j1 rule="para" parents="9169 5591"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(4089,a,9157,a),flip(a)].">
      <j1 rule="hyper" parents="4089 9157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7287,a(flip),b,9163,a),flip(a)].">
      <j1 rule="hyper" parents="64 7287 9163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,7277,a(flip),b,9172,a),flip(a)].">
      <j1 rule="hyper" parents="64 7277 9172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6116,a(flip),b,9173,a),flip(a)].">
      <j1 rule="hyper" parents="64 6116 9173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) = T(y,x) * K(y \ (z / x),y)
    ]]></literal>
    <justification jstring="[hyper(40,a,8052,a,b,9166,a(flip))].">
      <j1 rule="hyper" parents="40 8052 9166"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(9137(a,1),9160(a,1,1))].">
      <j1 rule="para" parents="9137 9160"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5588,a(flip),b,9161,a),flip(a)].">
      <j1 rule="hyper" parents="64 5588 9161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(4122(a,1),9178(a,2,1))].">
      <j1 rule="para" parents="4122 9178"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,7454,a(flip),b,9179,a)].">
      <j1 rule="hyper" parents="64 7454 9179"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,9179,a(flip),b,7454,a(flip))].">
      <j1 rule="hyper" parents="127 9179 7454"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(797,a,9180,a)].">
      <j1 rule="hyper" parents="797 9180"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      x * (K(y \ x,y) * z) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(568,a,9180,a)].">
      <j1 rule="hyper" parents="568 9180"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,152,a(flip),b,9180,a)].">
      <j1 rule="hyper" parents="127 152 9180"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,9180,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 9180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,8887,a,b,9180,a)].">
      <j1 rule="hyper" parents="64 8887 9180"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(127,a,9180,a(flip),b,8887,a)].">
      <j1 rule="hyper" parents="127 9180 8887"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(6616(a,1),9180(a,1,2))].">
      <j1 rule="para" parents="6616 9180"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      K(((x * y) * z) / (y * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(9180(a,1),6864(a,1,1,1))].">
      <j1 rule="para" parents="9180 6864"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      K(x,y) \ K(y * x,z) = (x * y) \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,4012,a,b,9187,a)].">
      <j1 rule="hyper" parents="127 4012 9187"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * ((x * y) \ z)) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,8558,a,b,9187,a)].">
      <j1 rule="hyper" parents="64 8558 9187"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,9187,a(flip),b,4312,a)].">
      <j1 rule="hyper" parents="131 9187 4312"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(130,a,9187,a(flip),b,197,a)].">
      <j1 rule="hyper" parents="130 9187 197"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) \ z) = y \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(127,a,9187,a(flip),b,4555,a)].">
      <j1 rule="hyper" parents="127 9187 4555"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(9187(a,1),4440(a,1,2))].">
      <j1 rule="para" parents="9187 4440"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9187(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="9187 5822"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      K(x * ((y * z) \ u),z) = K(x * ((z * y) \ u),z)
    ]]></literal>
    <justification jstring="[para(9187(a,1),6066(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9187 6066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(600,a,9188,a)].">
      <j1 rule="hyper" parents="600 9188"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(584,a,9188,a)].">
      <j1 rule="hyper" parents="584 9188"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(386,a,9188,a)].">
      <j1 rule="hyper" parents="386 9188"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(331,a,9188,a),flip(a)].">
      <j1 rule="hyper" parents="331 9188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      K(x,y * z) \ ((x * y) * z) = ((y * z) * x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,85,a(flip),b,9188,a)].">
      <j1 rule="hyper" parents="127 85 9188"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),9188(a,1,2,1))].">
      <j1 rule="para" parents="10 9188"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      K(x,(x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) * z) = u
    ]]></literal>
    <justification jstring="[para(9188(a,1),5844(a,1,2))].">
      <j1 rule="para" parents="9188 5844"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(9188(a,1),6650(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9188 6650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(9188(a,1),6679(a,1,2,2))].">
      <j1 rule="para" parents="9188 6679"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      ((x \ y) * x) \ 1 = y \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(341,a,9203,a),flip(a)].">
      <j1 rule="hyper" parents="341 9203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[para(7038(a,1),9203(a,1,2))].">
      <j1 rule="para" parents="7038 9203"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,4786,a,b,9189,a(flip))].">
      <j1 rule="hyper" parents="35 4786 9189"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(8057,a,9214,a)].">
      <j1 rule="hyper" parents="8057 9214"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8055,a(flip),b,9214,a),flip(a)].">
      <j1 rule="hyper" parents="64 8055 9214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4774,a(flip),b,9214,a)].">
      <j1 rule="hyper" parents="64 4774 9214"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,9214,a(flip),b,8055,a(flip))].">
      <j1 rule="hyper" parents="131 9214 8055"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(9214(a,1),51(a,2))].">
      <j1 rule="para" parents="9214 51"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9214,a,b,9215,a)].">
      <j1 rule="hyper" parents="319 9214 9215"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,508,a(flip),b,9215,a),flip(a)].">
      <j1 rule="hyper" parents="64 508 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),9215(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(110(a,1),9215(a,1,2))].">
      <j1 rule="para" parents="110 9215"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(8056(a,1),9219(a,1))].">
      <j1 rule="para" parents="8056 9219"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      L((x / y) \ z,y \ x,y) = (y * (x / y)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,96,a(flip),b,9222,a),flip(a)].">
      <j1 rule="hyper" parents="64 96 9222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) = ((y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(341,a,9201,a)].">
      <j1 rule="hyper" parents="341 9201"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      x * (((y \ x) * y) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[hyper(131,a,9201,a(flip),b,159,a(flip))].">
      <j1 rule="hyper" parents="131 9201 159"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(4041(a,1),9201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4041 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      (x * y) \ (y * (x * z)) = L(K(y,x) * z,x,y)
    ]]></literal>
    <justification jstring="[para(4317(a,1),9216(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4317 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6099(a,2),9216(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6099 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ y = z
    ]]></literal>
    <justification jstring="[para(9221(a,2),337(a,1))].">
      <j1 rule="para" parents="9221 337"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(9195(a,2),571(a,1))].">
      <j1 rule="para" parents="9195 571"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * (((x * (y * K(x,z))) * K(x,z)) \ u)
    ]]></literal>
    <justification jstring="[para(6819(a,1),9195(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6819 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(6646(a,2),9207(a,1,1))].">
      <j1 rule="para" parents="6646 9207"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(4129(a,1),9227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4129 9227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x,T(T(((y \ z) * y) \ u,w),K(y,y \ z) * u)) = K(x,T((K(y,y \ z) * u) / z,w))
    ]]></literal>
    <justification jstring="[para(9227(a,1),6913(a,1,2,1,1))].">
      <j1 rule="para" parents="9227 6913"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ z) = x * (z \ (z / y))
    ]]></literal>
    <justification jstring="[para(9237(a,1),374(a,2,2))].">
      <j1 rule="para" parents="9237 374"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      x \ (x / y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(9237(a,1),626(a,1))].">
      <j1 rule="para" parents="9237 626"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,((x \ y) * x) \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,9228,a(flip),b,4095,a),flip(a)].">
      <j1 rule="hyper" parents="128 9228 4095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9220(a,1),5381(a,1,2))].">
      <j1 rule="para" parents="9220 5381"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),9243(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 9243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (u * K(z,y)),K(y,z),x) = (K(y,z) * x) \ (x * T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6801(a,1),9231(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6801 9231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = x \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7846,a,b,9197,a)].">
      <j1 rule="hyper" parents="64 7846 9197"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = (y * z) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8190,a,b,9202,a)].">
      <j1 rule="hyper" parents="64 8190 9202"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(4081(a,1),9217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4081 9217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      T(x * (y * z),K(z * y,z)) = (y * z) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6898,a,b,9248,a)].">
      <j1 rule="hyper" parents="64 6898 9248"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,5126,a(flip),b,9250,a(flip))].">
      <j1 rule="hyper" parents="35 5126 9250"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7124,a,b,9251,a)].">
      <j1 rule="hyper" parents="64 7124 9251"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      T(T(x,y * z),K(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6392,a,b,9251,a)].">
      <j1 rule="hyper" parents="64 6392 9251"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) * z) = T(x,z * ((z / y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,8556,a(flip),b,9251,a)].">
      <j1 rule="hyper" parents="64 8556 9251"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),9251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      K(x,y * z) * (z * x) = z * T(x,z * y)
    ]]></literal>
    <justification jstring="[para(9251(a,1),6222(a,2,2))].">
      <j1 rule="para" parents="9251 6222"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(3803(a,1),9255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3803 9255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9258">
    <literal><![CDATA[
      T(T(x,y * z),K(z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6829,a(flip),b,9253,a)].">
      <j1 rule="hyper" parents="64 6829 9253"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(6807,a,9258,a)].">
      <j1 rule="hyper" parents="6807 9258"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(410,a,9258,a)].">
      <j1 rule="hyper" parents="410 9258"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5965,a(flip),b,9258,a),flip(a)].">
      <j1 rule="hyper" parents="64 5965 9258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9258(a,1),6811(a,1,1))].">
      <j1 rule="para" parents="9258 6811"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      T(x,y * z) \ T(x,K(z,y)) = K(z * y,T(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(9259(a,1),4001(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9259 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6899,a(flip),b,9260,a)].">
      <j1 rule="hyper" parents="64 6899 9260"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,9264,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 9264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9264(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6147,a,b,9266,a),flip(a)].">
      <j1 rule="hyper" parents="319 6147 9266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(3812(a,1),9266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3812 9266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9269">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(4105,a,9265,a)].">
      <j1 rule="hyper" parents="4105 9265"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6927,a,b,9265,a(flip))].">
      <j1 rule="hyper" parents="35 6927 9265"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6143,a,b,9265,a(flip))].">
      <j1 rule="hyper" parents="35 6143 9265"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6121,a,b,9265,a(flip))].">
      <j1 rule="hyper" parents="35 6121 9265"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9265(a,2),4089(a,1))].">
      <j1 rule="para" parents="9265 4089"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      K(x / y,z * x) = K(y \ x,x * z)
    ]]></literal>
    <justification jstring="[hyper(6133,a,9269,a),flip(a)].">
      <j1 rule="hyper" parents="6133 9269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7144,a,b,9269,a)].">
      <j1 rule="hyper" parents="64 7144 9269"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9269(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9269(a,1,2,1))].">
      <j1 rule="para" parents="109 9269"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z \ 1) * y,z)) = u
    ]]></literal>
    <justification jstring="[para(9269(a,1),7180(a,1))].">
      <j1 rule="para" parents="9269 7180"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      K(x,y * z) * T(y,z) = T(y,z) * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(9269(a,1),6192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9269 6192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(7163,a,9275,a)].">
      <j1 rule="hyper" parents="7163 9275"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9275(a,1,2,1))].">
      <j1 rule="para" parents="10 9275"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),9275(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      K(x / y,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9275(a,1),6352(a,1))].">
      <j1 rule="para" parents="9275 6352"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(3812(a,1),9276(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3812 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z)) = K(x,(z \ y) * T(z,u))
    ]]></literal>
    <justification jstring="[para(5621(a,1),9276(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5621 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(4045,a,9267,a)].">
      <j1 rule="hyper" parents="4045 9267"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,7146,a,b,9286,a),flip(a)].">
      <j1 rule="hyper" parents="319 7146 9286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9286(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(7180,a,9288,a)].">
      <j1 rule="hyper" parents="7180 9288"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(6938,a,9288,a),flip(a)].">
      <j1 rule="hyper" parents="6938 9288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      K(T(x * y,x),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(6261,a,9288,a)].">
      <j1 rule="hyper" parents="6261 9288"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6258,a,9288,a)].">
      <j1 rule="hyper" parents="6258 9288"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      K(x * y,z * x) = K(y * x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9269,a(flip),b,9288,a)].">
      <j1 rule="hyper" parents="64 9269 9288"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,9288,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="130 9288 6838"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9288(a,1),6113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9288 6113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(9288(a,1),6938(a,1))].">
      <j1 rule="para" parents="9288 6938"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      K(x * y,(z * y) \ y) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6258,a,9290,a)].">
      <j1 rule="hyper" parents="6258 9290"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),9290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 9290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      K(x * T(x \ y,z),T(u,x)) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[para(443(a,1),9290(a,1,1))].">
      <j1 rule="para" parents="443 9290"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(9290(a,1),6938(a,1))].">
      <j1 rule="para" parents="9290 6938"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(8189(a,1),9290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8189 9290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(3103(a,2),9298(a,1,1))].">
      <j1 rule="para" parents="3103 9298"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(4639(a,1),9298(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4639 9298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(4990(a,1),9298(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4990 9298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(9298(a,1),7240(a,1,1,2))].">
      <j1 rule="para" parents="9298 7240"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9275,a(flip),b,9277,a),flip(a)].">
      <j1 rule="hyper" parents="64 9275 9277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,9306,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 9306 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      T(x,T(y,z) * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9306,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 9306 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4130(a,1),9306(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 9306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ (T(u,z) * z)) = T(x,(T(u,z) * z) / y)
    ]]></literal>
    <justification jstring="[para(9306(a,1),7138(a,1,1,2))].">
      <j1 rule="para" parents="9306 7138"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(250(a,1),9307(a,1,2,1))].">
      <j1 rule="para" parents="250 9307"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      T(x,(T(y,z * u) * z) * u) = T(x,(z * u) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(433(a,1),9307(a,1,2))].">
      <j1 rule="para" parents="433 9307"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(9281(a,1),7162(a,1))].">
      <j1 rule="para" parents="9281 7162"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(9287(a,2),7163(a,1))].">
      <j1 rule="para" parents="9287 7163"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (x * K(z * x,y))) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(9295(a,1),7934(a,1,2,2))].">
      <j1 rule="para" parents="9295 7934"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9288,a(flip),b,9302,a),flip(a)].">
      <j1 rule="hyper" parents="319 9288 9302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      ((T(x,y) * y) \ z) * K(y * x,(T(x,y) * y) \ z) = z / (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9316,a(flip),b,4148,a)].">
      <j1 rule="hyper" parents="131 9316 4148"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      T(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9308(a,2),4089(a,1))].">
      <j1 rule="para" parents="9308 4089"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(6899(a,2),9273(a,1))].">
      <j1 rule="para" parents="6899 9273"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      K(x * K(y,(x \ z) \ 1),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((y * (z \ x)) / y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(4744(a,2),9300(a,1,1))].">
      <j1 rule="para" parents="4744 9300"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(9201(a,1),9314(a,1,1,1))].">
      <j1 rule="para" parents="9201 9314"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(250(a,1),9318(a,1,2,1))].">
      <j1 rule="para" parents="250 9318"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),9257(a,1,2))].">
      <j1 rule="para" parents="23 9257"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),9268(a,1,2))].">
      <j1 rule="para" parents="23 9268"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8803,a(flip),b,9280,a),flip(a)].">
      <j1 rule="hyper" parents="64 8803 9280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9284(a,1),6938(a,1))].">
      <j1 rule="para" parents="9284 6938"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,w),y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(650(a,1),9326(a,1,2,1))].">
      <j1 rule="para" parents="650 9326"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7144(a,1),9326(a,1))].">
      <j1 rule="para" parents="7144 9326"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),L(u,z,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(9218(a,1),9326(a,1,2,1))].">
      <j1 rule="para" parents="9218 9326"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9277(a,1),9326(a,1))].">
      <j1 rule="para" parents="9277 9326"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(6111(a,1),9328(a,1))].">
      <j1 rule="para" parents="6111 9328"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[hyper(5768,a,9289,a)].">
      <j1 rule="hyper" parents="5768 9289"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * (1 \ z)) / x)),T(u,y))
    ]]></literal>
    <justification jstring="[para(1828(a,1),9289(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1828 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(9292(a,1),5465(a,1,2))].">
      <j1 rule="para" parents="9292 5465"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      K(T(x * y,(z * y) \ y) \ ((x * y) * u),w) = K(K(y * x,z \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(9297(a,1),4426(a,2,1,1))].">
      <j1 rule="para" parents="9297 4426"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[para(443(a,1),9323(a,1,2,1,1))].">
      <j1 rule="para" parents="443 9323"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      T(x,T(T(K(y,z) * (u / y),u / y),w)) = T(x,T(u / ((z * y) / z),w))
    ]]></literal>
    <justification jstring="[para(5300(a,2),9323(a,2,2,1))].">
      <j1 rule="para" parents="5300 9323"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,T(u,z)) * z,w))
    ]]></literal>
    <justification jstring="[para(6926(a,1),9324(a,1,2,1,1))].">
      <j1 rule="para" parents="6926 9324"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),9262(a,1))].">
      <j1 rule="para" parents="23 9262"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      T(T(x,K(y,K(z,u))),K(z,z * u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = w
    ]]></literal>
    <justification jstring="[para(6706(a,1),9319(a,1,1,2))].">
      <j1 rule="para" parents="6706 9319"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      T(T(x,K(y,K(z,u))),K(u,z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6758(a,1),9319(a,1,1,2))].">
      <j1 rule="para" parents="6758 9319"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(9261(a,2),6102(a,1,1))].">
      <j1 rule="para" parents="9261 6102"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(x,y) = K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(6275,a,9279,a)].">
      <j1 rule="hyper" parents="6275 9279"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,T(T(z,u) / y,w) * y)
    ]]></literal>
    <justification jstring="[para(3794(a,1),9311(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3794 9311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,5176,a,b,9343,a),flip(a)].">
      <j1 rule="hyper" parents="40 5176 9343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      T(x,y * z) \ T(x,K(y,z)) = K(z * y,T(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6791(a,1),9263(a,1,2))].">
      <j1 rule="para" parents="6791 9263"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      K((x \ 1) * T((x \ 1) \ y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[hyper(7180,a,9299,a)].">
      <j1 rule="hyper" parents="7180 9299"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      K(x * y,T(z,K(x,y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y * x) \ K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(9346(a,1),4533(a,1))].">
      <j1 rule="para" parents="9346 4533"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(4314(a,1),9194(a,1,2))].">
      <j1 rule="para" parents="4314 9194"/>
    </justification>
  </clause>

  <clause id="9350">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = R(z,x,y) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7278,a(flip),b,9206,a),flip(a)].">
      <j1 rule="hyper" parents="64 7278 9206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = ((y * z) * x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5116,a,9350,a(flip))].">
      <j1 rule="hyper" parents="5116 9350"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,z * z),R(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,1047,a,b,9312,a),flip(a)].">
      <j1 rule="hyper" parents="319 1047 9312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,8015,a(flip),b,9332,a),flip(a)].">
      <j1 rule="hyper" parents="319 8015 9332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      K(x / ((y * z) * u),y) = K(x / (y * (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(4465,a,9131,a),flip(a)].">
      <j1 rule="hyper" parents="4465 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      K(x / (y * (z * x)),y) = K(z \ (y \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(6488,a,9354,a),flip(a)].">
      <j1 rule="hyper" parents="6488 9354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      K(x / ((y * x) * z),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(8900,a,9355,a)].">
      <j1 rule="hyper" parents="8900 9355"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      K((x \ y) / (z * y),z) = K(x \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9355(a,1,1,2,2))].">
      <j1 rule="para" parents="10 9355"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      K((x / y) \ (z \ 1),z) = K(y / (x * z),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),9356(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * (y / (y / x))),z) = K((x / y) \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(8241(a,1),9357(a,1,1,1))].">
      <j1 rule="para" parents="8241 9357"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8156,a(flip),b,9159,a),flip(a)].">
      <j1 rule="hyper" parents="64 8156 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(6545(a,2),9168(a,2,2))].">
      <j1 rule="para" parents="6545 9168"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) * y,w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9324,a(flip),b,9336,a)].">
      <j1 rule="hyper" parents="64 9324 9336"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(z,u) * y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),9362(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * (y / (y / x))),z) = K(y / (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9358,a(flip),b,9359,a),flip(a)].">
      <j1 rule="hyper" parents="319 9358 9359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      K(R(x \ (y / z),x,y / (y / z)),x) = K(y / (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4706,a,b,9364,a)].">
      <j1 rule="hyper" parents="64 4706 9364"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(9150,a,9365,a),flip(a)].">
      <j1 rule="hyper" parents="9150 9365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(8902,a,9366,a)].">
      <j1 rule="hyper" parents="8902 9366"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(9366(a,1),8218(a,2,2))].">
      <j1 rule="para" parents="9366 8218"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7286,a,b,9367,a)].">
      <j1 rule="hyper" parents="64 7286 9367"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(9370(a,1),5932(a,1,1))].">
      <j1 rule="para" parents="9370 5932"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(6189,a,9371,a)].">
      <j1 rule="hyper" parents="6189 9371"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7588,a(flip),b,9372,a)].">
      <j1 rule="hyper" parents="64 7588 9372"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(9373(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9373 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,9374,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 9374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6244,a,9375,a)].">
      <j1 rule="hyper" parents="6244 9375"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      K(x \ (y / z),x) \ y = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(9375(a,1),5927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9375 5927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(78(a,1),9376(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 9376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,(1 / z) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6464,a,b,9378,a)].">
      <j1 rule="hyper" parents="64 6464 9378"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      K(x \ (y \ z),T(x,y)) = K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,7962,a(flip),b,9175,a(flip))].">
      <j1 rule="hyper" parents="35 7962 9175"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      K(x \ ((y * z) / y),x) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),9380(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9382">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(4149,a,9317,a)].">
      <j1 rule="hyper" parents="4149 9317"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T((y / u) * K(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9323,a(flip),b,9337,a),flip(a)].">
      <j1 rule="hyper" parents="64 9323 9337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,y * T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[para(443(a,1),9344(a,2,2))].">
      <j1 rule="para" parents="443 9344"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),y / R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,9145,a)].">
      <j1 rule="hyper" parents="64 27 9145"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,(z \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(3750(a,1),9379(a,2,2))].">
      <j1 rule="para" parents="3750 9379"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3274,a(flip),b,9385,a),flip(a)].">
      <j1 rule="hyper" parents="319 3274 9385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,8045,a(flip),b,9386,a),flip(a)].">
      <j1 rule="hyper" parents="319 8045 9386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7142,a(flip),b,9388,a),flip(a)].">
      <j1 rule="hyper" parents="319 7142 9388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8184,a,9389,a),flip(a)].">
      <j1 rule="hyper" parents="8184 9389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,8164,a,b,9390,a)].">
      <j1 rule="hyper" parents="319 8164 9390"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      T(x,T(x \ y,z)) = T(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,9390,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 9390 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(8243,a,9390,a(flip))].">
      <j1 rule="hyper" parents="8243 9390"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),9390(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      T(T(x,x \ T(y,z)),T(u,x)) = T(T(x,u),T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(9392(a,1),3271(a,1,1))].">
      <j1 rule="para" parents="9392 3271"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(3794(a,1),9394(a,1,2))].">
      <j1 rule="para" parents="3794 9394"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      K(x \ 1,T(R(y,x,1 / x),z) / (x \ 1)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[para(2740(a,1),9396(a,2,2,1))].">
      <j1 rule="para" parents="2740 9396"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(73(a,1),9393(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="73 9393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,7142,a,b,9391,a),flip(a)].">
      <j1 rule="hyper" parents="319 7142 9391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(9399(a,2),7180(a,1))].">
      <j1 rule="para" parents="9399 7180"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      T(T(x,y),T(x \ z,u)) = T(T(x,y),x \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(3366,a,9395,a),flip(a)].">
      <j1 rule="hyper" parents="3366 9395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      T((x \ T(y,x)) \ y,K(z,x \ y)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6835,a,b,9402,a)].">
      <j1 rule="hyper" parents="64 6835 9402"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8042,a(flip),b,9398,a)].">
      <j1 rule="hyper" parents="64 8042 9398"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(8043,a,9404,a),flip(a)].">
      <j1 rule="hyper" parents="8043 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(478(a,1),9401(a,1,2))].">
      <j1 rule="para" parents="478 9401"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(3834(a,2),9406(a,1))].">
      <j1 rule="para" parents="3834 9406"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(2741(a,1),9397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2741 9397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,9270,a,b,9408,a)].">
      <j1 rule="hyper" parents="319 9270 9408"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,2917,a,b,9409,a)].">
      <j1 rule="hyper" parents="319 2917 9409"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,9410,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 9410 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = R(T(x,R(x,z,u) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,27,a,b,9387,a),flip(a)].">
      <j1 rule="hyper" parents="319 27 9387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      R(T(x,x \ ((y * (z * u)) / (z * u))),z,u) = R(T(x,R(x,z,u) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(9171(a,1),9412(a,1,1))].">
      <j1 rule="para" parents="9171 9412"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9413(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 9413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(605,a,9414,a),flip(a)].">
      <j1 rule="hyper" parents="605 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      T(x,R(x,y,z) \ u) = (x \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(43,a,796,a(flip),b,9414,a),flip(a)].">
      <j1 rule="hyper" parents="43 796 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,x \ w),y,z) * u) = K(R(x,y,z) \ w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(9414(a,1),4432(a,1,2,1))].">
      <j1 rule="para" parents="9414 4432"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      T(L(x,x,x),x \ y) = (L(x,x,x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(661(a,1),9416(a,1,2,1))].">
      <j1 rule="para" parents="661 9416"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(9416(a,1),1125(a,1,2))].">
      <j1 rule="para" parents="9416 1125"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,796,a(flip),b,9415,a)].">
      <j1 rule="hyper" parents="64 796 9415"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9415(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(318(a,1),9415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="318 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      (R(x / (x / y),z,u) \ x) \ x = R(y,z,u)
    ]]></literal>
    <justification jstring="[para(347(a,1),9415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="347 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[para(7267(a,1),9415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7267 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(4629(a,1),9422(a,2,1))].">
      <j1 rule="para" parents="4629 9422"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(9424(a,1),1589(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9424 1589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(9424(a,1),3875(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9424 3875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(9424(a,1),5605(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9424 5605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      R(x / (x / y),z,u) \ x = x / R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(207,a,9425,a),flip(a)].">
      <j1 rule="hyper" parents="207 9425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2313(a,1),9432(a,1,1,1))].">
      <j1 rule="para" parents="2313 9432"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,2971,a,b,9420,a),flip(a)].">
      <j1 rule="hyper" parents="319 2971 9420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1122(a,1),9423(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1122 9423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(5566(a,1),9426(a,1,1))].">
      <j1 rule="para" parents="5566 9426"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      T(K(x * R(y \ 1,y,z),y \ 1) / y,x) = R(1 / y,x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(9430(a,1),7978(a,1,1,1))].">
      <j1 rule="para" parents="9430 7978"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(734(a,1),9434(a,1,1)),flip(a)].">
      <j1 rule="para" parents="734 9434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3769,a,b,9436,a(flip))].">
      <j1 rule="hyper" parents="36 3769 9436"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,9442,a)].">
      <j1 rule="hyper" parents="145 9442"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(6099(a,2),9439(a,2,1))].">
      <j1 rule="para" parents="6099 9439"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      ((K(x,T(y,z)) * L(x,u,w)) * z) \ (L(x,u,w) * z) = R(K(y,L(x,z,L(x,u,w))),L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(7194(a,1),9445(a,2,1))].">
      <j1 rule="para" parents="7194 9445"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = L(T(R(x,y,z),u),u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,237,a(flip),b,9438,a),flip(a)].">
      <j1 rule="hyper" parents="319 237 9438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,890,a(flip),b,9447,a),flip(a)].">
      <j1 rule="hyper" parents="319 890 9447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      R(T(x,x * y),z,u) \ R(x,z,u) = K(R(x,z,u) * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9448(a,1),4027(a,1,1))].">
      <j1 rule="para" parents="9448 4027"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(8435(a,1),9441(a,1,2))].">
      <j1 rule="para" parents="8435 9441"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1920(a,1),9450(a,1,2,1))].">
      <j1 rule="para" parents="1920 9450"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(3547(a,1),9451(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3547 9451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,y,z)) = K(x * u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4252,a,9449,a),flip(a)].">
      <j1 rule="hyper" parents="4252 9449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5865,a,9453,a)].">
      <j1 rule="hyper" parents="5865 9453"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7929,a,b,9454,a),flip(a)].">
      <j1 rule="hyper" parents="319 7929 9454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(3585(a,1),9452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3585 9452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(199,a,9456,a)].">
      <j1 rule="hyper" parents="199 9456"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2796,a(flip),b,9457,a)].">
      <j1 rule="hyper" parents="64 2796 9457"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(3334(a,1),9236(a,1,1,1,1))].">
      <j1 rule="para" parents="3334 9236"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(885(a,1),9347(a,1,1))].">
      <j1 rule="para" parents="885 9347"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(6356,a,9463,a),flip(a)].">
      <j1 rule="hyper" parents="6356 9463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4824,a,9417,a),flip(a)].">
      <j1 rule="hyper" parents="4824 9417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,2976,a(flip),b,9465,a),flip(a)].">
      <j1 rule="hyper" parents="319 2976 9465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      T(R(x,y,z) * K(x \ u,R(x,y,z)),u) = L(R(x,y,z),R(x,y,z) \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(9465(a,1),3991(a,1,1,2))].">
      <j1 rule="para" parents="9465 3991"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9466(a,1),3716(a,1,2))].">
      <j1 rule="para" parents="9466 3716"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2532,a(flip),b,9468,a)].">
      <j1 rule="hyper" parents="64 2532 9468"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,3595,a(flip),b,9469,a),flip(a)].">
      <j1 rule="hyper" parents="319 3595 9469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4906,a(flip),b,9428,a),flip(a)].">
      <j1 rule="hyper" parents="319 4906 9428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      (R(x,y,z) \ u) \ T(u,R(x,y,z)) = R((x \ u) \ T(u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4904(a,1),9471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4904 9471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      (x / R(y,z,u)) * R((y \ w) \ T(w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9472(a,1),8679(a,1,2))].">
      <j1 rule="para" parents="9472 8679"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      T(R(x * K(x \ y,x),z,u),y) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(4502(a,1),9467(a,1,1))].">
      <j1 rule="para" parents="4502 9467"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      R(T(x * K(x \ y,x),y),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,9474,a)].">
      <j1 rule="hyper" parents="64 27 9474"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(L(x,x \ u,x),y,z)
    ]]></literal>
    <justification jstring="[para(3991(a,1),9475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3991 9475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = L(R(x,y,z),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,29,a(flip),b,9476,a),flip(a)].">
      <j1 rule="hyper" parents="319 29 9476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(9477(a,1),1153(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9477 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * z) / x)),T(u,y))
    ]]></literal>
    <justification jstring="[para(66(a,1),9333(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="66 9333"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ ((x * z) / x),T(u,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),9480(a,2,1,2))].">
      <j1 rule="para" parents="7 9480"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x * z) / x) / y,u) = w
    ]]></literal>
    <justification jstring="[para(9481(a,2),6990(a,1))].">
      <j1 rule="para" parents="9481 6990"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      ((K(x,y) * z) * ((K(y,x) \ 1) \ 1)) * K(u,y) = ((1 / (1 / K(y,x))) \ z) * (K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(4356(a,1),8364(a,1,1,1))].">
      <j1 rule="para" parents="4356 8364"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8447(a,1),8453(a,2,2,1,1))].">
      <j1 rule="para" parents="8447 8453"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4213(a,1),9484(a,2,2,1))].">
      <j1 rule="para" parents="4213 9484"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4213(a,1),9485(a,1,1,2,1))].">
      <j1 rule="para" parents="4213 9485"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = K(y,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4382,a(flip),b,9487,a)].">
      <j1 rule="hyper" parents="64 4382 9487"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = ((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) \ (((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) * x)
    ]]></literal>
    <justification jstring="[para(9487(a,1),524(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9487 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) * v6 = K(x,y) * (R(K(y,x),z,u) * v6)
    ]]></literal>
    <justification jstring="[para(9487(a,2),7975(a,1,1))].">
      <j1 rule="para" parents="9487 7975"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      R(K(x,K(y,z)) * R(K(y,K(z,x)),u,w),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(6705(a,1),9490(a,1,1,1,2,1))].">
      <j1 rule="para" parents="6705 9490"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,T(y,z)) * u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6816,a(flip),b,8562,a),flip(a)].">
      <j1 rule="hyper" parents="64 6816 8562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6160(a,1),8819(a,2,2))].">
      <j1 rule="para" parents="6160 8819"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(z,R(y \ 1,y,x))) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(6791(a,1),9098(a,1,2))].">
      <j1 rule="para" parents="6791 9098"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      (L(x,y,z) * (K(x,T(u,w)) * w)) \ (L(x,y,z) * w) = R(K(u,L(x,w,L(x,y,z))),L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(3471(a,1),9446(a,1,1))].">
      <j1 rule="para" parents="3471 9446"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)) = (x / R(y,z,u)) * R(R(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(3500(a,1),9473(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3500 9473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = ((K(y,x) * z) * K(x,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(2492(a,1),9483(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2492 9483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z,K(x,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(5966(a,1),9498(a,2,1))].">
      <j1 rule="para" parents="5966 9498"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,8651,a,b,9499,a),flip(a)].">
      <j1 rule="hyper" parents="319 8651 9499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2495(a,1),9500(a,1,1,1))].">
      <j1 rule="para" parents="2495 9500"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(4356(a,1),9501(a,1,1))].">
      <j1 rule="para" parents="4356 9501"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,9502,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 9502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),K(x,u)) = z * K(K(u,x) * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8751,a(flip),b,9502,a),flip(a)].">
      <j1 rule="hyper" parents="64 8751 9502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,y) * K(y,x)) = T(z * K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[para(2099(a,1),9503(a,1,2))].">
      <j1 rule="para" parents="2099 9503"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      T(x * K(y,z),K(u,z)) / (K(u,z) * x) = (K(y,z) * K(z,u)) * K(K(u,z) * x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,9505,a(flip),b,4095,a)].">
      <j1 rule="hyper" parents="128 9505 4095"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(6795(a,1),9504(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6795 9504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,R(z,y,x))) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(7474(a,1),9495(a,1,2))].">
      <j1 rule="para" parents="7474 9495"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,z)) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(9137(a,1),9508(a,1,2,2))].">
      <j1 rule="para" parents="9137 9508"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(3358(a,1),9509(a,2,2))].">
      <j1 rule="para" parents="3358 9509"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(x,T(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(6392(a,1),9510(a,1,2))].">
      <j1 rule="para" parents="6392 9510"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) = R(K(w,L(x,u,L(x,y,z))),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6839(a,1),9496(a,1,1,2))].">
      <j1 rule="para" parents="6839 9496"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7337,a,9513,a),flip(a)].">
      <j1 rule="hyper" parents="7337 9513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7749(a,1),9514(a,1,1))].">
      <j1 rule="para" parents="7749 9514"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5461,a(flip),b,9515,a)].">
      <j1 rule="hyper" parents="64 5461 9515"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5002,a(flip),b,9516,a),flip(a)].">
      <j1 rule="hyper" parents="319 5002 9516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8945,a,b,9518,a)].">
      <j1 rule="hyper" parents="64 8945 9518"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(7168,a,9519,a)].">
      <j1 rule="hyper" parents="7168 9519"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      L(x,L(y,K(z,u),u),(z * u) / z) = (u * (K(z,u) * y)) \ ((u * K(z,u)) * (y * x))
    ]]></literal>
    <justification jstring="[para(4538(a,1),4198(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4538 4198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      L(x,L(y,K(z,u),u),(z * u) / z) = (u * (K(z,u) * y)) \ (u * (K(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(4526(a,1),9521(a,2,2))].">
      <j1 rule="para" parents="4526 9521"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(x,L(y,K(z,u),u),(z * u) / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,484,a(flip),b,9522,a)].">
      <j1 rule="hyper" parents="319 484 9522"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(x,y,(z * u) / z)
    ]]></literal>
    <justification jstring="[para(4538(a,1),9523(a,2,2))].">
      <j1 rule="para" parents="4538 9523"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4506,a(flip),b,9524,a),flip(a)].">
      <j1 rule="hyper" parents="319 4506 9524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8053,a(flip),b,9525,a)].">
      <j1 rule="hyper" parents="64 8053 9525"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      L(x,y,K(z,u * u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,928,a(flip),b,9525,a),flip(a)].">
      <j1 rule="hyper" parents="42 928 9525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(7971,a,9527,a)].">
      <j1 rule="hyper" parents="7971 9527"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(9219,a,9526,a),flip(a)].">
      <j1 rule="hyper" parents="9219 9526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      L(x,y,T(z,u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9528,a(flip),b,9526,a),flip(a)].">
      <j1 rule="hyper" parents="64 9528 9526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5796,a(flip),b,9526,a),flip(a)].">
      <j1 rule="hyper" parents="64 5796 9526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(9526(a,1),9219(a,1))].">
      <j1 rule="para" parents="9526 9219"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,T(y,x)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(319,a,5138,a(flip),b,9529,a),flip(a)].">
      <j1 rule="hyper" parents="319 5138 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      L(T(x,y),z,T(u,z)) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a(flip),b,9529,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1683,a(flip),b,9529,a)].">
      <j1 rule="hyper" parents="64 1683 9529"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(111(a,1),9529(a,1,3)),flip(a)].">
      <j1 rule="para" parents="111 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4143(a,1),9529(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4143 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(9532(a,1),25(a,2,1))].">
      <j1 rule="para" parents="9532 25"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2034,a,b,9531,a)].">
      <j1 rule="hyper" parents="64 2034 9531"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      L(L(x,y,y \ z),K(u \ w,u),w / u) = L(x,y,z / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4239,a,b,9538,a)].">
      <j1 rule="hyper" parents="319 4239 9538"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,717,a(flip),b,9538,a),flip(a)].">
      <j1 rule="hyper" parents="64 717 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,506,a(flip),b,9538,a),flip(a)].">
      <j1 rule="hyper" parents="64 506 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9538,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="131 9538 97"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[para(9538(a,1),745(a,2,1))].">
      <j1 rule="para" parents="9538 745"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[para(9538(a,1),901(a,2,1))].">
      <j1 rule="para" parents="9538 901"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1775,a(flip),b,9545,a)].">
      <j1 rule="hyper" parents="64 1775 9545"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(226(a,1),9545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="226 9545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(276(a,1),9545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="276 9545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      a(L(x \ ((y * y) \ z),x,x),u,w) = a((y * y) * (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(9545(a,1),2243(a,1,1))].">
      <j1 rule="para" parents="9545 2243"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(5172(a,1),9545(a,1,2))].">
      <j1 rule="para" parents="5172 9545"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8824,a(flip),b,9554,a)].">
      <j1 rule="hyper" parents="64 8824 9554"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,3205,a(flip),b,9554,a),flip(a)].">
      <j1 rule="hyper" parents="64 3205 9554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      L(x,x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,227,a(flip),b,9554,a),flip(a)].">
      <j1 rule="hyper" parents="64 227 9554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      K(L(x,1 / y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9554(a,2),8169(a,1,1))].">
      <j1 rule="para" parents="9554 8169"/>
    </justification>
  </clause>

  <clause id="9565">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(4221,a,9561,a)].">
      <j1 rule="hyper" parents="4221 9561"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(9561(a,1),4412(a,1,2))].">
      <j1 rule="para" parents="9561 4412"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(6925(a,1),9561(a,1,3))].">
      <j1 rule="para" parents="6925 9561"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(9565(a,1),51(a,2))].">
      <j1 rule="para" parents="9565 51"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      L(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(5084(a,1),9565(a,1,3))].">
      <j1 rule="para" parents="5084 9565"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      L(x,y \ 1,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(4221,a,9560,a)].">
      <j1 rule="hyper" parents="4221 9560"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      L(x,y \ 1,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1740,a,9560,a)].">
      <j1 rule="hyper" parents="1740 9560"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,6227,a(flip),b,9560,a),flip(a)].">
      <j1 rule="hyper" parents="319 6227 9560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4963,a(flip),b,9560,a),flip(a)].">
      <j1 rule="hyper" parents="319 4963 9560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9560(a,2),5385(a,1,2))].">
      <j1 rule="para" parents="9560 5385"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K((1 / y) \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(302(a,1),9564(a,1,1))].">
      <j1 rule="para" parents="302 9564"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),9567(a,1,3,1))].">
      <j1 rule="para" parents="11 9567"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      (K(x,y \ z) * (z \ y)) * u = K(x,y \ z) * ((z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(1143,a,9569,a),flip(a)].">
      <j1 rule="hyper" parents="1143 9569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      L(x,y \ (y / z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),9569(a,1,3,2))].">
      <j1 rule="para" parents="81 9569"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y \ 1,u) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(9573(a,1),4826(a,1))].">
      <j1 rule="para" parents="9573 4826"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(9576(a,1),9196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9576 9196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      (K(x,y) \ (z \ (z / x))) * u = K(y,x) * ((z \ (z / x)) * u)
    ]]></literal>
    <justification jstring="[para(9579(a,1),4371(a,1,2))].">
      <j1 rule="para" parents="9579 4371"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,1584,a,b,9553,a),flip(a)].">
      <j1 rule="hyper" parents="319 1584 9553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      L(x,K(y,z),y * z) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,9182,a(flip),b,9557,a),flip(a)].">
      <j1 rule="hyper" parents="319 9182 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,7627,a(flip),b,9557,a),flip(a)].">
      <j1 rule="hyper" parents="319 7627 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (K(x,T(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,9557,a,b,9232,a)].">
      <j1 rule="hyper" parents="131 9557 9232"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9586(a,1),25(a,2,1))].">
      <j1 rule="para" parents="9586 25"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9586(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="9586 435"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4012(a,1),9586(a,1,2))].">
      <j1 rule="para" parents="4012 9586"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      (x * (K(y,z) * y)) * K(y,u) = x * (K(y,z) * T(y,u))
    ]]></literal>
    <justification jstring="[para(9586(a,1),5360(a,1,2,1))].">
      <j1 rule="para" parents="9586 5360"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      ((x * y) * K(x,y)) \ z = K(x,y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,9585,a)].">
      <j1 rule="hyper" parents="64 302 9585"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),9585(a,1,3))].">
      <j1 rule="para" parents="10 9585"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4881,a(flip),b,9597,a)].">
      <j1 rule="hyper" parents="64 4881 9597"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9589(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9589 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,u),w,v5) = x * (K(y,z) * L(T(y,u),w,v5))
    ]]></literal>
    <justification jstring="[para(9589(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="9589 435"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(9571(a,1),1741(a,1))].">
      <j1 rule="para" parents="9571 1741"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      T(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(9535(a,1),9533(a,1))].">
      <j1 rule="para" parents="9535 9533"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,9541,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      L(T(x,y),y,T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,612,a(flip),b,9541,a),flip(a)].">
      <j1 rule="hyper" parents="319 612 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      L(x,y * (1 / y),z) = x
    ]]></literal>
    <justification jstring="[hyper(495,a,9555,a),flip(a)].">
      <j1 rule="hyper" parents="495 9555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(78(a,1),9555(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 9555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      (x * (y * (1 / y))) \ z = (y * (1 / y)) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,9606,a)].">
      <j1 rule="hyper" parents="64 302 9606"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((x * (1 / x)) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(127,a,4882,a(flip),b,9606,a(flip))].">
      <j1 rule="hyper" parents="127 4882 9606"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      L(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(9584(a,2),1741(a,1))].">
      <j1 rule="para" parents="9584 1741"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      L(T((x \ y) * T(x,y),x),z,(x \ y) * T(x,y)) = L((x \ y) * x,z,T((x \ y) * T(x,y),u))
    ]]></literal>
    <justification jstring="[para(3338(a,1),9604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3338 9604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(T(x,y),z,T(x,y))
    ]]></literal>
    <justification jstring="[para(9604(a,1),8385(a,1,2,1))].">
      <j1 rule="para" parents="9604 8385"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      (x * (1 / x)) \ (((x \ 1) * x) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(48,a,9610,a)].">
      <j1 rule="hyper" parents="48 9610"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      (x * (1 / x)) \ (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(39,a,2697,a,b,9610,a),flip(a)].">
      <j1 rule="hyper" parents="39 2697 9610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),9610(a,1,2))].">
      <j1 rule="para" parents="9 9610"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(130,a,9615,a(flip),b,2335,a),flip(a)].">
      <j1 rule="hyper" parents="130 9615 2335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      ((x * (1 / x)) \ y) \ z = y \ (((x \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(9617(a,2),1660(a,2,2))].">
      <j1 rule="para" parents="9617 1660"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(9617(a,2),1661(a,1,1))].">
      <j1 rule="para" parents="9617 1661"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = (x * (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[para(9617(a,2),1662(a,1,1))].">
      <j1 rule="para" parents="9617 1662"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = y / ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(9618(a,2),3783(a,1,1))].">
      <j1 rule="para" parents="9618 3783"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      L(T((x / y) \ 1,y * (x / y)) \ 1,(x / y) \ 1,T(y * (x / y),(x / y) \ 1)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(8555(a,1),9534(a,2,1))].">
      <j1 rule="para" parents="8555 9534"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ ((x / (x * K(y,z))) * u)
    ]]></literal>
    <justification jstring="[para(5176(a,1),9548(a,1,3))].">
      <j1 rule="para" parents="5176 9548"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,x) = w
    ]]></literal>
    <justification jstring="[para(9541(a,2),9603(a,1))].">
      <j1 rule="para" parents="9541 9603"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      L(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(1775(a,2),9611(a,1))].">
      <j1 rule="para" parents="1775 9611"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(5172(a,1),9626(a,1,2))].">
      <j1 rule="para" parents="5172 9626"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),9598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 9598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = (y * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(434(a,1),9616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="434 9616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,u \ z) * z = (z / u) * (u * K(x,y))
    ]]></literal>
    <justification jstring="[para(6848(a,1),9550(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6848 9550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2130(a,1),9566(a,1,1))].">
      <j1 rule="para" parents="2130 9566"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5227,a(flip),b,9575,a),flip(a)].">
      <j1 rule="hyper" parents="319 5227 9575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,u) \ 1,x) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(9580,a,7617,a)].">
      <j1 rule="hyper" parents="9580 7617"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      K(x,y) \ ((x * y) \ z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(4163(a,1),9596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4163 9596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      K(x,y) * ((y * x) \ z) = (T(y,x) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4384,a,9636,a)].">
      <j1 rule="hyper" parents="4384 9636"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      (x * y) * (K(x,y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(131,a,69,a(flip),b,9636,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 69 9636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((T(x,y) * y) * z) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9638(a,1),4667(a,1,2))].">
      <j1 rule="para" parents="9638 4667"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = (x * (1 / x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(9618(a,2),9609(a,1,1))].">
      <j1 rule="para" parents="9618 9609"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      (x * y) \ ((x * (1 / x)) \ z) = (T(x,x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(4433(a,1),9620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4433 9620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = ((x \ 1) * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9617,a,b,9621,a),flip(a)].">
      <j1 rule="hyper" parents="319 9617 9621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      (x * y) / ((y * (1 / y)) \ z) = (x * T(y,y \ 1)) / z
    ]]></literal>
    <justification jstring="[para(2697(a,1),9622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2697 9622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4550,a(flip),b,9633,a),flip(a)].">
      <j1 rule="hyper" parents="64 4550 9633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ z) = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9620,a(flip),b,9640,a),flip(a)].">
      <j1 rule="hyper" parents="64 9620 9640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((y * x) / z) = (y * T(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(2697(a,1),9642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2697 9642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      x \ (K(y,x \ 1) * z) = K(y,x \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(600,a,9644,a)].">
      <j1 rule="hyper" parents="600 9644"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,66,a,b,9644,a)].">
      <j1 rule="hyper" parents="319 66 9644"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ ((x * (1 / x)) \ z)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(39,a,9615,a,b,9645,a)].">
      <j1 rule="hyper" parents="39 9615 9645"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ 1) = y \ ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(3638(a,1),9645(a,2,2))].">
      <j1 rule="para" parents="3638 9645"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      (x \ 1) \ (((y \ 1) * y) \ z) = (x \ ((y \ 1) * y)) \ z
    ]]></literal>
    <justification jstring="[para(9653(a,1),9619(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9653 9619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ z) = y \ (((x \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(9615(a,1),9652(a,1,2,2))].">
      <j1 rule="para" parents="9615 9652"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      x \ (((y \ 1) * y) \ (x * z)) = ((y \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),9655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * ((x \ 1) * z)) = y * L(x \ z,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,96,a,b,9656,a),flip(a)].">
      <j1 rule="hyper" parents="131 96 9656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9658">
    <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(9590(a,1),5486(a,2,1))].">
      <j1 rule="para" parents="9590 5486"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      (x * T(y,z)) * K(y,u) = x * (K(y,z) * T(y,u))
    ]]></literal>
    <justification jstring="[para(4022(a,2),9594(a,1,1,2))].">
      <j1 rule="para" parents="4022 9594"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      T(x,(T(y,z * (K(u,w) * T(u,v5))) * (z * T(u,w))) * K(u,v5)) = T(x,((z * T(u,w)) * K(u,v5)) * R(y,z * T(u,w),K(u,v5)))
    ]]></literal>
    <justification jstring="[para(9659(a,1),9312(a,1,2,1,1,2))].">
      <j1 rule="para" parents="9659 9312"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (((x \ (x / y)) * (1 / (x \ (x / y)))) \ z)
    ]]></literal>
    <justification jstring="[para(5056(a,1),9641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5056 9641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      T(x,(y * T(z,z \ 1)) / u) = T(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(9646(a,1),3784(a,1,2))].">
      <j1 rule="para" parents="9646 3784"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(4321,a,9650,a)].">
      <j1 rule="hyper" parents="4321 9650"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((y \ 1) \ z) = (y \ ((x \ 1) * x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,9655,a,b,9654,a)].">
      <j1 rule="hyper" parents="64 9655 9654"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      L(x,y,z / y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(9546(a,1),4551(a,1))].">
      <j1 rule="para" parents="9546 4551"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(8926,a,9635,a)].">
      <j1 rule="hyper" parents="8926 9635"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5721,a(flip),b,9667,a),flip(a)].">
      <j1 rule="hyper" parents="64 5721 9667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,6523,a(flip),b,9668,a),flip(a)].">
      <j1 rule="hyper" parents="319 6523 9668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(6349,a,9669,a)].">
      <j1 rule="hyper" parents="6349 9669"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6684,a(flip),b,9670,a)].">
      <j1 rule="hyper" parents="64 6684 9670"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(6479,a,9671,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6479 9671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z \ u,x),y) = K(L(z,x,x \ 1) \ u,T(x,y))
    ]]></literal>
    <justification jstring="[para(9672(a,1),4662(a,1,2,1,2))].">
      <j1 rule="para" parents="9672 4662"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      ((x \ y) * K(z,y \ x)) * u = K(z,y \ x) * ((x \ y) * u)
    ]]></literal>
    <justification jstring="[para(2154(a,1),9577(a,1,1))].">
      <j1 rule="para" parents="2154 9577"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8397,a(flip),b,9614,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 8397 9614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9678(a,1),8394(a,1,1,2))].">
      <j1 rule="para" parents="9678 8394"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      K(T(x,y * z) * z,T(x,y * z)) = a(x,z,x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(9678(a,1),8347(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9678 8347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      K(x,y \ z) * ((z \ y) * u) = (z \ y) * (K(x,y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(5103,a,9676,a),flip(a)].">
      <j1 rule="hyper" parents="5103 9676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8675(a,1),9680(a,1,1))].">
      <j1 rule="para" parents="8675 9680"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(y,x),z,y) = u
    ]]></literal>
    <justification jstring="[para(9683(a,2),9625(a,1))].">
      <j1 rule="para" parents="9683 9625"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      a((x * x) * (y * z),u,w) = a(y * ((x * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1962,a(flip),b,9556,a),flip(a)].">
      <j1 rule="hyper" parents="64 1962 9556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1954,a(flip),b,9686,a),flip(a)].">
      <j1 rule="hyper" parents="64 1954 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(178(a,1),9688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="178 9688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      a(x,(y * y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1951,a(flip),b,9690,a)].">
      <j1 rule="hyper" parents="64 1951 9690"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(226(a,1),9691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="226 9691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      a(x,K(y,z) * T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(4912(a,1),9691(a,1,2))].">
      <j1 rule="para" parents="4912 9691"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      a(x,y \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9076,a(flip),b,9693,a)].">
      <j1 rule="hyper" parents="64 9076 9693"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      a(x,y,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(9639(a,1),713(a,1))].">
      <j1 rule="para" parents="9639 713"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * ((x \ 1) * z)) = y * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(1591(a,1),9657(a,2,2))].">
      <j1 rule="para" parents="1591 9657"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      ((T(x,y) \ 1) \ 1) * ((x \ 1) * z) = T(x,y) * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(4852,a,9697,a)].">
      <j1 rule="hyper" parents="4852 9697"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7786,a(flip),b,9681,a),flip(a)].">
      <j1 rule="hyper" parents="64 7786 9681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6168,a,9699,a)].">
      <j1 rule="hyper" parents="6168 9699"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,T(y / x,u)) * K((x / y) \ 1,T(z,u)) = a((x / y) \ 1,z,(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(7701(a,1),9701(a,1,1))].">
      <j1 rule="para" parents="7701 9701"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6009,a(flip),b,9600,a),flip(a)].">
      <j1 rule="hyper" parents="64 6009 9600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),y) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y))
    ]]></literal>
    <justification jstring="[hyper(492,a,9704,a),flip(a)].">
      <j1 rule="hyper" parents="492 9704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(4663,a,9673,a),flip(a)].">
      <j1 rule="hyper" parents="4663 9673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(1591(a,1),9706(a,1,1,1))].">
      <j1 rule="para" parents="1591 9706"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3884,a(flip),b,9707,a)].">
      <j1 rule="hyper" parents="64 3884 9707"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6572,a(flip),b,9708,a),flip(a)].">
      <j1 rule="hyper" parents="319 6572 9708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7686,a(flip),b,9709,a),flip(a)].">
      <j1 rule="hyper" parents="64 7686 9709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(6990,a,9710,a),flip(a)].">
      <j1 rule="hyper" parents="6990 9710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5463,a(flip),b,9711,a),flip(a)].">
      <j1 rule="hyper" parents="319 5463 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9712(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9713(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(3911,a,9714,a)].">
      <j1 rule="hyper" parents="3911 9714"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(8841,a,9715,a)].">
      <j1 rule="hyper" parents="8841 9715"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(2418(a,2),9716(a,1,1,2))].">
      <j1 rule="para" parents="2418 9716"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,8838,a(flip),b,9717,a)].">
      <j1 rule="hyper" parents="64 8838 9717"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,8840,a(flip),b,9718,a)].">
      <j1 rule="hyper" parents="64 8840 9718"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(6914(a,1),9624(a,2,2,1))].">
      <j1 rule="para" parents="6914 9624"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),9551(a,2,2))].">
      <j1 rule="para" parents="12 9551"/>
    </justification>
  </clause>

  <clause id="9724">
    <literal><![CDATA[
      (x * T(y,x)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),9723(a,1,1,2,2))].">
      <j1 rule="para" parents="12 9723"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      (x * y) / a(y / z,z,T(x,(y / z) * z)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(109(a,1),9724(a,1,1))].">
      <j1 rule="para" parents="109 9724"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      L((x \ y) * x,z,T((x \ y) * T(x,y),u)) = L((x \ y) * x,z,(x \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(3338(a,1),9613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3338 9613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9727">
    <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(5935,a,9658,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5935 9658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9728">
    <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(184(a,1),9727(a,2,1,2))].">
      <j1 rule="para" parents="184 9727"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1531(a,1),9728(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1531 9728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5398,a,9729,a),flip(a)].">
      <j1 rule="hyper" parents="5398 9729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,9729,a,b,8619,a),flip(a)].">
      <j1 rule="hyper" parents="126 9729 8619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5374,a(flip),b,9729,a),flip(a)].">
      <j1 rule="hyper" parents="64 5374 9729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(5210,a,6685,a),flip(a)].">
      <j1 rule="hyper" parents="5210 6685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <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(4190(a,1),9733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4190 9733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <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(1565(a,2),8337(a,1,2,2))].">
      <j1 rule="para" parents="1565 8337"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K(x,y) * (R(K(z,y),K(x,y),u) * u) = (K(z,y) * K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(11(a,1),8566(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(7424(a,1),9736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7424 9736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      (R(R(x,y,z),u,R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8319(a,1),8700(a,1,1,1))].">
      <j1 rule="para" parents="8319 8700"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      ((R(x,y,R(x,z,u)) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(430(a,1),9740(a,1,1))].">
      <j1 rule="para" parents="430 9740"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,T(R(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(319,a,1153,a(flip),b,9478,a),flip(a)].">
      <j1 rule="hyper" parents="319 1153 9478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),9742(a,2,3))].">
      <j1 rule="para" parents="27 9742"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) * K((x / y) \ 1,T(z,y \ x)) = a((x / y) \ 1,z,(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(3893(a,1),9703(a,1,1))].">
      <j1 rule="para" parents="3893 9703"/>
    </justification>
  </clause>

  <clause id="9745">
    <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(94(a,1),9735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="94 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((y / x) \ 1,T(z,x \ y)) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(8917(a,1),9744(a,1,1))].">
      <j1 rule="para" parents="8917 9744"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,T(z,x \ y)) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(4645(a,1),9746(a,1,2))].">
      <j1 rule="para" parents="4645 9746"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7249(a,1),9747(a,1,2))].">
      <j1 rule="para" parents="7249 9747"/>
    </justification>
  </clause>

  <clause id="9749">
    <literal><![CDATA[
      (K(x,y) * K(x,T(y,z))) \ (T(K(x,y),z) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(6099(a,2),4570(a,1,1,2))].">
      <j1 rule="para" parents="6099 4570"/>
    </justification>
  </clause>

  <clause id="9750">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) / T(z,K(x,x \ y))) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(6818(a,1),4679(a,1,2,2))].">
      <j1 rule="para" parents="6818 4679"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) / T(z,K(x,y))) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(6827(a,1),9750(a,1,2,2))].">
      <j1 rule="para" parents="6827 9750"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * K(K(x,y),z)) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(5158(a,1),9751(a,1,2))].">
      <j1 rule="para" parents="5158 9751"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * K(x,K(y,z))) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(6705(a,1),9752(a,1,2,2))].">
      <j1 rule="para" parents="6705 9752"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(4083(a,1),5312(a,1,2,2,1))].">
      <j1 rule="para" parents="4083 5312"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5301(a,1),9754(a,1,2,2))].">
      <j1 rule="para" parents="5301 9754"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(174,a,9756,a)].">
      <j1 rule="hyper" parents="174 9756"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(66(a,1),9757(a,2,1))].">
      <j1 rule="para" parents="66 9757"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(127,a,4408,a(flip),b,9758,a)].">
      <j1 rule="hyper" parents="127 4408 9758"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      R((x * R(K(y,z),u,u \ 1)) * K(z,y),K(y,z),R(K(z,y),u,u \ 1)) = x / a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5578(a,1),5322(a,1,1,1))].">
      <j1 rule="para" parents="5578 5322"/>
    </justification>
  </clause>

  <clause id="9761">
    <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(64,a,8987,a(flip),b,5614,a),flip(a)].">
      <j1 rule="hyper" parents="64 8987 5614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(1 / y) \ 1) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(5083(a,1),6274(a,2,1))].">
      <j1 rule="para" parents="5083 6274"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,y) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(81(a,1),9763(a,2,1,2))].">
      <j1 rule="para" parents="81 9763"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(K(z,y) * (x * (1 / y)),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6056,a,b,9764,a),flip(a)].">
      <j1 rule="hyper" parents="319 6056 9764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(y,z) \ R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5975,a(flip),b,9766,a),flip(a)].">
      <j1 rule="hyper" parents="319 5975 9766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(9767(a,1),6311(a,1,2))].">
      <j1 rule="para" parents="9767 6311"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T(x \ L(x,z,u),y * x)
    ]]></literal>
    <justification jstring="[para(1063(a,1),6531(a,2,1))].">
      <j1 rule="para" parents="1063 6531"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = (K(y,z) * K(z,u)) * K(K(u,z) * x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(6791(a,1),9506(a,1,1))].">
      <j1 rule="para" parents="6791 9506"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      (K(x,y) \ K(y,T(x,z))) \ (T(K(y,x),z) * T(y,y \ x)) = L(R(y,y \ x,y),K(y,x),T(K(y,x),z))
    ]]></literal>
    <justification jstring="[para(4356(a,2),9749(a,1,1))].">
      <j1 rule="para" parents="4356 9749"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * K(z * L(y,u,w),y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,7624,a(flip),b,5505,a),flip(a)].">
      <j1 rule="hyper" parents="319 7624 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * (K(y,z) * K(z * L(y,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,8286,a(flip),b,9772,a),flip(a)].">
      <j1 rule="hyper" parents="319 8286 9772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(8743(a,1),9773(a,2,2))].">
      <j1 rule="para" parents="8743 9773"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      ((x / y) * K(y,z)) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5315,a,9774,a)].">
      <j1 rule="hyper" parents="5315 9774"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      ((x / y) * K(y,z)) * (y * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5502(a,1),9775(a,1,2))].">
      <j1 rule="para" parents="5502 9775"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      (x / y) * (T(y,z) * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7619,a(flip),b,9776,a)].">
      <j1 rule="hyper" parents="64 7619 9776"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6641(a,1),9777(a,1,2))].">
      <j1 rule="para" parents="6641 9777"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(L(T(x,K(z,u)),K(z,u),K(y,z)),K(y,z))
    ]]></literal>
    <justification jstring="[para(237(a,1),6567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="237 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(y,z))
    ]]></literal>
    <justification jstring="[para(8498(a,1),9779(a,2,1))].">
      <j1 rule="para" parents="8498 9779"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,9780,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 9780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8283,a(flip),b,9781,a),flip(a)].">
      <j1 rule="hyper" parents="64 8283 9781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2099(a,2),9783(a,2,2))].">
      <j1 rule="para" parents="2099 9783"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      T(x,K(y,z) * K(z,u)) \ x = K(x,K(z,y)) * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(9783(a,1),8658(a,1,1))].">
      <j1 rule="para" parents="9783 8658"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6807,a,9785,a)].">
      <j1 rule="hyper" parents="6807 9785"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(410,a,9785,a)].">
      <j1 rule="hyper" parents="410 9785"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9507,a,b,9785,a)].">
      <j1 rule="hyper" parents="64 9507 9785"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,R(y,w,v5))) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7473,a,b,9785,a)].">
      <j1 rule="hyper" parents="64 7473 9785"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,R(K(u,y),w,v5)),K(y,z))
    ]]></literal>
    <justification jstring="[para(7592(a,1),9787(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7592 9787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = T(u,K(y,z) * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(9787(a,1),8807(a,2,1))].">
      <j1 rule="para" parents="9787 8807"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9785,a(flip),b,9788,a)].">
      <j1 rule="hyper" parents="64 9785 9788"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      T(x * K(K(y,z) * K(u,y),x),K(y,u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4401,a,9793,a)].">
      <j1 rule="hyper" parents="4401 9793"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(4124,a,9793,a)].">
      <j1 rule="hyper" parents="4124 9793"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(((K(y,z) * K(u,y)) \ x) * (K(y,z) * K(u,y)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(9793(a,1),5855(a,1,2))].">
      <j1 rule="para" parents="9793 5855"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2099(a,2),9789(a,1,2,1))].">
      <j1 rule="para" parents="2099 9789"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,9789,a,b,9795,a)].">
      <j1 rule="hyper" parents="35 9789 9795"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(9795(a,1),4089(a,1))].">
      <j1 rule="para" parents="9795 4089"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[para(2099(a,2),9798(a,1,1))].">
      <j1 rule="para" parents="2099 9798"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(2099(a,1),9800(a,2,2))].">
      <j1 rule="para" parents="2099 9800"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,9797,a),flip(a)].">
      <j1 rule="hyper" parents="35 4019 9797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      T(T(x,K(y,z) * K(u,y)),K(y,u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(9797(a,1),9794(a,1,1))].">
      <j1 rule="para" parents="9797 9794"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9801,a(flip),b,9802,a),flip(a)].">
      <j1 rule="hyper" parents="64 9801 9802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * K(u,K(x,y) * K(z,x)) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,9802,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 9802 4012"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(9785(a,2),9799(a,1))].">
      <j1 rule="para" parents="9785 9799"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6791(a,1),9806(a,1,1))].">
      <j1 rule="para" parents="6791 9806"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(4046,a,9786,a),flip(a)].">
      <j1 rule="hyper" parents="4046 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,9798,a(flip),b,9808,a),flip(a)].">
      <j1 rule="hyper" parents="319 9798 9808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,R(K(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(5573(a,1),9808(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5573 9808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,9802,a,b,9809,a),flip(a)].">
      <j1 rule="hyper" parents="319 9802 9809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(u,K(z,w)))) = K(u,K(z,x) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8578,a,b,9809,a)].">
      <j1 rule="hyper" parents="64 8578 9809"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K((K(x,y) * K(z,x)) \ u,K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = (((K(x,y) * K(z,x)) \ u) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(9809(a,2),4202(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9809 4202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x * K(y,u),K(y,w)) = K(x * K(y,u),K(y,z) * K(w,y))
    ]]></literal>
    <justification jstring="[para(7116(a,1),9809(a,1,1))].">
      <j1 rule="para" parents="7116 9809"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(z,y) * K(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(9807,a,9790,a)].">
      <j1 rule="hyper" parents="9807 9790"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = K(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4001,a,b,9792,a),flip(a)].">
      <j1 rule="hyper" parents="319 4001 9792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) = K(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(4356(a,1),9816(a,1,2))].">
      <j1 rule="para" parents="4356 9816"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(z,u,w),y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(2099(a,1),9815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2099 9815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(9799,a,9818,a)].">
      <j1 rule="hyper" parents="9799 9818"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(z,R(y,u,w))) = T(x,K(y,R(z,u,w)) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,9819,a)].">
      <j1 rule="hyper" parents="319 4019 9819"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,K(y,R(u,w,v5))),K(y,z))
    ]]></literal>
    <justification jstring="[para(7471(a,1),9791(a,2,1))].">
      <j1 rule="para" parents="7471 9791"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / x = T(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(4149,a,9805,a)].">
      <j1 rule="hyper" parents="4149 9805"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = u * (K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(130,a,9805,a(flip),b,4016,a)].">
      <j1 rule="hyper" parents="130 9805 4016"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / x != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(u,y),x) = w
    ]]></literal>
    <justification jstring="[para(9823(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9823 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u) * K(y,z),K(u,z) * x) = w
    ]]></literal>
    <justification jstring="[para(9502(a,1),9824(a,1,1))].">
      <j1 rule="para" parents="9502 9824"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w)) * K(z,y)) = K(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,9820,a)].">
      <j1 rule="hyper" parents="35 4019 9820"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,9788,a(flip),b,9821,a),flip(a)].">
      <j1 rule="hyper" parents="319 9788 9821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      T(x,K(y,z) * R(K(u,y),w,v5)) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[para(7592(a,1),9827(a,1,2,2))].">
      <j1 rule="para" parents="7592 9827"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(v5,y)) = T(x,K(y,v5) * R(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,9793,a,b,9828,a)].">
      <j1 rule="hyper" parents="319 9793 9828"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(z,K(u,w)))) = K(u,K(z,x) * K(w,z))
    ]]></literal>
    <justification jstring="[para(6742(a,1),9812(a,1,2,2,2))].">
      <j1 rule="para" parents="6742 9812"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u)) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(7116(a,1),9814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7116 9814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u) * K(w,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,9809,a(flip),b,9831,a),flip(a)].">
      <j1 rule="hyper" parents="319 9809 9831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(9831(a,1),6021(a,1))].">
      <j1 rule="para" parents="9831 6021"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u) * K(w,y)) = K(z,K(y,u) * K(w,y))
    ]]></literal>
    <justification jstring="[para(5926(a,1),9832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5926 9832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      K(K(x,y) * z,K(u,y) * K(y,w)) = K(z,K(y,u) * K(w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9804,a(flip),b,9835,a)].">
      <j1 rule="hyper" parents="64 9804 9835"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = (K(y,z) * K(z,u)) * K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(9836(a,1),9770(a,2,2))].">
      <j1 rule="para" parents="9836 9770"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,x) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(9808(a,1),9833(a,1))].">
      <j1 rule="para" parents="9808 9833"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(x,y) * K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(9811(a,1),9833(a,1))].">
      <j1 rule="para" parents="9811 9833"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,z) * K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(9817(a,2),9839(a,1))].">
      <j1 rule="para" parents="9817 9839"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(4529,a,9830,a)].">
      <j1 rule="hyper" parents="4529 9830"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(6742(a,1),9841(a,1,1))].">
      <j1 rule="para" parents="6742 9841"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,K(y,R(w,z,u)))
    ]]></literal>
    <justification jstring="[para(7468(a,1),9810(a,2,2))].">
      <j1 rule="para" parents="7468 9810"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(K(x,y) * K(y,R(w,z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,9808,a(flip),b,9843,a),flip(a)].">
      <j1 rule="hyper" parents="319 9808 9843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,z),u,w),v5) = K(K(x,y) * K(y,R(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(5573(a,1),9844(a,1,1,2))].">
      <j1 rule="para" parents="5573 9844"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = K(y,z) * (K(z,u) * K(x,K(z,y) * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,8452,a(flip),b,9837,a),flip(a)].">
      <j1 rule="hyper" parents="319 8452 9837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      T(x,y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(208(a,1),7234(a,1,1,1))].">
      <j1 rule="para" parents="208 7234"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(T(z,1),y))
    ]]></literal>
    <justification jstring="[para(208(a,1),9848(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="208 9848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[para(208(a,1),9849(a,2,2,3,1))].">
      <j1 rule="para" parents="208 9849"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(4871(a,1),7427(a,2,1,1))].">
      <j1 rule="para" parents="4871 7427"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(4314(a,1),9851(a,2,1))].">
      <j1 rule="para" parents="4314 9851"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(175(a,1),9852(a,1,2,1,2,2))].">
      <j1 rule="para" parents="175 9852"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(5583(a,1),9854(a,1,2,1))].">
      <j1 rule="para" parents="5583 9854"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((x \ 1) * z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(600,a,9855,a)].">
      <j1 rule="hyper" parents="600 9855"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ 1,x,w) * L(L(x \ 1,x,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(7866(a,1),7867(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7866 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9859">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L((x \ 1) * L((x \ 1) \ 1,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,2636,a(flip),b,9858,a),flip(a)].">
      <j1 rule="hyper" parents="319 2636 9858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1063(a,1),9859(a,2,1))].">
      <j1 rule="para" parents="1063 9859"/>
    </justification>
  </clause>

  <clause id="9862">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1063(a,1),9861(a,1,1))].">
      <j1 rule="para" parents="1063 9861"/>
    </justification>
  </clause>

  <clause id="9863">
    <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(8962(a,1),8424(a,1,1,2))].">
      <j1 rule="para" parents="8962 8424"/>
    </justification>
  </clause>

  <clause id="9864">
    <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(7644(a,1),9863(a,1,1))].">
      <j1 rule="para" parents="7644 9863"/>
    </justification>
  </clause>

  <clause id="9865">
    <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),9864(a,1,2))].">
      <j1 rule="para" parents="27 9864"/>
    </justification>
  </clause>

  <clause id="9866">
    <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(280(a,1),9865(a,1,2,1))].">
      <j1 rule="para" parents="280 9865"/>
    </justification>
  </clause>

  <clause id="9867">
    <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(64,a,7694,a(flip),b,9866,a)].">
      <j1 rule="hyper" parents="64 7694 9866"/>
    </justification>
  </clause>

  <clause id="9868">
    <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(64,a,5765,a(flip),b,9867,a)].">
      <j1 rule="hyper" parents="64 5765 9867"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ ((u / R(y,z,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7799,a(flip),b,9868,a),flip(a)].">
      <j1 rule="hyper" parents="64 7799 9868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(5902(a,1),9870(a,2,2))].">
      <j1 rule="para" parents="5902 9870"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,3531,a(flip),b,9871,a),flip(a)].">
      <j1 rule="hyper" parents="319 3531 9871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u))
    ]]></literal>
    <justification jstring="[para(8423(a,1),9872(a,1,1,1))].">
      <j1 rule="para" parents="8423 9872"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u
    ]]></literal>
    <justification jstring="[para(8962(a,1),9873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8962 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9875">
    <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(9874(a,1),4338(a,1))].">
      <j1 rule="para" parents="9874 4338"/>
    </justification>
  </clause>

  <clause id="9876">
    <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),9734(a,2,1,1))].">
      <j1 rule="para" parents="9 9734"/>
    </justification>
  </clause>

  <clause id="9877">
    <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(319,a,7729,a(flip),b,9876,a),flip(a)].">
      <j1 rule="hyper" parents="319 7729 9876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9879">
    <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),9877(a,1,1,1))].">
      <j1 rule="para" parents="9 9877"/>
    </justification>
  </clause>

  <clause id="9880">
    <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),9879(a,1,2,2))].">
      <j1 rule="para" parents="9 9879"/>
    </justification>
  </clause>

  <clause id="9881">
    <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(4831(a,1),9880(a,1,2,1,3))].">
      <j1 rule="para" parents="4831 9880"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,K(x,w)) * (K(y,x) * T(z * K(x,y),u))
    ]]></literal>
    <justification jstring="[para(6705(a,1),7665(a,2,1))].">
      <j1 rule="para" parents="6705 7665"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8740,a(flip),b,8058,a)].">
      <j1 rule="hyper" parents="64 8740 8058"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(9107,a,9883,a)].">
      <j1 rule="hyper" parents="9107 9883"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((x * (x \ v5)) * R(x,z,R(x,u,w))))
    ]]></literal>
    <justification jstring="[para(8008(a,1),9884(a,2,2,2))].">
      <j1 rule="para" parents="8008 9884"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ (v5 * R(x,z,R(x,u,w))))
    ]]></literal>
    <justification jstring="[para(10(a,1),9887(a,2,2,2,1))].">
      <j1 rule="para" parents="10 9887"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),9888(a,2,2))].">
      <j1 rule="para" parents="9 9888"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,8730,a(flip),b,9889,a),flip(a)].">
      <j1 rule="hyper" parents="319 8730 9889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9108,a(flip),b,9891,a),flip(a)].">
      <j1 rule="hyper" parents="64 9108 9891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9891(a,1),3649(a,1))].">
      <j1 rule="para" parents="9891 3649"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      (1 / (K(x,y) * R(y,z,u))) \ (K(y,x) * (R(y,z,u) \ 1)) = (R(y,z,u) \ K(y,x)) * (K(y,x) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4356(a,1),8993(a,1,1,2))].">
      <j1 rule="para" parents="4356 8993"/>
    </justification>
  </clause>

  <clause id="9896">
    <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(7503(a,1),9061(a,1,2,1,1))].">
      <j1 rule="para" parents="7503 9061"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,6720,a(flip),b,9882,a),flip(a)].">
      <j1 rule="hyper" parents="319 6720 9882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,T(w,T(K(x,y) * z,u)))) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(6484,a,9897,a)].">
      <j1 rule="hyper" parents="6484 9897"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * K(x,u)) \ (K(x,u) * (R(x,y,z) \ 1)) = (R(x,y,z) \ K(x,u)) * (K(x,u) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(7643(a,1),9895(a,1,1))].">
      <j1 rule="para" parents="7643 9895"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9060,a(flip),b,9896,a),flip(a)].">
      <j1 rule="hyper" parents="64 9060 9896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(7797,a,9900,a),flip(a)].">
      <j1 rule="hyper" parents="7797 9900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(6989,a,9901,a)].">
      <j1 rule="hyper" parents="6989 9901"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7252,a,9902,a),flip(a)].">
      <j1 rule="hyper" parents="7252 9902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(9903(a,1),8209(a,1,1))].">
      <j1 rule="para" parents="9903 8209"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,8269,a(flip),b,9904,a)].">
      <j1 rule="hyper" parents="64 8269 9904"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(9170,a,9905,a),flip(a)].">
      <j1 rule="hyper" parents="9170 9905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5615,a(flip),b,9906,a),flip(a)].">
      <j1 rule="hyper" parents="64 5615 9906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),9907(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 9907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4351(a,1),9908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4351 9908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <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(9431(a,1),9908(a,1,1))].">
      <j1 rule="para" parents="9431 9908"/>
    </justification>
  </clause>

  <clause id="9911">
    <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(9909(a,1),9910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9909 9910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      L(x \ (y * z),x,K(y * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(5836(a,1),4843(a,1,3))].">
      <j1 rule="para" parents="5836 4843"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),x * u) = T(x \ L(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(6532,a,9769,a)].">
      <j1 rule="hyper" parents="6532 9769"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1063(a,1),9914(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1063 9914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      (K(x,y / z) * K(x,K(u,z \ y))) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u))
    ]]></literal>
    <justification jstring="[para(6756(a,1),7304(a,1,1,2))].">
      <j1 rule="para" parents="6756 7304"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      R(K(x,K(y,z)) * K(y,K(z,R(x,u,w))),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(7464(a,1),9492(a,1,1,1,2))].">
      <j1 rule="para" parents="7464 9492"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = L(T(y,x),u,w) \ (L(y,u,w) * (x * K(y,z)))
    ]]></literal>
    <justification jstring="[para(9599(a,1),9705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9599 9705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = K(x,L(y,u,w)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4439,a(flip),b,9918,a),flip(a)].">
      <j1 rule="hyper" parents="319 4439 9918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4081,a(flip),b,9919,a),flip(a)].">
      <j1 rule="hyper" parents="319 4081 9919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9599(a,1),9921(a,1,2))].">
      <j1 rule="para" parents="9599 9921"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6010,a(flip),b,9922,a)].">
      <j1 rule="hyper" parents="64 6010 9922"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) / T(K(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(7059(a,1),9916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7059 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) / K(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(6099(a,2),9925(a,2,2))].">
      <j1 rule="para" parents="6099 9925"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) * K(y \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6146,a(flip),b,9926,a),flip(a)].">
      <j1 rule="hyper" parents="319 6146 9926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,z \ y),K(K(x,z \ y),u)) = K(x,T(y / z,T(u,z))) * K(z \ y,T(x,u))
    ]]></literal>
    <justification jstring="[para(6758(a,1),9927(a,1,1))].">
      <j1 rule="para" parents="6758 9927"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      K(x,T(y / z,T(u,z))) * K(z \ y,T(x,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4956,a,9928,a),flip(a)].">
      <j1 rule="hyper" parents="4956 9928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      R(K(x,K(y,z) * K(R(z,u,w),y)),K(K(y,x),v5),v6) * v7 = K(z,K(y,x)) * (R(K(K(y,x),z),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(9842(a,1),9917(a,1,1,1))].">
      <j1 rule="para" parents="9842 9917"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = z * L(T(K(x,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),7753(a,2,2,1,2))].">
      <j1 rule="para" parents="10 7753"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = L(K(x,u),w,v5) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,242,a(flip),b,9932,a),flip(a)].">
      <j1 rule="hyper" parents="319 242 9932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(x,y) \ v5)) = L(K(x,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(242(a,1),9933(a,1,2))].">
      <j1 rule="para" parents="242 9933"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * v5)) = L(K(x,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(4356(a,1),9934(a,1,2,2))].">
      <j1 rule="para" parents="4356 9934"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(K(x,z) * L(K(x,z) \ 1,v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,2636,a(flip),b,9935,a),flip(a)].">
      <j1 rule="hyper" parents="319 2636 9935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      (1 / R(x,y,z)) \ (K(x,u) / R(x,y,z)) = (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u))
    ]]></literal>
    <justification jstring="[para(1629(a,1),8572(a,1,1))].">
      <j1 rule="para" parents="1629 8572"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      (1 / R(x,y,z)) \ (K(x,u) / R(x,y,z)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(6493,a,9937,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6493 9937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      (1 / R(x,y,z)) * K(x,u) = K(x,u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,9938,a)].">
      <j1 rule="hyper" parents="145 9938"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ (K(x,y) * (R(x,z,u) \ 1)) = (R(x,z,u) \ K(x,y)) * (K(x,y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9939(a,1),9899(a,1,1))].">
      <j1 rule="para" parents="9939 9899"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ (R(x,z,u) \ K(x,y)) = (R(x,z,u) \ K(x,y)) * (K(x,y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8992(a,1),9940(a,1,2))].">
      <j1 rule="para" parents="8992 9940"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ 1 = K(x,y) \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1092,a,9941,a)].">
      <j1 rule="hyper" parents="1092 9941"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ 1 = K(y,x) * R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a(flip),b,9942,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 9942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * K(w,R(x,y,R(x,z,u))) = K(w,x) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7362,a,b,9943,a)].">
      <j1 rule="hyper" parents="64 7362 9943"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2862,a,9944,a),flip(a)].">
      <j1 rule="hyper" parents="2862 9944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(6995,a,9945,a),flip(a)].">
      <j1 rule="hyper" parents="6995 9945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6985,a,9946,a),flip(a)].">
      <j1 rule="hyper" parents="6985 9946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      K(x,y) * (y \ R(T(y,x),z,R(T(y,u),w,v5))) = y \ R(y,z,R(T(y,u),w,v5))
    ]]></literal>
    <justification jstring="[para(9948(a,1),8106(a,1,1))].">
      <j1 rule="para" parents="9948 8106"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(T(x,u),w,v5)) = x \ R(x,z,R(T(x,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(4322,a,9950,a)].">
      <j1 rule="hyper" parents="4322 9950"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      K(x,y) * (y \ R(T(y,x),z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(8084(a,1),9950(a,1,2,2))].">
      <j1 rule="para" parents="8084 9950"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,z),y,R(T(x,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9951(a,1),8731(a,1))].">
      <j1 rule="para" parents="9951 8731"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * a(y,z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(8733(a,1),9952(a,1,2))].">
      <j1 rule="para" parents="8733 9952"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(4376,a,9954,a),flip(a)].">
      <j1 rule="hyper" parents="4376 9954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(9953,a,9955,a)].">
      <j1 rule="hyper" parents="9953 9955"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * ((y * K(x,z)) * K(x,z))) \ u)
    ]]></literal>
    <justification jstring="[para(5626(a,1),9235(a,2,2,1))].">
      <j1 rule="para" parents="5626 9235"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (K(x \ (x / y),(x / y) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(2480(a,1),9661(a,2,2,1))].">
      <j1 rule="para" parents="2480 9661"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (K(x \ (x / y),y) \ z)
    ]]></literal>
    <justification jstring="[para(81(a,1),9959(a,2,2,1,2))].">
      <j1 rule="para" parents="81 9959"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (((y \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[para(2669(a,1),9960(a,2,2,1))].">
      <j1 rule="para" parents="2669 9960"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = ((((x \ (x / y)) \ 1) \ 1) * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(110(a,1),9961(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="110 9961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = ((x \ (x / ((y \ 1) \ 1))) * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2751(a,1),9962(a,2,1,1))].">
      <j1 rule="para" parents="2751 9962"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = (x / ((y \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(5106(a,1),9964(a,2,1))].">
      <j1 rule="para" parents="5106 9964"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      R(x,(((y / z) \ 1) \ 1) \ (((z \ 1) * z) \ u),w) = R(x,(y / ((z \ 1) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(9965(a,1),8950(a,2,2))].">
      <j1 rule="para" parents="9965 8950"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      R(x,(((y / z) \ 1) \ ((z \ 1) * z)) \ u,w) = R(x,(y / ((z \ 1) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(9654(a,1),9966(a,1,2))].">
      <j1 rule="para" parents="9654 9966"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * (y * (K(x,z) * K(x,z)))) \ u)
    ]]></literal>
    <justification jstring="[para(8357(a,1),9958(a,2,2,1,2))].">
      <j1 rule="para" parents="8357 9958"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L(R(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),2017(a,2,2,1,1))].">
      <j1 rule="para" parents="20 2017"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      (((x * y) * L((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * L(R(x,y,w) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(1523(a,1),9969(a,1,1))].">
      <j1 rule="para" parents="1523 9969"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      (((x * L(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * L(R(x,u,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1541(a,1),9970(a,1,1,1))].">
      <j1 rule="para" parents="1541 9970"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ 1,u,w) = R(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(531,a,9971,a),flip(a)].">
      <j1 rule="hyper" parents="531 9971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ 1,x,1 / x) = R(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(744(a,1),9972(a,2,1,2))].">
      <j1 rule="para" parents="744 9972"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1126(a,1),9973(a,1,2))].">
      <j1 rule="para" parents="1126 9973"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(208(a,1),9974(a,2,1,2))].">
      <j1 rule="para" parents="208 9974"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1628(a,2),9975(a,2,1))].">
      <j1 rule="para" parents="1628 9975"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,1701,a(flip),b,9976,a),flip(a)].">
      <j1 rule="hyper" parents="319 1701 9976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,9443,a,b,9977,a),flip(a)].">
      <j1 rule="hyper" parents="35 9443 9977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,9979,a)].">
      <j1 rule="hyper" parents="134 9979"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,9470,a(flip),b,9980,a)].">
      <j1 rule="hyper" parents="64 9470 9980"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(8730(a,1),9981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8730 9981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      R(T(x,y),T(y,x),R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(3648(a,1),9982(a,2,1))].">
      <j1 rule="para" parents="3648 9982"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(7933(a,1),9983(a,1,1))].">
      <j1 rule="para" parents="7933 9983"/>
    </justification>
  </clause>

  <clause id="9985">
    <literal><![CDATA[
      R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(R(x,z,u),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(8761(a,1),9984(a,2,1))].">
      <j1 rule="para" parents="8761 9984"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      a(T(x,y),y,R(T(x,y),z,u)) \ 1 = a(R(x,z,u),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9982,a(flip),b,9985,a)].">
      <j1 rule="hyper" parents="64 9982 9985"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(9956(a,1),9986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9956 9986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(289,a,9987,a),flip(a)].">
      <j1 rule="hyper" parents="289 9987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      (x * L(R(T(y,x),z,u),y \ T(x,y),y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,3652,a,b,9988,a)].">
      <j1 rule="hyper" parents="319 3652 9988"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      (x * L(R(T(y,x),z,u),y \ x,y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(7839(a,1),9990(a,1,1,2))].">
      <j1 rule="para" parents="7839 9990"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      (L(R(x,y,z),x \ u,x) * u) \ (u * R(T(x,u),y,z)) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u))
    ]]></literal>
    <justification jstring="[para(649(a,1),9992(a,1,1))].">
      <j1 rule="para" parents="649 9992"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (L(R(x,z,u),x \ y,x) * y) \ (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(243(a,1),9993(a,1,2)),flip(a)].">
      <j1 rule="para" parents="243 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,T(R(x,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,1153,a(flip),b,9994,a),flip(a)].">
      <j1 rule="hyper" parents="319 1153 9994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),9995(a,2,3))].">
      <j1 rule="para" parents="27 9995"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      a(T(x,y),T(x,y) \ y,R(T(x,y),z,u)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9988,a(flip),b,9996,a)].">
      <j1 rule="hyper" parents="64 9988 9996"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      a(x,T(x,y) \ y,R(x,z,u)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9956,a(flip),b,9997,a)].">
      <j1 rule="hyper" parents="64 9956 9997"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9892,a(flip),b,9998,a),flip(a)].">
      <j1 rule="hyper" parents="64 9892 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9743,a,b,10000,a)].">
      <j1 rule="hyper" parents="64 9743 10000"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(8353,a,10002,a)].">
      <j1 rule="hyper" parents="8353 10002"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,y \ (w * y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(10003(a,1),9497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10003 9497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,T(w,y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),10004(a,2,2,2))].">
      <j1 rule="para" parents="22 10004"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(8814(a,1),10005(a,2,2))].">
      <j1 rule="para" parents="8814 10005"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ (x * y)))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(197(a,1),2500(a,1,2,2,2,2))].">
      <j1 rule="para" parents="197 2500"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * ((y * z) * (1 / (1 / ((y * z) \ y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,2959,a(flip),b,10007,a),flip(a)].">
      <j1 rule="hyper" parents="64 2959 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ (y \ y))))))
    ]]></literal>
    <justification jstring="[para(2797(a,1),10008(a,2,2))].">
      <j1 rule="para" parents="2797 10008"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ 1)))))
    ]]></literal>
    <justification jstring="[para(68(a,1),10010(a,2,2,2,2,2,2,2))].">
      <j1 rule="para" parents="68 10010"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / z)))
    ]]></literal>
    <justification jstring="[para(78(a,1),10011(a,2,2,2,2,2))].">
      <j1 rule="para" parents="78 10011"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1628(a,2),10013(a,2,2,2))].">
      <j1 rule="para" parents="1628 10013"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,3736,a,b,10014,a),flip(a)].">
      <j1 rule="hyper" parents="35 3736 10014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,10015,a(flip),b,1628,a(flip))].">
      <j1 rule="hyper" parents="127 10015 1628"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,10017,a(flip),b,1636,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 10017 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4714(a,2),10017(a,1,2))].">
      <j1 rule="para" parents="4714 10017"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      K(L(x,y,z) \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10019(a,1),8222(a,1,1,2,1))].">
      <j1 rule="para" parents="10019 8222"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4715,a(flip),b,10020,a)].">
      <j1 rule="hyper" parents="64 4715 10020"/>
    </justification>
  </clause>

  <clause id="10024">
    <literal><![CDATA[
      (1 / x) * ((L(x,y,z) \ 1) * x) = T(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(10022(a,1),1176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10022 1176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      (x \ 1) \ T(1 / L(x,y,z),x) = (L(x,y,z) \ 1) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,10024,a(flip),b,2690,a)].">
      <j1 rule="hyper" parents="127 10024 2690"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = (x \ 1) \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3957(a,1),10025(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3957 10025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,3791,a(flip),b,10026,a(flip))].">
      <j1 rule="hyper" parents="131 3791 10026"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4895,a,b,10027,a)].">
      <j1 rule="hyper" parents="319 4895 10027"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2185,a,10028,a)].">
      <j1 rule="hyper" parents="2185 10028"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ 1 = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8392,a(flip),b,10029,a),flip(a)].">
      <j1 rule="hyper" parents="319 8392 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10031">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * T(y / R(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(10030(a,1),8373(a,1,1,2))].">
      <j1 rule="para" parents="10030 8373"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      K(x \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8964,a(flip),b,10021,a)].">
      <j1 rule="hyper" parents="64 8964 10021"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      K((1 / L(x,y,z)) \ u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8600,a(flip),b,10032,a)].">
      <j1 rule="hyper" parents="64 8600 10032"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5227,a(flip),b,10033,a)].">
      <j1 rule="hyper" parents="64 5227 10033"/>
    </justification>
  </clause>

  <clause id="10035">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5865,a,10034,a)].">
      <j1 rule="hyper" parents="5865 10034"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7840,a(flip),b,10035,a),flip(a)].">
      <j1 rule="hyper" parents="319 7840 10035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),10036(a,2,1))].">
      <j1 rule="para" parents="66 10036"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      T(L(x,y,z) * K(u * x,L(x,y,z)),u) = R(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10037(a,1),4191(a,1,1,2))].">
      <j1 rule="para" parents="10037 4191"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) * K(L(y,z,u),L(y,z,u) \ (x * L(y,z,u))) = a(L(y,z,u),L(y,z,u) \ (x * L(y,z,u)),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10037(a,1),8317(a,1,1))].">
      <j1 rule="para" parents="10037 8317"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      T(L(x * K(y * x,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4625(a,1),10038(a,1,1))].">
      <j1 rule="para" parents="4625 10038"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4281(a,1),10040(a,1,1,1,2))].">
      <j1 rule="para" parents="4281 10040"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(T(x * K(x * u,x),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(9603,a,10041,a),flip(a)].">
      <j1 rule="hyper" parents="9603 10041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4399(a,1),10042(a,2,1))].">
      <j1 rule="para" parents="4399 10042"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(150,a,10043,a)].">
      <j1 rule="hyper" parents="150 10043"/>
    </justification>
  </clause>

  <clause id="10045">
    <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(10043(a,1),5720(a,1,2))].">
      <j1 rule="para" parents="10043 5720"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4191,a,b,10044,a)].">
      <j1 rule="hyper" parents="319 4191 10044"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(10044(a,1),8005(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10044 8005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(10044(a,1),8817(a,1,1,2,2))].">
      <j1 rule="para" parents="10044 8817"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10044(a,1),9778(a,1,2))].">
      <j1 rule="para" parents="10044 9778"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      T(R(x,y,z) * K(u * x,R(x,y,z)),u) = R(R(x,y,z),u,L(R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(9455(a,1),10046(a,1,1,2))].">
      <j1 rule="para" parents="9455 10046"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8674,a(flip),b,10050,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 8674 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10054">
    <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(9030(a,1),10045(a,1))].">
      <j1 rule="para" parents="9030 10045"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6233,a(flip),b,10048,a),flip(a)].">
      <j1 rule="hyper" parents="319 6233 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9730,a(flip),b,10055,a)].">
      <j1 rule="hyper" parents="64 9730 10055"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6041,a(flip),b,10055,a),flip(a)].">
      <j1 rule="hyper" parents="64 6041 10055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(94(a,1),10055(a,1,1))].">
      <j1 rule="para" parents="94 10055"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      T(x * K(y,x),x * (L(x,z,u) \ y)) = x
    ]]></literal>
    <justification jstring="[para(10058(a,1),4130(a,1,1,2))].">
      <j1 rule="para" parents="10058 4130"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(8193,a,10059,a)].">
      <j1 rule="hyper" parents="8193 10059"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5396,a(flip),b,10057,a),flip(a)].">
      <j1 rule="hyper" parents="319 5396 10057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9520,a,b,10065,a)].">
      <j1 rule="hyper" parents="64 9520 10065"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9732,a(flip),b,10065,a)].">
      <j1 rule="hyper" parents="64 9732 10065"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(10065(a,1),7399(a,1,1,2))].">
      <j1 rule="para" parents="10065 7399"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      T(x,x * (L(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10062(a,1),4135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10062 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      T(x,y) \ ((x \ (x * (L(x,z,u) \ y))) \ (x * (L(x,z,u) \ y))) = a(x,x \ (x * (L(x,z,u) \ y)),x)
    ]]></literal>
    <justification jstring="[para(10069(a,1),8351(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10069 8351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = x * K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,10070,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 10070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(4105,a,10073,a)].">
      <j1 rule="hyper" parents="4105 10073"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(9331,a,10074,a)].">
      <j1 rule="hyper" parents="9331 10074"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) * (y * x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(376(a,1),10075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="376 10075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,8779,a(flip),b,10067,a),flip(a)].">
      <j1 rule="hyper" parents="319 8779 10067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,5006,a(flip),b,10067,a),flip(a)].">
      <j1 rule="hyper" parents="319 5006 10067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(10067(a,2),5008(a,1))].">
      <j1 rule="para" parents="10067 5008"/>
    </justification>
  </clause>

  <clause id="10085">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10083(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10083(a,1),3993(a,1,2))].">
      <j1 rule="para" parents="10083 3993"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),10084(a,1,1,2))].">
      <j1 rule="para" parents="94 10084"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      T(x * ((y * z) \ (y * u)),K(x,z \ u)) = x * L(z \ u,z,y)
    ]]></literal>
    <justification jstring="[para(96(a,1),10086(a,1,1,2))].">
      <j1 rule="para" parents="96 10086"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(94(a,1),10082(a,1,1,2))].">
      <j1 rule="para" parents="94 10082"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(6485,a,10090,a)].">
      <j1 rule="hyper" parents="6485 10090"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,8786,a(flip),b,10091,a),flip(a)].">
      <j1 rule="hyper" parents="319 8786 10091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10093">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7891,a(flip),b,10092,a)].">
      <j1 rule="hyper" parents="64 7891 10092"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),10093(a,2,1))].">
      <j1 rule="para" parents="18 10093"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10054,a,10094,a),flip(a)].">
      <j1 rule="hyper" parents="10054 10094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8252,a,10095,a)].">
      <j1 rule="hyper" parents="8252 10095"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(10095(a,1),8252(a,1))].">
      <j1 rule="para" parents="10095 8252"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9593(a,1),10095(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9593 10095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(302(a,1),10098(a,1,2))].">
      <j1 rule="para" parents="302 10098"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(5752,a,10096,a)].">
      <j1 rule="hyper" parents="5752 10096"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(5415,a,10096,a),flip(a)].">
      <j1 rule="hyper" parents="5415 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      K(L(x,y,z),u) \ 1 = L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4213,a,b,10096,a)].">
      <j1 rule="hyper" parents="319 4213 10096"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      L(K(x,y \ z),y,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,5285,a(flip),b,10096,a),flip(a)].">
      <j1 rule="hyper" parents="319 5285 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * K(L(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(206,a,10096,a,b,5176,a)].">
      <j1 rule="hyper" parents="206 10096 5176"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      K(L(x,y,z),u) \ w = L(K(u,x),y,z) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,10096,a,b,4364,a),flip(a)].">
      <j1 rule="hyper" parents="130 10096 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8611,a,b,10096,a)].">
      <j1 rule="hyper" parents="64 8611 10096"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7411,a,b,10096,a)].">
      <j1 rule="hyper" parents="64 7411 10096"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5377,a,b,10096,a)].">
      <j1 rule="hyper" parents="64 5377 10096"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7414,a(flip),b,10096,a)].">
      <j1 rule="hyper" parents="64 7414 10096"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5277,a(flip),b,10096,a),flip(a)].">
      <j1 rule="hyper" parents="64 5277 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5275,a(flip),b,10096,a),flip(a)].">
      <j1 rule="hyper" parents="64 5275 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4712,a(flip),b,10096,a),flip(a)].">
      <j1 rule="hyper" parents="64 4712 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,10096,a(flip),b,95,a)].">
      <j1 rule="hyper" parents="131 10096 95"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,10096,a(flip),b,9216,a(flip))].">
      <j1 rule="hyper" parents="131 10096 9216"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,10096,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 10096 18"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(302(a,1),10096(a,2,2))].">
      <j1 rule="para" parents="302 10096"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(504(a,1),10096(a,2,2))].">
      <j1 rule="para" parents="504 10096"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,L(u,y,x))) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(10096(a,1),480(a,1,2,2))].">
      <j1 rule="para" parents="10096 480"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      L(K(x,y),z,u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(y,z,u),x) \ w = v5
    ]]></literal>
    <justification jstring="[para(10096(a,2),4393(a,1,1))].">
      <j1 rule="para" parents="10096 4393"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(x,w)) \ T(x,w) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10096(a,2),4709(a,1,1,1))].">
      <j1 rule="para" parents="10096 4709"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(10096(a,1),5520(a,1))].">
      <j1 rule="para" parents="10096 5520"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      K(x,L(T(x,y) * z,u,w)) = L(K(x,x * z),u,w)
    ]]></literal>
    <justification jstring="[para(5846(a,1),10096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5846 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(x,L(y,z,u))) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10096(a,1),7260(a,1,2))].">
      <j1 rule="para" parents="10096 7260"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10096(a,1),8607(a,1,2))].">
      <j1 rule="para" parents="10096 8607"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(10096(a,1),8610(a,1,2))].">
      <j1 rule="para" parents="10096 8610"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(10096(a,1),8612(a,1,1))].">
      <j1 rule="para" parents="10096 8612"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(10096(a,1),9549(a,1,2))].">
      <j1 rule="para" parents="10096 9549"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(40,a,4835,a,b,10102,a)].">
      <j1 rule="hyper" parents="40 4835 10102"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10102(a,1),4229(a,1))].">
      <j1 rule="para" parents="10102 4229"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a,b,10129,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 10129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10096,a(flip),b,10129,a),flip(a)].">
      <j1 rule="hyper" parents="64 10096 10129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(503(a,1),10129(a,2,1))].">
      <j1 rule="para" parents="503 10129"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      L(K(x,y),z,u) \ R(y,w,y) = R(T(y,L(x,z,u)),w,y)
    ]]></literal>
    <justification jstring="[para(10129(a,2),5781(a,1,1))].">
      <j1 rule="para" parents="10129 5781"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(10129(a,2),6080(a,1,1))].">
      <j1 rule="para" parents="10129 6080"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10129(a,2),6758(a,1,2))].">
      <j1 rule="para" parents="10129 6758"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,L(x,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(10129(a,2),6780(a,1))].">
      <j1 rule="para" parents="10129 6780"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10129(a,1),8607(a,1,2))].">
      <j1 rule="para" parents="10129 8607"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,L(x,z,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(130,a,10133,a(flip),b,4359,a)].">
      <j1 rule="hyper" parents="130 10133 4359"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x \ y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(504(a,1),10133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="504 10133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / T(L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10133(a,1),5201(a,1,2,1))].">
      <j1 rule="para" parents="10133 5201"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10133(a,1),4919(a,1,1,2))].">
      <j1 rule="para" parents="10133 4919"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      K(x * K(y,L(x,z,u)),w) = K(x,T(w,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(10133(a,1),6883(a,1,1,2))].">
      <j1 rule="para" parents="10133 6883"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(10133(a,1),6789(a,1,2))].">
      <j1 rule="para" parents="10133 6789"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      K(x,K(x / y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10133(a,1),7019(a,2,2))].">
      <j1 rule="para" parents="10133 7019"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10133(a,1),6362(a,1,1,2,2))].">
      <j1 rule="para" parents="10133 6362"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,T((y / z) \ 1,y),u)) = K(x,L(((y / z) \ 1) \ z,z,u))
    ]]></literal>
    <justification jstring="[para(3557(a,2),10107(a,1,2,2))].">
      <j1 rule="para" parents="3557 10107"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      (x * (y / z)) * K(u,(x * y) / (x * (y / z))) = K(u,L(z,y,x)) * (x * (y / z))
    ]]></literal>
    <justification jstring="[para(10107(a,1),8259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10107 8259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(10096(a,1),10097(a,1,2))].">
      <j1 rule="para" parents="10096 10097"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10133(a,2),10097(a,1))].">
      <j1 rule="para" parents="10133 10097"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(5277(a,1),10130(a,1))].">
      <j1 rule="para" parents="5277 10130"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(5334(a,2),10130(a,1))].">
      <j1 rule="para" parents="5334 10130"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y * x,z)) = w
    ]]></literal>
    <justification jstring="[para(5363(a,1),10130(a,1))].">
      <j1 rule="para" parents="5363 10130"/>
    </justification>
  </clause>

  <clause id="10155">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(8611(a,2),10130(a,1))].">
      <j1 rule="para" parents="8611 10130"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(10129(a,1),10130(a,1))].">
      <j1 rule="para" parents="10129 10130"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,K(x,y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6748(a,2),10151(a,1))].">
      <j1 rule="para" parents="6748 10151"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      L(K(x,y),z,u) \ R(T(x,L(y,z,u)),w,x) = R(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,5781,a(flip),b,10105,a(flip))].">
      <j1 rule="hyper" parents="127 5781 10105"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(10106(a,1),4375(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10106 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(508(a,1),10110(a,2,2))].">
      <j1 rule="para" parents="508 10110"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) * K(z,u) = w
    ]]></literal>
    <justification jstring="[para(10125(a,1),2104(a,1))].">
      <j1 rule="para" parents="10125 2104"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(10125(a,1),4299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10125 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(10126(a,1),5193(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10126 5193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y \ L(y,w,v5))) * K(u,L(y \ L(y,w,v5),y,x)) = K(u,y \ L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(9862(a,1),10126(a,1,2,2))].">
      <j1 rule="para" parents="9862 10126"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8620,a(flip),b,10127,a)].">
      <j1 rule="hyper" parents="64 8620 10127"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) * K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(10127(a,1),2100(a,1))].">
      <j1 rule="para" parents="10127 2100"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),10165(a,1,3))].">
      <j1 rule="para" parents="6748 10165"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(7414(a,1),10137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7414 10137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8614,a(flip),b,10139,a)].">
      <j1 rule="hyper" parents="64 8614 10139"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (u * x) / T(u,L(x,z,y)) = w
    ]]></literal>
    <justification jstring="[para(10139(a,1),5231(a,1,2))].">
      <j1 rule="para" parents="10139 5231"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,y \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10095(a,1),10139(a,1,2))].">
      <j1 rule="para" parents="10095 10139"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,L(y,u,w))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(10136(a,1),10139(a,1,2))].">
      <j1 rule="para" parents="10136 10139"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10170(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10170(a,1),8660(a,2,2))].">
      <j1 rule="para" parents="10170 8660"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),T(z * u,u \ 1),(u * z) \ z)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5140(a,1),10101(a,2,2,2))].">
      <j1 rule="para" parents="5140 10101"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(10103(a,1),10130(a,1))].">
      <j1 rule="para" parents="10103 10130"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(1 / y,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(381(a,1),10111(a,1,2,1,1))].">
      <j1 rule="para" parents="381 10111"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,L(w,L(x,y,z) \ 1,x)) = x * ((L(x,y,z) \ 1) * K(u,w))
    ]]></literal>
    <justification jstring="[para(1169(a,1),10115(a,1,1))].">
      <j1 rule="para" parents="1169 10115"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      x * (y * K(x * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(10115(a,1),4089(a,1))].">
      <j1 rule="para" parents="10115 4089"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) * v5) = K(x,(y * (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(10115(a,1),5969(a,2,2,1))].">
      <j1 rule="para" parents="10115 5969"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y / z,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(6148(a,1),10115(a,2,2))].">
      <j1 rule="para" parents="6148 10115"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) / v5) = K(x,(y * (z * K(u,w))) / v5)
    ]]></literal>
    <justification jstring="[para(10115(a,1),7435(a,2,2,1))].">
      <j1 rule="para" parents="10115 7435"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      K(x,y / (z * (u * K(x,w)))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(10115(a,1),7528(a,1,2,2))].">
      <j1 rule="para" parents="10115 7528"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      K(x,y / (T(z * u,x) * K(w,L(v5,u,z)))) = K(x,y / (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(10115(a,1),7526(a,2,2,2))].">
      <j1 rule="para" parents="10115 7526"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(10096(a,1),10115(a,1,2,2))].">
      <j1 rule="para" parents="10096 10115"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,8261,a,b,10134,a),flip(a)].">
      <j1 rule="hyper" parents="319 8261 10134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10154,a,10133,a)].">
      <j1 rule="hyper" parents="10154 10133"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),10188(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(10189(a,1),10115(a,1,2))].">
      <j1 rule="para" parents="10189 10115"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,5849,a(flip),b,10099,a),flip(a)].">
      <j1 rule="hyper" parents="319 5849 10099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      K(x,L(T(x,y) * z,u,w)) = K(x,L(x * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,10096,a(flip),b,10123,a),flip(a)].">
      <j1 rule="hyper" parents="319 10096 10123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7019,a(flip),b,10146,a)].">
      <j1 rule="hyper" parents="64 7019 10146"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(x / w,(z * y) \ u))
    ]]></literal>
    <justification jstring="[para(302(a,1),10146(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="302 10146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9923,a,b,10162,a)].">
      <j1 rule="hyper" parents="64 9923 10162"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10125,a(flip),b,10172,a),flip(a)].">
      <j1 rule="hyper" parents="64 10125 10172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) = a(x,z \ y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,10174,a,b,10197,a)].">
      <j1 rule="hyper" parents="319 10174 10197"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      K(x,y / (z * ((u / x) * w))) = K(x,y / (z * ((x \ u) * w)))
    ]]></literal>
    <justification jstring="[para(6421(a,1),10184(a,1,2,2,2))].">
      <j1 rule="para" parents="6421 10184"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(10196(a,1),4135(a,1,1))].">
      <j1 rule="para" parents="10196 4135"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ ((T(y,z \ u) \ 1) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(4928(a,1),10100(a,1,2,1))].">
      <j1 rule="para" parents="4928 10100"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      L(K(x,((y \ z) \ z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9223,a(flip),b,10118,a)].">
      <j1 rule="hyper" parents="64 9223 10118"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10118(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="10118 481"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(9547(a,1),10128(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9547 10128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(6742(a,1),10138(a,1,1))].">
      <j1 rule="para" parents="6742 10138"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(9554(a,2),10145(a,1,2,2))].">
      <j1 rule="para" parents="9554 10145"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(2099(a,2),10159(a,1))].">
      <j1 rule="para" parents="2099 10159"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(10172(a,1),10159(a,1))].">
      <j1 rule="para" parents="10172 10159"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10198(a,2),10208(a,1))].">
      <j1 rule="para" parents="10198 10208"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11(a,1),10209(a,1,2))].">
      <j1 rule="para" parents="11 10209"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      K(x,L(T(y \ 1,((y * z) \ z) \ z) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(3233(a,1),10160(a,2,2,1))].">
      <j1 rule="para" parents="3233 10160"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(8614(a,1),10163(a,1))].">
      <j1 rule="para" parents="8614 10163"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8620(a,1),10207(a,1))].">
      <j1 rule="para" parents="8620 10207"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x,x * y),z,u) * T(x,y)) = R(T(x,L(x * y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8830,a,b,10135,a)].">
      <j1 rule="hyper" parents="64 8830 10135"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,(z * y) \ K(z,1 / z)))
    ]]></literal>
    <justification jstring="[para(511(a,1),10169(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="511 10169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      L(x,y,z) \ ((u / x) \ (L(x,y,z) * (x \ u))) = x \ (x * a(z,y,K(x \ u,x)))
    ]]></literal>
    <justification jstring="[para(10175(a,1),7722(a,2,2))].">
      <j1 rule="para" parents="10175 7722"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(10101(a,2),10177(a,1))].">
      <j1 rule="para" parents="10101 10177"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      x * (y * K(z,K(x * y,u))) = T(x * y,K(z,L(u,y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,6749,a(flip),b,10186,a),flip(a)].">
      <j1 rule="hyper" parents="64 6749 10186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(6448(a,1),10187(a,1,1))].">
      <j1 rule="para" parents="6448 10187"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(10206,a,xx),flip(a)].">
      <j1 rule="hyper" parents="10206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),10219(a,1,2,2))].">
      <j1 rule="para" parents="6758 10219"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10115(a,1),10143(a,1,1))].">
      <j1 rule="para" parents="10115 10143"/>
    </justification>
  </clause>

  <clause id="10224">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(4925,a,10223,a)].">
      <j1 rule="hyper" parents="4925 10223"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(109(a,1),10223(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 10223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(5271(a,1),10224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5271 10224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6113(a,1),10224(a,1,2))].">
      <j1 rule="para" parents="6113 10224"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(6185(a,1),10224(a,1,2))].">
      <j1 rule="para" parents="6185 10224"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6851(a,1),10227(a,1,2,1))].">
      <j1 rule="para" parents="6851 10227"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      K(x,y \ z) \ T(x,(y \ z) * x) = L(x,y \ T(z,x),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4459,a,b,10226,a)].">
      <j1 rule="hyper" parents="319 4459 10226"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,10226,a(flip),b,95,a)].">
      <j1 rule="hyper" parents="131 10226 95"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      L(x,(y \ T(x,y \ x)) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(3120(a,1),10228(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3120 10228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4116(a,1),10229(a,1,2))].">
      <j1 rule="para" parents="4116 10229"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(4292(a,1),10229(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 10229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,8910,a(flip),b,10225,a)].">
      <j1 rule="hyper" parents="319 8910 10225"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(9199(a,2),10237(a,1,3))].">
      <j1 rule="para" parents="9199 10237"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10235(a,1),10107(a,1,2))].">
      <j1 rule="para" parents="10235 10107"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8428,a(flip),b,10239,a)].">
      <j1 rule="hyper" parents="64 8428 10239"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10234(a,2),10239(a,1,2))].">
      <j1 rule="para" parents="10234 10239"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      K(x,L(T(y,z),u * y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),10241(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,K(w,L(u,y,x))) * K(z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10173(a,1),5942(a,1))].">
      <j1 rule="para" parents="10173 5942"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      K(x,y / (x * ((x \ z) * u))) = K(x,x \ (y / ((z / x) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9152,a(flip),b,10199,a),flip(a)].">
      <j1 rule="hyper" parents="64 9152 10199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      K(x / (y \ z),u) \ (y \ z) = y \ (z * K(u,z \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6221,a,b,10203,a)].">
      <j1 rule="hyper" parents="319 6221 10203"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      K(x,x \ (y / ((z / x) * u))) = K(x,x \ (y / ((x \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9152,a(flip),b,10244,a),flip(a)].">
      <j1 rule="hyper" parents="64 9152 10244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      K(x / (y \ z),u) \ (y \ z) = y \ (K((y * x) / z,u) \ z)
    ]]></literal>
    <justification jstring="[para(6221(a,2),10245(a,2,2))].">
      <j1 rule="para" parents="6221 10245"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      T(x / (y \ z),u) \ x = y \ (K((y * x) / z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(4561,a,10247,a)].">
      <j1 rule="hyper" parents="4561 10247"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      T(1 / (x \ y),z) \ 1 = x \ (K(x / y,z) \ y)
    ]]></literal>
    <justification jstring="[para(8(a,1),10248(a,2,2,1,1,1))].">
      <j1 rule="para" parents="8 10248"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ (K(y,T(z,x)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(6871(a,1),10249(a,2,2,1))].">
      <j1 rule="para" parents="6871 10249"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ ((x / y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(6959(a,1),10250(a,2,2))].">
      <j1 rule="para" parents="6959 10250"/>
    </justification>
  </clause>

  <clause id="10252">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ (x / T(y,z))
    ]]></literal>
    <justification jstring="[para(5163(a,1),10251(a,2,2))].">
      <j1 rule="para" parents="5163 10251"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      K(x,y) \ (z \ (z / x)) = z \ (z / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5034,a(flip),b,10252,a)].">
      <j1 rule="hyper" parents="64 5034 10252"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      K(x,y) * ((z \ (z / y)) * u) = (z \ (z / T(y,x))) * u
    ]]></literal>
    <justification jstring="[para(10253(a,1),9582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10253 9582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      K(x,y) \ ((z \ (z / x)) * u) = (z \ (z / T(x,y))) * u
    ]]></literal>
    <justification jstring="[hyper(4393,a,10254,a)].">
      <j1 rule="hyper" parents="4393 10254"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4838(a,1),10124(a,1,1))].">
      <j1 rule="para" parents="4838 10124"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5331,a(flip),b,10256,a),flip(a)].">
      <j1 rule="hyper" parents="319 5331 10256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,L(y,u,w))) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[hyper(6810,a,10257,a)].">
      <j1 rule="hyper" parents="6810 10257"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8684,a(flip),b,10049,a)].">
      <j1 rule="hyper" parents="64 8684 10049"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      a(L(x,y / x,z),u,L(x,y / x,z)) = L(a(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),10259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(5006(a,1),10068(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5006 10068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4912,a(flip),b,10262,a),flip(a)].">
      <j1 rule="hyper" parents="319 4912 10262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1165(a,1),10263(a,1,1))].">
      <j1 rule="para" parents="1165 10263"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(10264(a,1),7922(a,2,2))].">
      <j1 rule="para" parents="10264 7922"/>
    </justification>
  </clause>

  <clause id="10266">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4913,a,b,10265,a),flip(a)].">
      <j1 rule="hyper" parents="319 4913 10265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6125,a(flip),b,10204,a),flip(a)].">
      <j1 rule="hyper" parents="64 6125 10204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(10241(a,1),10182(a,1,2))].">
      <j1 rule="para" parents="10241 10182"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(9429(a,1),10178(a,1,2))].">
      <j1 rule="para" parents="9429 10178"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      T(R(x * K(y * x,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4502(a,1),10051(a,1,1))].">
      <j1 rule="para" parents="4502 10051"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      T(R(x * K(x * y,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4281(a,1),10270(a,1,1,1,2))].">
      <j1 rule="para" parents="4281 10270"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      R(T(x * K(x * y,x),y),z,u) = R(R(x,z,u),y,L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,10271,a)].">
      <j1 rule="hyper" parents="64 27 10271"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      R(R(x,y,z),u,L(R(x,y,z),w,v5)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4399(a,1),10272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4399 10272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10044,a(flip),b,10273,a)].">
      <j1 rule="hyper" parents="64 10044 10273"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),w,L(R(y,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(10273(a,1),9778(a,1,2))].">
      <j1 rule="para" parents="10273 9778"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u)
    ]]></literal>
    <justification jstring="[para(10274(a,1),430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10274 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(319,a,105,a(flip),b,10276,a),flip(a)].">
      <j1 rule="hyper" parents="319 105 10276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * u) * w = (R(T(x,y),z,R(x,u,w)) * u) * w
    ]]></literal>
    <justification jstring="[para(8084(a,1),10277(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8084 10277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      ((R(x,y,x) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(10277(a,1),9741(a,1,1))].">
      <j1 rule="para" parents="10277 9741"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(a(x,u,x),x * y,z) = w
    ]]></literal>
    <justification jstring="[para(10279(a,1),8707(a,1))].">
      <j1 rule="para" parents="10279 8707"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),10142(a,2,2))].">
      <j1 rule="para" parents="25 10142"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,x * y),y,x)) = K(u,L(z,y,x)) * (x * (y / z))
    ]]></literal>
    <justification jstring="[para(10240(a,1),10149(a,1,2))].">
      <j1 rule="para" parents="10240 10149"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * (z / y)) = u * (z / T(y,T(x,u * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10268,a(flip),b,10282,a),flip(a)].">
      <j1 rule="hyper" parents="64 10268 10282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x * y,x),z,u) \ T(x,y)) = R(T(x,L(x * y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(4838(a,2),10214(a,1,2))].">
      <j1 rule="para" parents="4838 10214"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      L(x,y,z) \ T(L(x,y,z) * K(u,x),u) = x \ (x * a(z,y,K(x \ u,x)))
    ]]></literal>
    <justification jstring="[para(10266(a,1),10216(a,1,2))].">
      <j1 rule="para" parents="10266 10216"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(6091,a,10285,a),flip(a)].">
      <j1 rule="hyper" parents="6091 10285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(10133(a,1),10286(a,2,1))].">
      <j1 rule="para" parents="10133 10286"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,10127,a(flip),b,10287,a),flip(a)].">
      <j1 rule="hyper" parents="319 10127 10287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(332,a,10288,a),flip(a)].">
      <j1 rule="hyper" parents="332 10288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(10288(a,1),330(a,1))].">
      <j1 rule="para" parents="10288 330"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),10289(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 10289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4166(a,1),10289(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4166 10289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(4652(a,1),10289(a,1,3))].">
      <j1 rule="para" parents="4652 10289"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,u * z))
    ]]></literal>
    <justification jstring="[para(4995(a,1),10289(a,1,3))].">
      <j1 rule="para" parents="4995 10289"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(8217(a,1),10289(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8217 10289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) \ K(w,z) = K(w,z) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10292(a,2),8645(a,1,1))].">
      <j1 rule="para" parents="10292 8645"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,5632,a(flip),b,10293,a),flip(a)].">
      <j1 rule="hyper" parents="319 5632 10293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,10298,a)].">
      <j1 rule="hyper" parents="53 10298"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(10299(a,1),6127(a,2,1))].">
      <j1 rule="para" parents="10299 6127"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,8645,a(flip),b,10297,a(flip))].">
      <j1 rule="hyper" parents="35 8645 10297"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10295,a,b,10301,a)].">
      <j1 rule="hyper" parents="64 10295 10301"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10301(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4394(a,2),10301(a,1,3))].">
      <j1 rule="para" parents="4394 10301"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(10077(a,1),10301(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10077 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10302,a(flip),b,10305,a),flip(a)].">
      <j1 rule="hyper" parents="64 10302 10305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10294,a(flip),b,10306,a)].">
      <j1 rule="hyper" parents="64 10294 10306"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(4996(a,1),10306(a,1,3))].">
      <j1 rule="para" parents="4996 10306"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5006(a,1),10307(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5006 10307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6615(a,1),10300(a,1,2,2))].">
      <j1 rule="para" parents="6615 10300"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6125,a(flip),b,10310,a),flip(a)].">
      <j1 rule="hyper" parents="64 6125 10310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8542,a(flip),b,10311,a),flip(a)].">
      <j1 rule="hyper" parents="64 8542 10311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(8510(a,1),10312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8510 10312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(331,a,10313,a),flip(a)].">
      <j1 rule="hyper" parents="331 10313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10006,a(flip),b,10275,a),flip(a)].">
      <j1 rule="hyper" parents="64 10006 10275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      x * a(R(y,z,u),w,R(y,z,u)) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(477(a,1),10315(a,1,2,3))].">
      <j1 rule="para" parents="477 10315"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(286,a,10316,a),flip(a)].">
      <j1 rule="hyper" parents="286 10316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10280,a,10317,a)].">
      <j1 rule="hyper" parents="10280 10317"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10003,a(flip),b,10317,a),flip(a)].">
      <j1 rule="hyper" parents="64 10003 10317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),10318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      R(T(x,y),z,R(x,x \ u,w)) = T(x,y) * R(a(x,z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,10320,a(flip),b,8739,a),flip(a)].">
      <j1 rule="hyper" parents="131 10320 8739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,10320,a(flip),b,8730,a),flip(a)].">
      <j1 rule="hyper" parents="131 10320 8730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      T(x,y) * R(a(T(x,y),z,T(x,y)),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,8084,a(flip),b,10322,a),flip(a)].">
      <j1 rule="hyper" parents="64 8084 10322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(10319(a,1),8816(a,1,1))].">
      <j1 rule="para" parents="10319 8816"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      R(T(x,y),z,R(x,T(x,y) \ u,w)) = T(x,y) * R(a(x,z,x),u,w)
    ]]></literal>
    <justification jstring="[para(9678(a,1),10323(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9678 10323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      R(T(x,y),z,R(x,T(x,y) \ u,w)) = R(T(x,y),z,R(x,x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,10321,a,b,10325,a),flip(a)].">
      <j1 rule="hyper" parents="319 10321 10325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(T(x,y),z,R(x,x \ u,w)) * (T(x,y) \ u)) * w
    ]]></literal>
    <justification jstring="[para(10326(a,1),10278(a,2,1,1))].">
      <j1 rule="para" parents="10326 10278"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      T(x,y) \ ((x \ (x * (L(x,z,u) \ y))) \ (x * (L(x,z,u) \ y))) = a(x,L(x,z,u) \ y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),10071(a,2,2))].">
      <j1 rule="para" parents="9 10071"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      T(x,y) \ ((L(x,z,u) \ y) \ (x * (L(x,z,u) \ y))) = a(x,L(x,z,u) \ y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),10329(a,1,2,1))].">
      <j1 rule="para" parents="9 10329"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      T(x,y) \ T(x,L(x,z,u) \ y) = a(x,L(x,z,u) \ y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),10330(a,1,2))].">
      <j1 rule="para" parents="22 10330"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,x) = T(x,u) \ T(x,x \ u)
    ]]></literal>
    <justification jstring="[para(8723(a,1),10333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8723 10333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,x) = a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8352,a(flip),b,10334,a),flip(a)].">
      <j1 rule="hyper" parents="319 8352 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * T(y \ L(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(8371(a,1),10031(a,1,2,1))].">
      <j1 rule="para" parents="8371 10031"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * T(y \ L(y,z,y),y \ R(y,z,y)) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(2969(a,1),10337(a,1,2,2))].">
      <j1 rule="para" parents="2969 10337"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(2587(a,1),10338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2587 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      R(x,(y \ L(y,z,y)) \ 1,y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(8371(a,1),10339(a,1,2,1))].">
      <j1 rule="para" parents="8371 10339"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,y \ R(y,z,y),y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(10030(a,1),10341(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10030 10341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,y \ R(y,z,y),y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(8371(a,1),10342(a,2,3))].">
      <j1 rule="para" parents="8371 10342"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,8703,a(flip),b,10343,a),flip(a)].">
      <j1 rule="hyper" parents="319 8703 10343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      (x * (K(T(y,z),u) * K(y * u,T(y,z)))) * (y \ L(y,u,y)) = x
    ]]></literal>
    <justification jstring="[para(8129(a,2),10344(a,1,1,2))].">
      <j1 rule="para" parents="8129 10344"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      K(x,T(y,z)) * K(T(y,z),y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(8366,a,10346,a)].">
      <j1 rule="hyper" parents="8366 10346"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,T(y * x,z)) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(6474,a,10347,a)].">
      <j1 rule="hyper" parents="6474 10347"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = (y \ L(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,10348,a(flip),b,4915,a),flip(a)].">
      <j1 rule="hyper" parents="130 10348 4915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3941,a(flip),b,10349,a),flip(a)].">
      <j1 rule="hyper" parents="319 3941 10349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      K(x \ 1,T(y,z)) * T(y,T(x \ y,z)) = L(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7446(a,1),10350(a,1,2))].">
      <j1 rule="para" parents="7446 10350"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      K(x * y,z) * T(z,T(z * (y * x),y)) = L(z,y * x,z)
    ]]></literal>
    <justification jstring="[para(9288(a,1),10350(a,1,1))].">
      <j1 rule="para" parents="9288 10350"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      K(x \ (y \ x),z) * T(z,T(y \ z,x)) = L(z,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(6212(a,2),10351(a,1,1))].">
      <j1 rule="para" parents="6212 10351"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      K((x / y) \ 1,z) * T(z,T(z * ((y / x) * ((y / x) \ ((x / y) \ 1))),y / x)) = L(z,(y / x) * ((y / x) \ ((x / y) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(3773(a,1),10352(a,1,1,1))].">
      <j1 rule="para" parents="3773 10352"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      L(x,y \ (z \ y),x) = L(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8796,a(flip),b,10353,a)].">
      <j1 rule="hyper" parents="64 8796 10353"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(81(a,1),10355(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 10355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      L(x,y * (y \ ((z / u) \ 1)),x) = L(x,z \ u,x)
    ]]></literal>
    <justification jstring="[para(10(a,2),10357(a,1,2))].">
      <j1 rule="para" parents="10 10357"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      T(T(x,y) / (T(y,x) \ x),y * (x / T(y,x))) = L((y \ x) \ x,T(y,x) \ x,(y \ x) \ x)
    ]]></literal>
    <justification jstring="[para(6700(a,1),7982(a,1,1,1))].">
      <j1 rule="para" parents="6700 7982"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(3269(a,1),10359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3269 10359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6020,a(flip),b,10360,a),flip(a)].">
      <j1 rule="hyper" parents="319 6020 10360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      (((K(x,y) * K(y,z)) \ u) \ u) \ 1 = (K(x,y) * K(y,z)) \ K(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8365(a,1),8495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8365 8495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      (((K(x,y) * K(y,z)) \ u) \ u) \ 1 = (K(y,x) * K(z,y)) * K(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,8031,a(flip),b,10363,a),flip(a)].">
      <j1 rule="hyper" parents="319 8031 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      (((K(x,y) * K(y,z)) \ u) \ u) \ 1 = T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a,b,10364,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 10364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      ((K(x,y) * (K(z,x) * u)) \ u) \ 1 = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[para(8030(a,1),10366(a,1,1,1))].">
      <j1 rule="para" parents="8030 10366"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      ((K(x,y) * (K(y,z) * u)) \ u) \ 1 = T(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8499(a,1),10367(a,1,1,1))].">
      <j1 rule="para" parents="8499 10367"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = (R(T(x,u),w,v5) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,430,a(flip),b,8865,a),flip(a)].">
      <j1 rule="hyper" parents="319 430 8865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      (K(x,y) * R(K(x,y) \ T(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[hyper(64,a,1457,a(flip),b,10369,a)].">
      <j1 rule="hyper" parents="64 1457 10369"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      (K(x,y) * R(T(T(x,y),T(z,y)) * K(y,x),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(4368(a,1),10370(a,1,1,2,1))].">
      <j1 rule="para" parents="4368 10370"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      (K(x,y) * R(x * K(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(4657(a,1),10371(a,1,1,2,1))].">
      <j1 rule="para" parents="4657 10371"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(x,w)) * v5 = (K(x,w) * R(T(x,y),z,u)) * v5
    ]]></literal>
    <justification jstring="[para(6872(a,1),10372(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6872 10372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      (K(x,y) * R(T(x,z),u,w)) * v5 = R(T(x,z),u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,3453,a(flip),b,10373,a),flip(a)].">
      <j1 rule="hyper" parents="64 3453 10373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      (K(x,y) \ (R(T(x,z),u,w) * (K(x,y) * v5))) / (K(x,y) \ (R(T(x,z),u,w) * v5)) = R(K(x,y),R(T(x,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(10374(a,1),1131(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10374 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      (K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5))) / (K(y,x) \ (R(T(y,z),u,w) * v5)) = R(K(y,x),R(T(y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(4356(a,1),10376(a,1,1))].">
      <j1 rule="para" parents="4356 10376"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      (R(T(x,y),z,u) * w) / (K(x,v5) \ (R(T(x,y),z,u) * w)) = R(K(x,v5),R(T(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9019(a,1),10377(a,1,1))].">
      <j1 rule="para" parents="9019 10377"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(297,a,10378,a),flip(a)].">
      <j1 rule="hyper" parents="297 10378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,R(T(x,y),z,u) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5569,a(flip),b,10379,a)].">
      <j1 rule="hyper" parents="64 5569 10379"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6208,a(flip),b,10382,a),flip(a)].">
      <j1 rule="hyper" parents="319 6208 10382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,5882,a(flip),b,10383,a),flip(a)].">
      <j1 rule="hyper" parents="64 5882 10383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,8977,a(flip),b,10384,a),flip(a)].">
      <j1 rule="hyper" parents="319 8977 10384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(7173,a,10386,a)].">
      <j1 rule="hyper" parents="7173 10386"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(K(x,z) * L(K(z,x),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(4213(a,1),9936(a,2,1,2,1))].">
      <j1 rule="para" parents="4213 9936"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(a(v6,v5,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8607(a,1),10389(a,2,1))].">
      <j1 rule="para" parents="8607 10389"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(z,x),u,w),v5,v6))) = L(a(v6,v5,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(4835(a,1),10390(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4835 10390"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = L(a(v5,w,K(x,y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(4473,a,10391,a)].">
      <j1 rule="hyper" parents="4473 10391"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      a(x,y,L(K(z,u),w,v5)) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,9043,a(flip),b,10392,a)].">
      <j1 rule="hyper" parents="64 9043 10392"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),z,w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4948(a,1),10393(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4948 10393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(10096(a,1),10393(a,1,3))].">
      <j1 rule="para" parents="10096 10393"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,10394,a)].">
      <j1 rule="hyper" parents="54 10394"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(6851(a,1),10396(a,1,3,3))].">
      <j1 rule="para" parents="6851 10396"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      (x * y) * a(z,u,K(w,L(v5,y,x))) = x * (y * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(131,a,10395,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="131 10395 18"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ (((y \ 1) \ 1) \ (T(y,y \ 1) * z))),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2422(a,1),7610(a,2,1,2))].">
      <j1 rule="para" parents="2422 7610"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ z),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(426(a,1),10399(a,1,1,2,2))].">
      <j1 rule="para" parents="426 10399"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2439(a,1),10400(a,1,1,2))].">
      <j1 rule="para" parents="2439 10400"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3904,a(flip),b,10401,a),flip(a)].">
      <j1 rule="hyper" parents="64 3904 10401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(x \ (x * K(y,z)),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(8283(a,1),8288(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8283 8288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(K(y,z),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10403(a,2,1,2,1))].">
      <j1 rule="para" parents="9 10403"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * K(z,v5) = x * (R(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[para(8283(a,1),10404(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8283 10404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2102(a,1),10406(a,2,2))].">
      <j1 rule="para" parents="2102 10406"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      x / (K(y,z) * R(K(z,u),w,v5)) = x * (K(z,y) * R(K(u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,8602,a,b,10407,a)].">
      <j1 rule="hyper" parents="64 8602 10407"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      R(x * (K(y,z) * R(K(z,y),u,u \ 1)),K(z,y),R(K(y,z),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(10407(a,1),9760(a,1,1))].">
      <j1 rule="para" parents="10407 9760"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,u),w,v5))) * (K(z,y) * R(K(u,z),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(257,a,10408,a),flip(a)].">
      <j1 rule="hyper" parents="257 10408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      R(x * a(K(y,z),u,u \ 1),K(y,z),R(K(z,y),u,u \ 1)) = x / a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4366(a,1),10409(a,1,1,2))].">
      <j1 rule="para" parents="4366 10409"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(8295,a,10411,a),flip(a)].">
      <j1 rule="hyper" parents="8295 10411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3790,a,10412,a)].">
      <j1 rule="hyper" parents="3790 10412"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10413(a,1),8861(a,1,2))].">
      <j1 rule="para" parents="10413 8861"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(9069(a,1),10415(a,1,2))].">
      <j1 rule="para" parents="9069 10415"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,10416,a)].">
      <j1 rule="hyper" parents="55 10416"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = K(x,y) \ R(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,2448,a,b,10417,a),flip(a)].">
      <j1 rule="hyper" parents="319 2448 10417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      T(K(x,y) * R(K(y,x),z \ 1,z),u) = K(y,x) \ R(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4372(a,2),10418(a,1,1))].">
      <j1 rule="para" parents="4372 10418"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      K(x,T(y,z)) * R(K(y,T(x,z)),u \ 1,u) = K(y,x) \ R(K(y,x),u \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7969,a,b,10419,a)].">
      <j1 rule="hyper" parents="64 7969 10419"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * R(K(y,T(z,x)),u \ 1,u)) = K(y,z) \ R(K(y,z),u \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6616,a,b,10420,a)].">
      <j1 rule="hyper" parents="64 6616 10420"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,8946,a,b,10421,a)].">
      <j1 rule="hyper" parents="36 8946 10421"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2736(a,1),10422(a,1,2,2))].">
      <j1 rule="para" parents="2736 10422"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6758,a,b,10423,a),flip(a)].">
      <j1 rule="hyper" parents="319 6758 10423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10425">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(538(a,1),10424(a,1,2,2))].">
      <j1 rule="para" parents="538 10424"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(129,a,10425,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 10425 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(4594(a,2),10425(a,1,2))].">
      <j1 rule="para" parents="4594 10425"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(4596(a,1),10425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4596 10425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6969,a(flip),b,10426,a),flip(a)].">
      <j1 rule="hyper" parents="319 6969 10426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      T(T(x,K(y,z / u)),(z * (u \ 1)) * y) = T(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(10426(a,1),9260(a,1,1))].">
      <j1 rule="para" parents="10426 9260"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(4596(a,1),10429(a,1,2))].">
      <j1 rule="para" parents="4596 10429"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      K(x,K(y,K(z,y) / u)) = K(x,K(y,1 / u))
    ]]></literal>
    <justification jstring="[para(5848(a,1),10427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5848 10427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7177,a,10428,a)].">
      <j1 rule="hyper" parents="7177 10428"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(6789,a,10428,a)].">
      <j1 rule="hyper" parents="6789 10428"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(6139(a,1),10428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6139 10428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(K(y,z * x),x \ 1),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(10431(a,1),4204(a,1,1))].">
      <j1 rule="para" parents="10431 4204"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      (K(x,y) / z) * K(u,K(y,1 / z)) = T(K(x,y) / z,K(u,y))
    ]]></literal>
    <justification jstring="[para(10432(a,1),6754(a,1,2))].">
      <j1 rule="para" parents="10432 6754"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),10433(a,2,2,2))].">
      <j1 rule="para" parents="12 10433"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(4603(a,2),10433(a,1,2))].">
      <j1 rule="para" parents="4603 10433"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6744,a,10438,a)].">
      <j1 rule="hyper" parents="6744 10438"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      a(x,y * ((1 / z) / u),K(w,K(v5,u * z))) = a(x,y,K((1 / z) / u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(10439(a,1),10167(a,1,3))].">
      <j1 rule="para" parents="10439 10167"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7043,a(flip),b,10440,a)].">
      <j1 rule="hyper" parents="64 7043 10440"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(10442(a,1),7812(a,1,1))].">
      <j1 rule="para" parents="10442 7812"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(10442(a,1),7948(a,1,1))].">
      <j1 rule="para" parents="10442 7948"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6758(a,1),10445(a,1,1))].">
      <j1 rule="para" parents="6758 10445"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7466,a(flip),b,10446,a)].">
      <j1 rule="hyper" parents="64 7466 10446"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(78(a,1),10448(a,1,2,2,2))].">
      <j1 rule="para" parents="78 10448"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(6786,a,10444,a)].">
      <j1 rule="hyper" parents="6786 10444"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,192,a(flip),b,10444,a),flip(a)].">
      <j1 rule="hyper" parents="64 192 10444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(6703(a,1),10450(a,1,1))].">
      <j1 rule="para" parents="6703 10450"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6748(a,1),10451(a,2,1))].">
      <j1 rule="para" parents="6748 10451"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(7814,a,10453,a)].">
      <j1 rule="hyper" parents="7814 10453"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(199,a,10454,a)].">
      <j1 rule="hyper" parents="199 10454"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      K((T(x \ L(x,y,z),x * u) / w) / ((x \ L(x,y,z)) / w),v5) = K(x \ L(x,y,z),K(u * x,v5))
    ]]></literal>
    <justification jstring="[para(9915(a,1),10455(a,1,1,1,1))].">
      <j1 rule="para" parents="9915 10455"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,4123,a,b,10456,a)].">
      <j1 rule="hyper" parents="64 4123 10456"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,10458,a)].">
      <j1 rule="hyper" parents="54 10458"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),10459(a,1,3))].">
      <j1 rule="para" parents="9 10459"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(6080(a,2),10459(a,1,1))].">
      <j1 rule="para" parents="6080 10459"/>
    </justification>
  </clause>

  <clause id="10462">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(6703(a,1),10460(a,1,1))].">
      <j1 rule="para" parents="6703 10460"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,v6)) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(319,a,6764,a,b,10461,a),flip(a)].">
      <j1 rule="hyper" parents="319 6764 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(9271(a,1),10435(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9271 10435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7122,a,10464,a)].">
      <j1 rule="hyper" parents="7122 10464"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10464(a,2,2,2))].">
      <j1 rule="para" parents="12 10464"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10464(a,1),6771(a,1,2,2))].">
      <j1 rule="para" parents="10464 6771"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7121,a(flip),b,10465,a),flip(a)].">
      <j1 rule="hyper" parents="64 7121 10465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(10466(a,1),7406(a,2,2))].">
      <j1 rule="para" parents="10466 7406"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10222,a(flip),b,10467,a)].">
      <j1 rule="hyper" parents="64 10222 10467"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,u)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(10471(a,1),10119(a,1,2))].">
      <j1 rule="para" parents="10471 10119"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(v6,K(w,v5))
    ]]></literal>
    <justification jstring="[para(10449(a,1),10463(a,2,2))].">
      <j1 rule="para" parents="10449 10463"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = T(L(K(z,u),y,x),T(x * y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(10472(a,1),111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10472 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = T(x * y,K(z,u)) / ((x * (y * K(z,u))) / L(K(z,u),y,x))
    ]]></literal>
    <justification jstring="[para(10472(a,1),4233(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10472 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,6729,a(flip),b,10437,a),flip(a)].">
      <j1 rule="hyper" parents="64 6729 10437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,1 / z)) / z
    ]]></literal>
    <justification jstring="[para(6099(a,2),10476(a,2,1))].">
      <j1 rule="para" parents="6099 10476"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7149(a,1),10477(a,2,1))].">
      <j1 rule="para" parents="7149 10477"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) * K(u,z) = K(x,T(y,z)) / T(z,u)
    ]]></literal>
    <justification jstring="[hyper(130,a,10478,a,b,5167,a)].">
      <j1 rule="hyper" parents="130 10478 5167"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7016,a,10468,a),flip(a)].">
      <j1 rule="hyper" parents="7016 10468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7122,a,10480,a)].">
      <j1 rule="hyper" parents="7122 10480"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      K(x,K((y * z) * u,u \ ((y * z) \ (y * (z * u))))) = K(x,K(y * (z * u),a(y,z,u) * (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(4396(a,2),10481(a,2,2))].">
      <j1 rule="para" parents="4396 10481"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(6748(a,2),10473(a,2,2))].">
      <j1 rule="para" parents="6748 10473"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(6080(a,1),10483(a,1,1))].">
      <j1 rule="para" parents="6080 10483"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = a(K(w,K(v5,v6)),v7,v7 \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,9809,a(flip),b,10484,a)].">
      <j1 rule="hyper" parents="319 9809 10484"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,10462,a(flip),b,10485,a),flip(a)].">
      <j1 rule="hyper" parents="319 10462 10485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9826,a(flip),b,10486,a)].">
      <j1 rule="hyper" parents="64 9826 10486"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),10487(a,1,2,2,2,3))].">
      <j1 rule="para" parents="9 10487"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = L(T(K(z,u),x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,3272,a(flip),b,10474,a),flip(a)].">
      <j1 rule="hyper" parents="319 3272 10474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(6099(a,2),10489(a,2,1))].">
      <j1 rule="para" parents="6099 10489"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      K(K(((x \ L(x,y,z)) / u) / (u \ 1),x * w),v5) = K(x \ L(x,y,z),K(w * x,v5))
    ]]></literal>
    <justification jstring="[para(4318(a,2),10457(a,1,1))].">
      <j1 rule="para" parents="4318 10457"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      K(x,K(((y \ L(y,z,u)) / w) / (w \ 1),y * v5)) = K(y \ L(y,z,u),K(v5 * y,x))
    ]]></literal>
    <justification jstring="[hyper(6976,a,10491,a)].">
      <j1 rule="hyper" parents="6976 10491"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      K(x,K(y * z,((y \ L(y,u,w)) / v5) * v5)) = K(y \ L(y,u,w),K(z * y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10434,a(flip),b,10492,a)].">
      <j1 rule="hyper" parents="64 10434 10492"/>
    </justification>
  </clause>

  <clause id="10494">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(w,K(x * u,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),10493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      K(x,K(y * z,y \ L(y,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,y \ L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(10494(a,1),6732(a,1))].">
      <j1 rule="para" parents="10494 6732"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K((y * z) * u,u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[para(18(a,2),10482(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 10482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(y,K(z * x,x \ 1)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(6705(a,1),10436(a,1,2,1,2))].">
      <j1 rule="para" parents="6705 10436"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(y,K(x,z * x)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(7029(a,1),10497(a,1,2,1,2))].">
      <j1 rule="para" parents="7029 10497"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(6745(a,1),10498(a,1,2,1,2))].">
      <j1 rule="para" parents="6745 10498"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(4068(a,2),10499(a,1,2,1))].">
      <j1 rule="para" parents="4068 10499"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4339,a,b,10500,a)].">
      <j1 rule="hyper" parents="64 4339 10500"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x,K(u,w)) * (L(T(x,K(u,w)),y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(7045(a,1),10501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7045 10501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z))
    ]]></literal>
    <justification jstring="[para(1196(a,1),10502(a,2,2))].">
      <j1 rule="para" parents="1196 10502"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6785,a(flip),b,10503,a),flip(a)].">
      <j1 rule="hyper" parents="319 6785 10503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10505">
    <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),5425(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10506">
    <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(319,a,6106,a(flip),b,10505,a),flip(a)].">
      <j1 rule="hyper" parents="319 6106 10505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10508">
    <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(319,a,7574,a(flip),b,10506,a),flip(a)].">
      <j1 rule="hyper" parents="319 7574 10506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10509">
    <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(64,a,7795,a(flip),b,10508,a)].">
      <j1 rule="hyper" parents="64 7795 10508"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(7577,a,10509,a)].">
      <j1 rule="hyper" parents="7577 10509"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(6993,a,10510,a),flip(a)].">
      <j1 rule="hyper" parents="6993 10510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(8998,a,10511,a)].">
      <j1 rule="hyper" parents="8998 10511"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      K(x,(y * z) / (R(x,y,z) \ u)) = K(x,((x * y) * z) / u)
    ]]></literal>
    <justification jstring="[para(105(a,1),10511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 10511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6353,a,10513,a),flip(a)].">
      <j1 rule="hyper" parents="6353 10513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7458,a,b,10515,a)].">
      <j1 rule="hyper" parents="64 7458 10515"/>
    </justification>
  </clause>

  <clause id="10517">
    <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(64,a,9761,a,b,10516,a)].">
      <j1 rule="hyper" parents="64 9761 10516"/>
    </justification>
  </clause>

  <clause id="10518">
    <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),10517(a,2,2,1))].">
      <j1 rule="para" parents="20 10517"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7678,a(flip),b,10518,a),flip(a)].">
      <j1 rule="hyper" parents="64 7678 10518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      K(R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4356(a,1),7857(a,1,1,1))].">
      <j1 rule="para" parents="4356 7857"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,T(y * (x / y),(x / y) \ 1)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(6530(a,1),9623(a,1,1,1))].">
      <j1 rule="para" parents="6530 9623"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,y * (T(x,(x / y) \ 1) / y)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(3795(a,1),10522(a,1,3))].">
      <j1 rule="para" parents="3795 10522"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,y * (T(x,x \ y) / y)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(3221(a,1),10523(a,1,3,2,1))].">
      <j1 rule="para" parents="3221 10523"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,(x \ y) \ T(y,y \ x)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(5348(a,2),10524(a,1,3))].">
      <j1 rule="para" parents="5348 10524"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      K(x,L(T(y \ 1,T(y * z,z)) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(5738(a,1),10211(a,1,2,1,1))].">
      <j1 rule="para" parents="5738 10211"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(9251(a,1),10526(a,1,2,1,1))].">
      <j1 rule="para" parents="9251 10526"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,x),z,u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(9487(a,1),10521(a,1,1))].">
      <j1 rule="para" parents="9487 10521"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,x),z,u),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5096,a(flip),b,10528,a)].">
      <j1 rule="hyper" parents="64 5096 10528"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      K(K(x,y) * K(y,R(x,z,u)),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,9845,a(flip),b,10529,a)].">
      <j1 rule="hyper" parents="64 9845 10529"/>
    </justification>
  </clause>

  <clause id="10532">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,R(y,z,u)) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(9840,a,10531,a),flip(a)].">
      <j1 rule="hyper" parents="9840 10531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,y) * K(y,R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,9826,a(flip),b,10532,a),flip(a)].">
      <j1 rule="hyper" parents="319 9826 10532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,10488,a(flip),b,10533,a),flip(a)].">
      <j1 rule="hyper" parents="319 10488 10533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5096,a(flip),b,10534,a)].">
      <j1 rule="hyper" parents="64 5096 10534"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10536(a,1),4208(a,1,1))].">
      <j1 rule="para" parents="10536 4208"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9488(a,1),10537(a,1,2))].">
      <j1 rule="para" parents="9488 10537"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,10538,a)].">
      <j1 rule="hyper" parents="133 10538"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      1 * (K(x,K(y,z)) * R(K(x,K(y,z)),u,w)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(6757(a,1),10538(a,1,2,1))].">
      <j1 rule="para" parents="6757 10538"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(4374,a,10539,a)].">
      <j1 rule="hyper" parents="4374 10539"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2106,a,10539,a)].">
      <j1 rule="hyper" parents="2106 10539"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,10539,a(flip),b,4312,a)].">
      <j1 rule="hyper" parents="131 10539 4312"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(5557(a,1),10539(a,1,2))].">
      <j1 rule="para" parents="5557 10539"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(7672(a,1),10539(a,1,2))].">
      <j1 rule="para" parents="7672 10539"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(10539(a,1),9829(a,2,2))].">
      <j1 rule="para" parents="10539 9829"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(10539(a,1),10410(a,1,1,2))].">
      <j1 rule="para" parents="10539 10410"/>
    </justification>
  </clause>

  <clause id="10549">
    <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(10541(a,1),8078(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10541 8078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(10542(a,1),8601(a,2,2))].">
      <j1 rule="para" parents="10542 8601"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(10539(a,1),10548(a,1,2))].">
      <j1 rule="para" parents="10539 10548"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      (T(x,x \ y) * a(K(z,u),w,v5)) \ ((x \ y) \ y) = a(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(127,a,110,a(flip),b,10551,a)].">
      <j1 rule="hyper" parents="127 110 10551"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(10551(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="10551 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      1 * (K(x,K(y,z)) * K(y,K(z,R(x,u,w)))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7466(a,1),10540(a,1,2,2))].">
      <j1 rule="para" parents="7466 10540"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      1 * K(x,K(y,z) * K(R(z,u,w),y)) = a(K(z,K(y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(9842(a,1),10555(a,1,2))].">
      <j1 rule="para" parents="9842 10555"/>
    </justification>
  </clause>

  <clause id="10557">
    <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(319,a,10550,a(flip),b,10549,a),flip(a)].">
      <j1 rule="hyper" parents="319 10550 10549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,1 / (1 / ((x * y) / x))) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(7835(a,1),5313(a,2,1))].">
      <j1 rule="para" parents="7835 5313"/>
    </justification>
  </clause>

  <clause id="10559">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(2755(a,1),10558(a,1,2))].">
      <j1 rule="para" parents="2755 10558"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(4408(a,1),10559(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4408 10559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,9759,a(flip),b,10560,a),flip(a)].">
      <j1 rule="hyper" parents="319 9759 10560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),1179(a,1,2,2,1,1))].">
      <j1 rule="para" parents="18 1179"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),10563(a,1,2,2,2))].">
      <j1 rule="para" parents="18 10563"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(18(a,2),10564(a,2,2))].">
      <j1 rule="para" parents="18 10564"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(3939(a,1),10565(a,1,2,2))].">
      <j1 rule="para" parents="3939 10565"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(713,a,10566,a),flip(a)].">
      <j1 rule="hyper" parents="713 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * R(R(x * T(x \ 1,u),y,z) \ 1,w,v5) = R((x * T(x \ 1,u)) * R(K(u,x \ 1),w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(4264(a,1),5218(a,1,1))].">
      <j1 rule="para" parents="4264 5218"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(R(x,w,v5) \ 1,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(4264(a,1),10568(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4264 10568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(y,R(x,w,v5) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(4213(a,1),10569(a,2,2,1))].">
      <j1 rule="para" parents="4213 10569"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * K(y,R(R(x,w,v5),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5557(a,1),10570(a,2,2))].">
      <j1 rule="para" parents="5557 10570"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * R(K(u,x \ 1),w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(4013(a,1),10571(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4013 10571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * K(u,R(x,w,v5) \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(5557(a,1),10572(a,2,1,2))].">
      <j1 rule="para" parents="5557 10572"/>
    </justification>
  </clause>

  <clause id="10574">
    <literal><![CDATA[
      R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(y,R(x,w,v5) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10545,a(flip),b,10573,a),flip(a)].">
      <j1 rule="hyper" parents="64 10545 10573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * L(x,y,z)),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4173(a,1),10039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4173 10039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * ((x / y) * ((x / y) \ ((y / x) \ 1))),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(4645(a,1),10354(a,1,1))].">
      <j1 rule="para" parents="4645 10354"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * ((y / x) \ 1),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10576(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 10576"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      K(x / y,z) * T(z,T((y / x) \ z,x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(7446(a,1),10577(a,1,2))].">
      <j1 rule="para" parents="7446 10577"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = T(x * y,K(z,u)) / (x * y)
    ]]></literal>
    <justification jstring="[para(197(a,1),10475(a,2,2))].">
      <j1 rule="para" parents="197 10475"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = K(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4011,a,b,10580,a),flip(a)].">
      <j1 rule="hyper" parents="319 4011 10580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a,b,10581,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 10581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),L(K(z,T(u,x * y)),y,x)) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(10490(a,1),10583(a,1,2))].">
      <j1 rule="para" parents="10490 10583"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),K(z,L(T(u,x * y),y,x))) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(10096(a,1),10584(a,1,2))].">
      <j1 rule="para" parents="10096 10584"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      K(x,K(T(y * z,K(x,u)),L(T(u,y * z),z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(6744,a,10585,a)].">
      <j1 rule="hyper" parents="6744 10585"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      K(x,K(y * z,L(T(u,y * z),z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(5960,a,10586,a)].">
      <j1 rule="hyper" parents="5960 10586"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(4174(a,1),10587(a,1,2))].">
      <j1 rule="para" parents="4174 10587"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ (x / x) = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),2410(a,1,2,1))].">
      <j1 rule="para" parents="12 2410"/>
    </justification>
  </clause>

  <clause id="10590">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ 1 = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),10589(a,1,2))].">
      <j1 rule="para" parents="75 10589"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(339,a,10590,a)].">
      <j1 rule="hyper" parents="339 10590"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2618(a,1),10592(a,1,1))].">
      <j1 rule="para" parents="2618 10592"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7328,a(flip),b,10595,a),flip(a)].">
      <j1 rule="hyper" parents="64 7328 10595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,3968,a(flip),b,10596,a),flip(a)].">
      <j1 rule="hyper" parents="319 3968 10596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,8099,a(flip),b,10597,a),flip(a)].">
      <j1 rule="hyper" parents="319 8099 10597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1063(a,1),10598(a,1,2))].">
      <j1 rule="para" parents="1063 10598"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),u) = K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(130,a,10599,a(flip),b,4056,a)].">
      <j1 rule="hyper" parents="130 10599 4056"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(w,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6758,a,b,10600,a),flip(a)].">
      <j1 rule="hyper" parents="319 6758 10600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ L(x,y,z),K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(10600(a,2),6789(a,1))].">
      <j1 rule="para" parents="10600 6789"/>
    </justification>
  </clause>

  <clause id="10603">
    <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(6425(a,1),8596(a,1,2,1))].">
      <j1 rule="para" parents="6425 8596"/>
    </justification>
  </clause>

  <clause id="10604">
    <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(3078(a,1),10603(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3078 10603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10605">
    <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(7093(a,1),10604(a,2,2))].">
      <j1 rule="para" parents="7093 10604"/>
    </justification>
  </clause>

  <clause id="10606">
    <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),10605(a,2,2,1))].">
      <j1 rule="para" parents="9 10605"/>
    </justification>
  </clause>

  <clause id="10607">
    <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(9458(a,1),10606(a,1,1,2))].">
      <j1 rule="para" parents="9458 10606"/>
    </justification>
  </clause>

  <clause id="10608">
    <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(6690(a,1),10607(a,1,1))].">
      <j1 rule="para" parents="6690 10607"/>
    </justification>
  </clause>

  <clause id="10610">
    <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(9458(a,1),10608(a,1,2,1))].">
      <j1 rule="para" parents="9458 10608"/>
    </justification>
  </clause>

  <clause id="10611">
    <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(4618(a,1),10610(a,1,2))].">
      <j1 rule="para" parents="4618 10610"/>
    </justification>
  </clause>

  <clause id="10612">
    <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(6414(a,1),10611(a,1,2))].">
      <j1 rule="para" parents="6414 10611"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5718(a,1),10612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5718 10612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5982,a,b,10613,a),flip(a)].">
      <j1 rule="hyper" parents="319 5982 10613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10616">
    <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(7372(a,1),4872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7372 4872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10617">
    <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(319,a,5920,a,b,10616,a),flip(a)].">
      <j1 rule="hyper" parents="319 5920 10616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <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(4081(a,1),10617(a,2,1))].">
      <j1 rule="para" parents="4081 10617"/>
    </justification>
  </clause>

  <clause id="10620">
    <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(319,a,7912,a(flip),b,10619,a),flip(a)].">
      <j1 rule="hyper" parents="319 7912 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10621">
    <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(3333(a,2),10620(a,1,2))].">
      <j1 rule="para" parents="3333 10620"/>
    </justification>
  </clause>

  <clause id="10622">
    <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(7368(a,1),10621(a,1,2,1))].">
      <j1 rule="para" parents="7368 10621"/>
    </justification>
  </clause>

  <clause id="10623">
    <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(3327(a,2),10622(a,1,2,1))].">
      <j1 rule="para" parents="3327 10622"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K((K(x,y) * K(z,x)) \ u,K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = ((K(y,x) * (K(x,z) * u)) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(8547(a,1),9813(a,2,1,1))].">
      <j1 rule="para" parents="8547 9813"/>
    </justification>
  </clause>

  <clause id="10626">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K((K(x,y) * K(z,x)) \ u,K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,10368,a(flip),b,10625,a),flip(a)].">
      <j1 rule="hyper" parents="319 10368 10625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(K(y,x) * (K(x,z) * u),K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8547(a,1),10626(a,1,2,1,1))].">
      <j1 rule="para" parents="8547 10626"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(u,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(7247(a,1),10627(a,1,2,1))].">
      <j1 rule="para" parents="7247 10627"/>
    </justification>
  </clause>

  <clause id="10629">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(y,u)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(6758(a,1),10628(a,1,2,1))].">
      <j1 rule="para" parents="6758 10628"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(y,u)) * K(K(y,x) * (K(x,z) * u),K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8547(a,1),10629(a,1,2,2,1))].">
      <j1 rule="para" parents="8547 10629"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(y,u)) * K(x,K(u,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(7247(a,1),10631(a,1,2,2))].">
      <j1 rule="para" parents="7247 10631"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(u,K(x,y) * K(z,x)) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(9841(a,1),10632(a,1,2))].">
      <j1 rule="para" parents="9841 10632"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * K(u,K(y,x) * K(z,y))) = T(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8575,a,10634,a)].">
      <j1 rule="hyper" parents="8575 10634"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = T(K(z,u) * K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9846,a,b,10635,a)].">
      <j1 rule="hyper" parents="64 9846 10635"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(y,x) * u) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(9825,a,10636,a)].">
      <j1 rule="hyper" parents="9825 10636"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R((y \ T(y * (x \ 1),y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9081(a,1),9082(a,2,2,1,1))].">
      <j1 rule="para" parents="9081 9082"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ (T(y * (x \ 1),y) * R(T(y * (x \ 1),y) \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,1432,a(flip),b,10638,a),flip(a)].">
      <j1 rule="hyper" parents="319 1432 10638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T((y * (x \ 1)) * R((y * (x \ 1)) \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1833(a,1),10639(a,2,2))].">
      <j1 rule="para" parents="1833 10639"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * ((x \ 1) * R((x \ 1) \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(983(a,1),10640(a,2,2,1))].">
      <j1 rule="para" parents="983 10640"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1070(a,1),10641(a,2,2,1,2))].">
      <j1 rule="para" parents="1070 10641"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      T(x \ (a(y,x \ 1,y) * R(a(y,x \ 1,y) \ x,z,u)),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1432(a,1),10642(a,1,1))].">
      <j1 rule="para" parents="1432 10642"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),K((x * y) * z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7689,a(flip),b,7803,a),flip(a)].">
      <j1 rule="hyper" parents="319 7689 7803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(u,K(a(x,y,z),(x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a(flip),b,10644,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 10644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),K(z,L(y,u,x))) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x)
    ]]></literal>
    <justification jstring="[para(10096(a,1),8415(a,1,2,2))].">
      <j1 rule="para" parents="10096 8415"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,9,a(flip),b,9489,a),flip(a)].">
      <j1 rule="hyper" parents="319 9 9489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10649">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(9487(a,1),10647(a,1,3))].">
      <j1 rule="para" parents="9487 10647"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(10539(a,1),10649(a,1,3))].">
      <j1 rule="para" parents="10539 10649"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      (a(K(x,y),z,u) * K(x,w)) * v5 = a(K(x,y),z,u) * (K(x,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1143,a,10651,a),flip(a)].">
      <j1 rule="hyper" parents="1143 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10653">
    <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(64,a,10557,a(flip),b,10652,a),flip(a)].">
      <j1 rule="hyper" parents="64 10557 10652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),10653(a,1,2))].">
      <j1 rule="para" parents="4363 10653"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(6845(a,1),10654(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6845 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(245,a,10655,a),flip(a)].">
      <j1 rule="hyper" parents="245 10655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(u,K(L(z,y,x),x * (K(z,u) * y))) = T(x * (K(z,u) * y),L(K(u,z),y,x)) * L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10469,a(flip),b,10646,a)].">
      <j1 rule="hyper" parents="64 10469 10646"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(L(y,u,x),x * u))
    ]]></literal>
    <justification jstring="[para(7927(a,1),10657(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7927 10657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(x * u,L(y,u,x)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),10658(a,2,2))].">
      <j1 rule="para" parents="6758 10658"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(y,x * u))
    ]]></literal>
    <justification jstring="[para(10588(a,1),10659(a,2,2))].">
      <j1 rule="para" parents="10588 10659"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[para(6742(a,1),10661(a,2,2))].">
      <j1 rule="para" parents="6742 10661"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      T(x * (K(y,z) * u),K(z,L(y,u,x))) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[para(10096(a,1),10662(a,1,1,2))].">
      <j1 rule="para" parents="10096 10662"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(z,L(y,u,x))) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8939,a,b,10663,a)].">
      <j1 rule="hyper" parents="64 8939 10663"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,K(u,x * y)) = T(x * T(y,K(z,u)),K(u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(8412(a,1),10664(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8412 10664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,L(z,y,x))) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ ((x * T(y,K(z,u))) * K(z,K(u,x * y))) = v5
    ]]></literal>
    <justification jstring="[para(10665(a,1),571(a,1))].">
      <j1 rule="para" parents="10665 571"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      T((((x * y) \ x) * (z * K(y \ 1,u))) / T((x * y) \ x,u),(((x * y) \ x) * z) / L(y \ 1,y,x)) = (((x * y) \ x) * z) / L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4995(a,1),6361(a,1,1,1,2,2))].">
      <j1 rule="para" parents="4995 6361"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      T(((x \ 1) * (y * K(x \ 1,z))) / T(x \ 1,z),(((u * x) \ u) * y) / L(x \ 1,x,u)) = (((u * x) \ u) * y) / L(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[para(8097(a,1),10667(a,1,1))].">
      <j1 rule="para" parents="8097 10667"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(((z * x) \ z) * y) / L(x \ 1,x,z)) = (((z * x) \ z) * y) / L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(5631(a,1),10669(a,1,1))].">
      <j1 rule="para" parents="5631 10669"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      (((x * y) \ x) * z) / L(y \ 1,y,x) = ((y \ 1) * z) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(188,a,10670,a)].">
      <j1 rule="hyper" parents="188 10670"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T((K(z,y) * (K(y,u) * x)) * (K(y,z) * K(u,y)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(8547(a,1),9796(a,1,2,1,1))].">
      <j1 rule="para" parents="8547 9796"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(T((K(y,u) * x) * K(u,y),K(y,z)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(9502(a,1),10673(a,1,2,1))].">
      <j1 rule="para" parents="9502 10673"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(T(T(x,K(y,u)),K(y,z)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(6795(a,1),10674(a,1,2,1,1))].">
      <j1 rule="para" parents="6795 10674"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(T(x,K(y,z) * K(u,y)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(9788(a,1),10675(a,1,2,1))].">
      <j1 rule="para" parents="9788 10675"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),(K(x,y) * K(z,x)) \ u) = (u * (K(x,y) * K(z,x))) / u
    ]]></literal>
    <justification jstring="[para(9803(a,1),10676(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9803 10676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),(K(x,y) * K(z,x)) \ u) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,9822,a(flip),b,10677,a),flip(a)].">
      <j1 rule="hyper" parents="319 9822 10677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(y,x) * (K(x,z) * u)) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[para(8547(a,1),10678(a,1,2))].">
      <j1 rule="para" parents="8547 10678"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(x,z) * u) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10637,a(flip),b,10679,a)].">
      <j1 rule="hyper" parents="64 10637 10679"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,u) * z) = T(K(x,u) * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8032,a(flip),b,10680,a)].">
      <j1 rule="hyper" parents="64 8032 10680"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8407,a(flip),b,10681,a)].">
      <j1 rule="hyper" parents="64 8407 10681"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,T(x,z)) * w) = T(K(x,y) * K(u,x),z) * w
    ]]></literal>
    <justification jstring="[para(10682(a,1),8028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10682 8028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      T(K(x,y) * K(y * R(x,z,u),x),w) * v5 = R(T(x,w),y,R(x,z,u)) * (T(x,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,9062,a(flip),b,10683,a),flip(a)].">
      <j1 rule="hyper" parents="64 9062 10683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5) = a(x,z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(8873(a,1),10684(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8873 10684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (a(x,z,R(x,x \ u,w)) * u) * w
    ]]></literal>
    <justification jstring="[para(10685(a,1),10328(a,2,1))].">
      <j1 rule="para" parents="10685 10328"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(10320(a,1),10687(a,2,1,1))].">
      <j1 rule="para" parents="10320 10687"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      (R(T(x,y),z,x) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(5912(a,1),10688(a,1,1,1))].">
      <j1 rule="para" parents="5912 10688"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      (T(x,y) * (L(T(x,y),z,x) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(9007(a,1),10690(a,1,1))].">
      <j1 rule="para" parents="9007 10690"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(8397(a,1),10692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 10692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      ((a(x,y,x) * z) * u) \ ((z * a(x,y,x)) * u) = a(R(a(x,y,x),z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,10693,a(flip),b,714,a)].">
      <j1 rule="hyper" parents="127 10693 714"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(9151,a,10694,a),flip(a)].">
      <j1 rule="hyper" parents="9151 10694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(8509(a,1),10695(a,2,2))].">
      <j1 rule="para" parents="8509 10695"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,8513,a(flip),b,10696,a),flip(a)].">
      <j1 rule="hyper" parents="319 8513 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,10697,a)].">
      <j1 rule="hyper" parents="53 10697"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (T(z,R(a(x,y,x),z,u)) * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(206,a,10700,a(flip),b,9216,a(flip))].">
      <j1 rule="hyper" parents="206 10700 9216"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8554(a,1),10701(a,1,1,2,1))].">
      <j1 rule="para" parents="8554 10701"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(532,a,10702,a),flip(a)].">
      <j1 rule="hyper" parents="532 10702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8507,a(flip),b,10703,a),flip(a)].">
      <j1 rule="hyper" parents="35 8507 10703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      ((a(x,y,x) * R(z,u,w)) * (u * w)) / ((z * u) * w) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,528,a,b,10705,a)].">
      <j1 rule="hyper" parents="64 528 10705"/>
    </justification>
  </clause>

  <clause id="10708">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10318,a(flip),b,10705,a)].">
      <j1 rule="hyper" parents="64 10318 10705"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(130,a,10705,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 10705 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(10705(a,1),10700(a,1,3))].">
      <j1 rule="para" parents="10705 10700"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,10712,a)].">
      <j1 rule="hyper" parents="64 302 10712"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(206,a,10712,a(flip),b,8249,a(flip))].">
      <j1 rule="hyper" parents="206 10712 8249"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(10712(a,1),51(a,2))].">
      <j1 rule="para" parents="10712 51"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = ((a(x,y,x) * (z * u)) * w) / (u * w)
    ]]></literal>
    <justification jstring="[para(10712(a,1),485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10712 485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(10712(a,1),8527(a,2,1))].">
      <j1 rule="para" parents="10712 8527"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10052,a,b,10708,a),flip(a)].">
      <j1 rule="hyper" parents="319 10052 10708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      z \ (a(x,y,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(302(a,1),10715(a,1))].">
      <j1 rule="para" parents="302 10715"/>
    </justification>
  </clause>

  <clause id="10724">
    <literal><![CDATA[
      a(x,T(y,x),L(x,z,u)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(9893,a,10720,a),flip(a)].">
      <j1 rule="hyper" parents="9893 10720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      x \ (a(y,z,y) * (u * x)) = T(a(y,z,y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,10709,a),flip(a)].">
      <j1 rule="hyper" parents="417 10709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10726">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (((a(x,y,x) * z) * u) * w) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10709(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10709 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) \ ((a(x,y,x) * z) * (u * w)) = L(w,u,a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(10709(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10709 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(10709(a,1),713(a,1,1,2))].">
      <j1 rule="para" parents="10709 713"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(8507(a,1),10709(a,1,1))].">
      <j1 rule="para" parents="8507 10709"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8507,a(flip),b,10714,a),flip(a)].">
      <j1 rule="hyper" parents="319 8507 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(127,a,156,a(flip),b,10714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 156 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      a(x,x \ (y * x),L(x,z,u)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,1),10724(a,1,2))].">
      <j1 rule="para" parents="22 10724"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,10313,a(flip),b,10729,a),flip(a)].">
      <j1 rule="hyper" parents="319 10313 10729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10736">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[para(8319(a,1),10730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8319 10730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(8393(a,1),10731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8393 10731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,8818,a,b,10733,a)].">
      <j1 rule="hyper" parents="64 8818 10733"/>
    </justification>
  </clause>

  <clause id="10739">
    <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(8520(a,1),10707(a,1,1,1))].">
      <j1 rule="para" parents="8520 10707"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = K(y * x,L(x,w,v5)) * K(L(x,w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9494,a(flip),b,10738,a),flip(a)].">
      <j1 rule="hyper" parents="64 9494 10738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * L(x,y,z)),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10575,a,b,10741,a)].">
      <j1 rule="hyper" parents="319 10575 10741"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      (((x * a(y,x,y)) * z) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(105(a,1),10739(a,1,1))].">
      <j1 rule="para" parents="105 10739"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(10735(a,1),10744(a,1,1,1))].">
      <j1 rule="para" parents="10735 10744"/>
    </justification>
  </clause>

  <clause id="10746">
    <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),10745(a,1,2,1))].">
      <j1 rule="para" parents="10 10745"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(10314(a,1),10746(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10314 10746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,10747,a),flip(a)].">
      <j1 rule="hyper" parents="319 20 10747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),10748(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10705,a(flip),b,10749,a),flip(a)].">
      <j1 rule="hyper" parents="64 10705 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10705,a,b,10750,a)].">
      <j1 rule="hyper" parents="319 10705 10750"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(10750(a,1),8522(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10750 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(10751(a,1),366(a,1)),flip(b)].">
      <j1 rule="para" parents="10751 366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8522,a(flip),b,10752,a),flip(a)].">
      <j1 rule="hyper" parents="319 8522 10752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10756">
    <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(10755(a,1),10623(a,1,2))].">
      <j1 rule="para" parents="10755 10623"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(780(a,1),10756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="780 10756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10759">
    <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(206,a,10757,a(flip),b,4030,a(flip))].">
      <j1 rule="hyper" parents="206 10757 4030"/>
    </justification>
  </clause>

  <clause id="10760">
    <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(64,a,10614,a(flip),b,10759,a)].">
      <j1 rule="hyper" parents="64 10614 10759"/>
    </justification>
  </clause>

  <clause id="10761">
    <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(10546(a,1),10760(a,1,1))].">
      <j1 rule="para" parents="10546 10760"/>
    </justification>
  </clause>

  <clause id="10762">
    <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(64,a,10656,a,b,10761,a),flip(a)].">
      <j1 rule="hyper" parents="64 10656 10761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(183(a,1),10762(a,2,1,2))].">
      <j1 rule="para" parents="183 10762"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      R(K(x * y,x * R(y,z,u)),x * R(y,z,u),w) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(8214,a,10763,a)].">
      <j1 rule="hyper" parents="8214 10763"/>
    </justification>
  </clause>

  <clause id="10765">
    <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),10763(a,1,1))].">
      <j1 rule="para" parents="12 10763"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7343,a(flip),b,10765,a)].">
      <j1 rule="hyper" parents="64 7343 10765"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9325,a(flip),b,10766,a)].">
      <j1 rule="hyper" parents="64 9325 10766"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(4167(a,1),10767(a,2,1))].">
      <j1 rule="para" parents="4167 10767"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      R(a(K(x,y),z * y,u),x * R(y,z,u),w) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(10763(a,1),10764(a,1,1))].">
      <j1 rule="para" parents="10763 10764"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      a(L(x,y,z),T(u,L(x,y,z)),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,2),10742(a,1,2))].">
      <j1 rule="para" parents="22 10742"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) \ (a(x,y,x) * (z * (u * w))) = L(w,u,a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(10709(a,1),10727(a,1,2))].">
      <j1 rule="para" parents="10709 10727"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,u)) = L(x,y,a(u,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(801,a,10772,a)].">
      <j1 rule="hyper" parents="801 10772"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(10715,a,10773,a),flip(a)].">
      <j1 rule="hyper" parents="10715 10773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10777">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8319(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8319 10774"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8327(a,1),10774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8327 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8332(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8332 10774"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8306(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8306 10774"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8507(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8507 10774"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(8685(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8685 10774"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(8681(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8681 10774"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(8708(a,1),10774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8708 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      L(x,y,z * (T(u,z) / z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8711(a,1),10774(a,1,3))].">
      <j1 rule="para" parents="8711 10774"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(3414(a,1),10777(a,1,3))].">
      <j1 rule="para" parents="3414 10777"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(5976(a,1),10777(a,1,3))].">
      <j1 rule="para" parents="5976 10777"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8305(a,1),10776(a,1,3))].">
      <j1 rule="para" parents="8305 10776"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8393(a,1),10776(a,1,3))].">
      <j1 rule="para" parents="8393 10776"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      L(x \ a(y,z,y),x,y) = (L(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,8391,a(flip),b,10790,a),flip(a)].">
      <j1 rule="hyper" parents="64 8391 10790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(3296(a,1),10790(a,1,3))].">
      <j1 rule="para" parents="3296 10790"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4394(a,2),10778(a,1,3))].">
      <j1 rule="para" parents="4394 10778"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      L(x,y,K(z \ 1,((u * z) \ u) * w)) = L(x,y,K((u * z) \ u,w))
    ]]></literal>
    <justification jstring="[para(4995(a,1),10778(a,1,3))].">
      <j1 rule="para" parents="4995 10778"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(6533(a,1),10778(a,2,3))].">
      <j1 rule="para" parents="6533 10778"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      L(x,y,K(z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,3203,a(flip),b,10779,a),flip(a)].">
      <j1 rule="hyper" parents="319 3203 10779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9912,a(flip),b,10779,a),flip(a)].">
      <j1 rule="hyper" parents="64 9912 10779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      L(x,y \ z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),10797(a,1,3,1))].">
      <j1 rule="para" parents="10 10797"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      (K(x * y,x) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(10797(a,1),300(a,1,2))].">
      <j1 rule="para" parents="10797 300"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(4283(a,1),10797(a,1,3))].">
      <j1 rule="para" parents="4283 10797"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4221,a,10799,a)].">
      <j1 rule="hyper" parents="4221 10799"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,10799,a)].">
      <j1 rule="hyper" parents="64 302 10799"/>
    </justification>
  </clause>

  <clause id="10804">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(10799(a,1),4412(a,1,2))].">
      <j1 rule="para" parents="10799 4412"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(10801(a,1),4466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10801 4466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(7973,a,10780,a)].">
      <j1 rule="hyper" parents="7973 10780"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),w,a(v5,v6,v5)) = L(x,y,K(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,10712,a,b,10780,a)].">
      <j1 rule="hyper" parents="319 10712 10780"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(206,a,10807,a(flip),b,8249,a(flip))].">
      <j1 rule="hyper" parents="206 10807 8249"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),10782(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 10782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,z \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),10782(a,2,3))].">
      <j1 rule="para" parents="10 10782"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      L(x,y,T((T(z,z \ u) / u) * u,T(z,z \ u) / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5348(a,2),10782(a,2,3))].">
      <j1 rule="para" parents="5348 10782"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,z * (u / z))
    ]]></literal>
    <justification jstring="[para(231(a,1),10785(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="231 10785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(5057(a,1),10787(a,1,3))].">
      <j1 rule="para" parents="5057 10787"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      L(x,y,T(z,z \ ((u \ w) \ z))) = L(x,y,T(z,w \ (u * z)))
    ]]></literal>
    <justification jstring="[para(5283(a,1),10787(a,2,3))].">
      <j1 rule="para" parents="5283 10787"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(6340(a,2),10788(a,1,3))].">
      <j1 rule="para" parents="6340 10788"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,T(y * z,z))) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(10788(a,1),10527(a,1,2))].">
      <j1 rule="para" parents="10788 10527"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4169(a,1),10789(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4169 10789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(9533,a,10792,a)].">
      <j1 rule="hyper" parents="9533 10792"/>
    </justification>
  </clause>

  <clause id="10820">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10819(a,2,3))].">
      <j1 rule="para" parents="9 10819"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T((x \ y) * x,w)) = L(T((x \ y) * x,z),u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9604,a,b,10810,a)].">
      <j1 rule="hyper" parents="64 9604 10810"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      L(x,y,(z \ T(u * K(z,u),w)) * z) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(4135(a,1),10810(a,2,3))].">
      <j1 rule="para" parents="4135 10810"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      L(x,y,(((z \ u) \ w) \ w) * ((z \ u) \ w)) = L(x,y,T(w,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(5283(a,1),10810(a,2,3))].">
      <j1 rule="para" parents="5283 10810"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      L(x,y,T(z * K(u,w),u)) = L(x,y,(u \ z) * T(u,w))
    ]]></literal>
    <justification jstring="[para(5621(a,1),10810(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5621 10810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(3414(a,1),10783(a,1,3,2))].">
      <j1 rule="para" parents="3414 10783"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(3401(a,1),10784(a,1,3,1))].">
      <j1 rule="para" parents="3401 10784"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(4374,a,10806,a)].">
      <j1 rule="hyper" parents="4374 10806"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (T(x,y) / y) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,3302,a,b,10806,a),flip(a)].">
      <j1 rule="hyper" parents="319 3302 10806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4016(a,1),10820(a,1,3))].">
      <j1 rule="para" parents="4016 10820"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7683,a,10827,a)].">
      <j1 rule="hyper" parents="7683 10827"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10830(a,1,2))].">
      <j1 rule="para" parents="9 10830"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10831(a,1),7959(a,2,2))].">
      <j1 rule="para" parents="10831 7959"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      (x / y) \ (K(x,y) \ z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(599,a,10828,a),flip(a)].">
      <j1 rule="hyper" parents="599 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      (x / y) \ (K(y,x) * z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[para(4356(a,1),10834(a,1,2))].">
      <j1 rule="para" parents="4356 10834"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      (((x \ y) * T(x,y)) / x) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(3338(a,1),10835(a,2,1,1))].">
      <j1 rule="para" parents="3338 10835"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      (L(x,y,x) * z) \ x = (x * z) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8321,a(flip),b,10791,a),flip(a)].">
      <j1 rule="hyper" parents="64 8321 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a,b,10833,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 10833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3764,a(flip),b,10839,a)].">
      <j1 rule="hyper" parents="64 3764 10839"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),10841(a,1,2,1,2))].">
      <j1 rule="para" parents="12 10841"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7221,a,b,10842,a)].">
      <j1 rule="hyper" parents="64 7221 10842"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,10843,a)].">
      <j1 rule="hyper" parents="319 4019 10843"/>
    </justification>
  </clause>

  <clause id="10845">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,10844,a)].">
      <j1 rule="hyper" parents="35 4019 10844"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(9132,a,10845,a),flip(a)].">
      <j1 rule="hyper" parents="9132 10845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(7252,a,10845,a)].">
      <j1 rule="hyper" parents="7252 10845"/>
    </justification>
  </clause>

  <clause id="10848">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) / (y \ x) = T(y,T((z * y) / u,x))
    ]]></literal>
    <justification jstring="[para(10845(a,1),6917(a,1,1,2))].">
      <j1 rule="para" parents="10845 6917"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      K(x,(y / z) \ x) \ T(x,z / y) = R(x,z / y,x)
    ]]></literal>
    <justification jstring="[para(10847(a,2),4461(a,1,1))].">
      <j1 rule="para" parents="10847 4461"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(4314(a,1),10803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4314 10803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(4356(a,1),10850(a,1,2))].">
      <j1 rule="para" parents="4356 10850"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,10782,a(flip),b,10814,a),flip(a)].">
      <j1 rule="hyper" parents="319 10782 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),10816(a,2,3))].">
      <j1 rule="para" parents="23 10816"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(4921(a,1),10825(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4921 10825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(10808(a,1),496(a,1)),flip(b)].">
      <j1 rule="para" parents="10808 496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10818(a,2),10855(a,1))].">
      <j1 rule="para" parents="10818 10855"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      L(x,y,T((z \ (u * K(z,u))) * z,w)) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(3813(a,2),10822(a,1,3))].">
      <j1 rule="para" parents="3813 10822"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      L((x \ y) * x,z,T((x \ y) * T(x,y),u)) = L((x \ y) * x,z,T(y * K(x,y),x))
    ]]></literal>
    <justification jstring="[hyper(319,a,9726,a,b,10824,a)].">
      <j1 rule="hyper" parents="319 9726 10824"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(4921(a,1),10854(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4921 10854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,w)) = L(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4055(a,1),10857(a,1,3,1,1,2))].">
      <j1 rule="para" parents="4055 10857"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      L(x,y,T((z \ u) * T(z,u),w)) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(4200(a,1),10857(a,1,3,1))].">
      <j1 rule="para" parents="4200 10857"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10811,a(flip),b,10860,a),flip(a)].">
      <j1 rule="hyper" parents="64 10811 10860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ z),u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23(a,1),10862(a,1,3))].">
      <j1 rule="para" parents="23 10862"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      L(x,y,T(z,(u \ w) \ 1)) = L(x,y,T(z,w \ (u * z)))
    ]]></literal>
    <justification jstring="[para(3217(a,1),10815(a,1,3))].">
      <j1 rule="para" parents="3217 10815"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      L(x,y,T(z,u \ (w * z))) = L(x,y,T(z,u \ w))
    ]]></literal>
    <justification jstring="[para(5058(a,1),10864(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5058 10864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(7094,a,10848,a),flip(a)].">
      <j1 rule="hyper" parents="7094 10848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7279,a(flip),b,10866,a)].">
      <j1 rule="hyper" parents="64 7279 10866"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      T(x,T((y / z) \ x,u)) = T(x,T(x * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(7850,a,10867,a)].">
      <j1 rule="hyper" parents="7850 10867"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * (x / y),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(10868(a,1),10579(a,1,2))].">
      <j1 rule="para" parents="10868 10579"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      L(x,y,K(z \ 1,((u * z) \ u) * w)) = L(x,y,K(z \ 1,w))
    ]]></literal>
    <justification jstring="[para(4995(a,1),10794(a,2,3))].">
      <j1 rule="para" parents="4995 10794"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      L(x,y,K(z * u,R(z,u,u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(266(a,1),10795(a,1,3,2))].">
      <j1 rule="para" parents="266 10795"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(5585(a,1),10873(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5585 10873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,10779,a(flip),b,10874,a),flip(a)].">
      <j1 rule="hyper" parents="319 10779 10874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      L(x,y,T(z,u \ (w * z))) = L(x,y,(w \ u) * (z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(3157(a,1),10823(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3157 10823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      L(x,y,(z \ u) * (w / (z \ u))) = L(x,y,T(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10865,a(flip),b,10877,a),flip(a)].">
      <j1 rule="hyper" parents="64 10865 10877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(T(y,x),w)) = L(T((x \ y) * x,z),u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10860,a(flip),b,10821,a)].">
      <j1 rule="hyper" parents="64 10860 10821"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = (a(x,y,x) * ((z * u) * w)) / (u * w)
    ]]></literal>
    <justification jstring="[para(10709(a,1),10716(a,2,1))].">
      <j1 rule="para" parents="10709 10716"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * (((z * u) * w) / (u * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,10714,a(flip),b,10880,a),flip(a)].">
      <j1 rule="hyper" parents="319 10714 10880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),10881(a,2,2))].">
      <j1 rule="para" parents="20 10881"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(10712(a,1),10882(a,1,2))].">
      <j1 rule="para" parents="10712 10882"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      T(x \ R(a(y,x \ 1,y) * (a(y,x \ 1,y) \ x),z,u),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(10883(a,2),10643(a,1,1,2))].">
      <j1 rule="para" parents="10883 10643"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10709(a,1),10726(a,1,2,1))].">
      <j1 rule="para" parents="10709 10726"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(4915(a,1),10836(a,1,1))].">
      <j1 rule="para" parents="4915 10836"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(5624(a,2),10886(a,1,1))].">
      <j1 rule="para" parents="5624 10886"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,x * (x \ y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(6024(a,1),10887(a,1,2,1))].">
      <j1 rule="para" parents="6024 10887"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,y) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),10888(a,1,2,1,2))].">
      <j1 rule="para" parents="10 10888"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      L((x \ y) * x,z,T((x \ y) * T(x,y),u)) = L((x \ y) * x,z,y)
    ]]></literal>
    <justification jstring="[para(4130(a,1),10858(a,2,3))].">
      <j1 rule="para" parents="4130 10858"/>
    </justification>
  </clause>

  <clause id="10892">
    <literal><![CDATA[
      L((x \ y) * x,z,T(y,u)) = L((x \ y) * x,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10861,a(flip),b,10891,a)].">
      <j1 rule="hyper" parents="64 10861 10891"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(y,w)) = T(L((x \ y) * x,u,y),z)
    ]]></literal>
    <justification jstring="[para(10892(a,1),25(a,2,1))].">
      <j1 rule="para" parents="10892 25"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(y,w)) = L(T((x \ y) * x,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,10894,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 10894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(T(y,x),w)) = L(T((x \ y) * x,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10879,a,b,10895,a)].">
      <j1 rule="hyper" parents="64 10879 10895"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (a(x,y,x) * ((z * u) * w)) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10709(a,1),10885(a,1,2))].">
      <j1 rule="para" parents="10709 10885"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(802,a,10898,a)].">
      <j1 rule="hyper" parents="802 10898"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(10715,a,10899,a),flip(a)].">
      <j1 rule="hyper" parents="10715 10899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      a(K(x * y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8332(a,1),10900(a,1,1))].">
      <j1 rule="para" parents="8332 10900"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8306(a,1),10900(a,1,1))].">
      <j1 rule="para" parents="8306 10900"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(8507(a,1),10900(a,1,1))].">
      <j1 rule="para" parents="8507 10900"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(8685(a,1),10900(a,1,1))].">
      <j1 rule="para" parents="8685 10900"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(8704(a,1),10900(a,1,1))].">
      <j1 rule="para" parents="8704 10900"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8305(a,1),10902(a,1,1))].">
      <j1 rule="para" parents="8305 10902"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(8344(a,1),10902(a,1,1))].">
      <j1 rule="para" parents="8344 10902"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8393(a,1),10902(a,1,1))].">
      <j1 rule="para" parents="8393 10902"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3296(a,1),10910(a,1,1))].">
      <j1 rule="para" parents="3296 10910"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(7628(a,1),10910(a,1,1))].">
      <j1 rule="para" parents="7628 10910"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10361(a,1),10910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10361 10910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8335(a,1),10905(a,1,1))].">
      <j1 rule="para" parents="8335 10905"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(8705(a,1),10905(a,1,1))].">
      <j1 rule="para" parents="8705 10905"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10768,a,b,10908,a)].">
      <j1 rule="hyper" parents="64 10768 10908"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(4169(a,1),10908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4169 10908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(3651,a,10915,a)].">
      <j1 rule="hyper" parents="3651 10915"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(3414(a,1),10907(a,1,1,1))].">
      <j1 rule="para" parents="3414 10907"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      a(((x * ((x / y) / x)) \ T(x,y \ 1)) \ T(x,y \ 1),z,u) = a(T(x * ((x / y) / x),y),z,u)
    ]]></literal>
    <justification jstring="[para(3048(a,1),10912(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3048 10912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,10904,a(flip),b,10917,a),flip(a)].">
      <j1 rule="hyper" parents="319 10904 10917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4351(a,1),10921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4351 10921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10909,a,b,10922,a)].">
      <j1 rule="hyper" parents="64 10909 10922"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(2920(a,1),10923(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2920 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(y,x * z,u) \ 1,x),w,v5)
    ]]></literal>
    <justification jstring="[para(9176(a,2),10923(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9176 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10545,a,b,10924,a)].">
      <j1 rule="hyper" parents="64 10545 10924"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,y \ R(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8668,a,b,10916,a)].">
      <j1 rule="hyper" parents="64 8668 10916"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(y \ 1,R(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(5586(a,1),10925(a,2,1))].">
      <j1 rule="para" parents="5586 10925"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(x,z,u),y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,10923,a(flip),b,10928,a),flip(a)].">
      <j1 rule="hyper" parents="319 10923 10928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(R(x,z,u),y),w,v5)
    ]]></literal>
    <justification jstring="[para(9176(a,1),10929(a,1,1))].">
      <j1 rule="para" parents="9176 10929"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),T(z,z \ u) / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10812(a,1,3,1))].">
      <j1 rule="para" parents="12 10812"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),u \ T(z,z \ u))) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(3116(a,1),10931(a,1,3))].">
      <j1 rule="para" parents="3116 10931"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),z / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(7558(a,1),10933(a,1,3))].">
      <j1 rule="para" parents="7558 10933"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),u \ z)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5737(a,1),10934(a,1,3))].">
      <j1 rule="para" parents="5737 10934"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      L(x,y,(z \ u) \ T(u,u \ z)) = L(x,y,T(T(z,u \ z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10816,a(flip),b,10935,a),flip(a)].">
      <j1 rule="hyper" parents="64 10816 10935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10937">
    <literal><![CDATA[
      L(x,y,(z \ u) \ T(u,u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,10863,a(flip),b,10936,a),flip(a)].">
      <j1 rule="hyper" parents="319 10863 10936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10939">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,x) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10525,a(flip),b,10937,a),flip(a)].">
      <j1 rule="hyper" parents="64 10525 10937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      (((x \ y) \ 1) * y) \ (x * (y / x)) = (((y / x) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(9233,a,10939,a),flip(a)].">
      <j1 rule="hyper" parents="9233 10939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      (K(x,T(x,x * y) * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4790,a(flip),b,10798,a),flip(a)].">
      <j1 rule="hyper" parents="64 4790 10798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(5846(a,1),10943(a,1,1,1))].">
      <j1 rule="para" parents="5846 10943"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(3131(a,1),10944(a,1,2,1))].">
      <j1 rule="para" parents="3131 10944"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = K(y / z,x) * T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[para(6297(a,1),10869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6297 10869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = L(x,y / z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4295,a(flip),b,10947,a),flip(a)].">
      <j1 rule="hyper" parents="319 4295 10947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10358,a(flip),b,10948,a),flip(a)].">
      <j1 rule="hyper" parents="64 10358 10948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      L(x,(y \ z) \ z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(78(a,1),10949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 10949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,(y * (z * u)) \ ((y * z) * u),x)
    ]]></literal>
    <justification jstring="[para(2972(a,2),10949(a,1,2))].">
      <j1 rule="para" parents="2972 10949"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(4189(a,2),10949(a,1,2))].">
      <j1 rule="para" parents="4189 10949"/>
    </justification>
  </clause>

  <clause id="10954">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(3288(a,2),10951(a,1,2))].">
      <j1 rule="para" parents="3288 10951"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      L(x,T(y,z),x) = T(x,T(x * y,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,8718,a,b,10954,a),flip(a)].">
      <j1 rule="hyper" parents="319 8718 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      L(x,T(y,z),x) = x / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8387,a,b,10954,a),flip(a)].">
      <j1 rule="hyper" parents="319 8387 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(4136(a,1),10954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4136 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,8387,a,b,10956,a(flip))].">
      <j1 rule="hyper" parents="37 8387 10956"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10956(a,2),8390(a,1))].">
      <j1 rule="para" parents="10956 8390"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      a(x,T(y,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a,b,10958,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 10958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,10771,a(flip),b,10958,a),flip(a)].">
      <j1 rule="hyper" parents="64 10771 10958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),10958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 10958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10964">
    <literal><![CDATA[
      a(x,R(y / z,u,w),x) = a(x,R(z \ y,u,w),x)
    ]]></literal>
    <justification jstring="[para(252(a,1),10958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="252 10958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      a(x,R(y / z,z,u),x) = a(x,(z * u) \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(543(a,1),10958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="543 10958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4130(a,1),10958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4130 10958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      a(1 / ((x * y) \ x),z,1 / ((x * y) \ x)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(10958(a,1),8346(a,1,1))].">
      <j1 rule="para" parents="10958 8346"/>
    </justification>
  </clause>

  <clause id="10968">
    <literal><![CDATA[
      R(x,T(y,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8320,a,10960,a)].">
      <j1 rule="hyper" parents="8320 10960"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      a(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10960(a,2),8325(a,1))].">
      <j1 rule="para" parents="10960 8325"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      R(x,y / z,x) = R(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),10968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 10968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      R(x,y \ (y \ (T(y,z) * u)),x) = R(x,y \ ((y \ u) * T(y,z)),x)
    ]]></literal>
    <justification jstring="[para(7897(a,1),10968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7897 10968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      K(x,(y / z) \ x) \ T(x,z / y) = R(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10849,a,b,10972,a)].">
      <j1 rule="hyper" parents="64 10849 10972"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10720,a(flip),b,10962,a),flip(a)].">
      <j1 rule="hyper" parents="319 10720 10962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10708,a(flip),b,10962,a),flip(a)].">
      <j1 rule="hyper" parents="319 10708 10962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10261,a(flip),b,10979,a)].">
      <j1 rule="hyper" parents="64 10261 10979"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,x) \ u = (L(x,y,z) \ u) * T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10979(a,1),8539(a,1,1))].">
      <j1 rule="para" parents="10979 8539"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y * K(w,y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10966,a,b,10981,a),flip(a)].">
      <j1 rule="hyper" parents="319 10966 10981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,10981,a(flip),b,3631,a)].">
      <j1 rule="hyper" parents="131 10981 3631"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(130,a,10981,a(flip),b,8553,a)].">
      <j1 rule="hyper" parents="130 10981 8553"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(10981(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="10981 481"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      a(x,y * K(z,y),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10984(a,1),496(a,1)),flip(b)].">
      <j1 rule="para" parents="10984 496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10993">
    <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(4625(a,1),10984(a,2,2))].">
      <j1 rule="para" parents="4625 10984"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      L(a(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(10984(a,2),8349(a,1))].">
      <j1 rule="para" parents="10984 8349"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      a(x,y / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(4097(a,1),10992(a,1,2))].">
      <j1 rule="para" parents="4097 10992"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(529,a,10987,a)].">
      <j1 rule="hyper" parents="529 10987"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / ((y * z) * a(u,w,u)) = R(R(x,y,z),y * z,a(u,w,u))
    ]]></literal>
    <justification jstring="[para(10987(a,1),527(a,1,1))].">
      <j1 rule="para" parents="10987 527"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(8808,a,10996,a)].">
      <j1 rule="hyper" parents="8808 10996"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = a(z,u,z) * y
    ]]></literal>
    <justification jstring="[hyper(331,a,10988,a),flip(a)].">
      <j1 rule="hyper" parents="331 10988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(8507(a,2),10988(a,2,2))].">
      <j1 rule="para" parents="8507 10988"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(10988(a,1),10713(a,1,1))].">
      <j1 rule="para" parents="10988 10713"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(8341(a,1),10990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8341 10990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(10987(a,1),10990(a,1,2))].">
      <j1 rule="para" parents="10987 10990"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(244,a,10729,a,b,11002,a),flip(a)].">
      <j1 rule="hyper" parents="244 10729 11002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = a(y,z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(600,a,11004,a)].">
      <j1 rule="hyper" parents="600 11004"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,11004,a)].">
      <j1 rule="hyper" parents="127 153 11004"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10729,a,b,11004,a)].">
      <j1 rule="hyper" parents="64 10729 11004"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      a(x,y,x) * (z \ (u * z)) = T(a(x,y,x) * u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10725,a(flip),b,11010,a),flip(a)].">
      <j1 rule="hyper" parents="64 10725 11010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      a(x,y,x) * (z \ x) = z \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8319(a,1),11010(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8319 11010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      L(x,a(y,z,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,11012,a)].">
      <j1 rule="hyper" parents="488 11012"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(127,a,74,a(flip),b,11012,a)].">
      <j1 rule="hyper" parents="127 74 11012"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ (((x * a(y,z,y)) * u) * w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(11012(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11012 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      (x / a(y,z,y)) * u = x * (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(131,a,11017,a(flip),b,9548,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 11017 9548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ ((x * a(z,u,z)) * (y * w)) = L(w,L(y,a(z,u,z),x),x * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(11017(a,1),8528(a,1,2,2,1))].">
      <j1 rule="para" parents="11017 8528"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(8507(a,2),11018(a,1,1))].">
      <j1 rule="para" parents="8507 11018"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(8511(a,1),11020(a,1,1))].">
      <j1 rule="para" parents="8511 11020"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      ((x * y) * (a(z,u,z) \ w)) / ((y * (a(z,u,z) \ 1)) * w) = R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(11020(a,1),8689(a,1,1))].">
      <j1 rule="para" parents="11020 8689"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(10721,a,11022,a),flip(a)].">
      <j1 rule="hyper" parents="10721 11022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      ((a(x,y,x) * z) \ u) * a(x,y,x) = z \ u
    ]]></literal>
    <justification jstring="[hyper(130,a,11022,a,b,8511,a)].">
      <j1 rule="hyper" parents="130 11022 8511"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      x \ ((a(y,z,y) \ x) * u) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(571,a,11023,a)].">
      <j1 rule="hyper" parents="571 11023"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8393(a,1),11025(a,2,2))].">
      <j1 rule="para" parents="8393 11025"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x * u)) = z \ (L(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(8523(a,1),11025(a,2,2))].">
      <j1 rule="para" parents="8523 11025"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(11025(a,1),8525(a,1,1))].">
      <j1 rule="para" parents="11025 8525"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      (x \ L(y,z,y)) / L(y,z,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,11028,a(flip),b,8536,a)].">
      <j1 rule="hyper" parents="128 11028 8536"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),11026(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,z,y)) * u) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[para(11028(a,1),11027(a,1,2,1))].">
      <j1 rule="para" parents="11028 11027"/>
    </justification>
  </clause>

  <clause id="11034">
    <literal><![CDATA[
      L(x,y,x) \ (z \ L(x,y,x)) = T((z \ x) / x,x)
    ]]></literal>
    <justification jstring="[para(11031(a,1),5701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11031 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(206,a,202,a(flip),b,11032,a)].">
      <j1 rule="hyper" parents="206 202 11032"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8312(a,1),11035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8312 11035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(11035(a,2),10776(a,1,3))].">
      <j1 rule="para" parents="11035 10776"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(11036(a,1),10776(a,1,3))].">
      <j1 rule="para" parents="11036 10776"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      a(x / R(y,z,y),u,w) = a(x / y,u,w)
    ]]></literal>
    <justification jstring="[para(11036(a,1),10902(a,1,1))].">
      <j1 rule="para" parents="11036 10902"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(4902(a,1),11039(a,1,3))].">
      <j1 rule="para" parents="4902 11039"/>
    </justification>
  </clause>

  <clause id="11042">
    <literal><![CDATA[
      a(K(x,y) * (x \ y),z,u) = a(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(4902(a,1),11040(a,1,1))].">
      <j1 rule="para" parents="4902 11040"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      ((K(x,y) * (x \ y)) * z) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a(flip),b,11041,a)].">
      <j1 rule="hyper" parents="64 18 11041"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      L(x,y,((z * u) / z) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(4293(a,2),11041(a,1,3))].">
      <j1 rule="para" parents="4293 11041"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(232(a,1),11044(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="232 11044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(x,y,z) * a(x,u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(131,a,10978,a(flip),b,8309,a),flip(a)].">
      <j1 rule="hyper" parents="131 10978 8309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(10715,a,10998,a),flip(a)].">
      <j1 rule="hyper" parents="10715 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(10998(a,1),10715(a,1))].">
      <j1 rule="para" parents="10998 10715"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,11047,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 11047 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      T(x,(y * z) * y) = T(x,y * (z * y))
    ]]></literal>
    <justification jstring="[para(85(a,1),11047(a,1,2))].">
      <j1 rule="para" parents="85 11047"/>
    </justification>
  </clause>

  <clause id="11052">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8335(a,1),11047(a,1,2))].">
      <j1 rule="para" parents="8335 11047"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8389(a,1),11047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8389 11047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(8507(a,2),11047(a,1,2))].">
      <j1 rule="para" parents="8507 11047"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(8512(a,1),11047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8512 11047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10987(a,1),11047(a,1,2))].">
      <j1 rule="para" parents="10987 11047"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = u / T(u,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,11055,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 11055 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(9349(a,1),11055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9349 11055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(11015(a,1),11055(a,1,2))].">
      <j1 rule="para" parents="11015 11055"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(11036(a,1),11056(a,1,2))].">
      <j1 rule="para" parents="11036 11056"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3266(a,1),11052(a,1,2))].">
      <j1 rule="para" parents="3266 11052"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(23(a,1),11064(a,1,2,2))].">
      <j1 rule="para" parents="23 11064"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      T(x,((y * y) * z) / T(u,(y * y) * z)) = T(x,((y * y) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(638(a,2),11064(a,2,2))].">
      <j1 rule="para" parents="638 11064"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (u / T(z,u))) = T(x,(u / T(z,u)) * y)
    ]]></literal>
    <justification jstring="[para(11064(a,1),9307(a,1,2,1))].">
      <j1 rule="para" parents="11064 9307"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,11050,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 11050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(11050(a,2),4106(a,1))].">
      <j1 rule="para" parents="11050 4106"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8335(a,1),11068(a,1,2))].">
      <j1 rule="para" parents="8335 11068"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8389(a,1),11068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8389 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      K(x,L(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(8396(a,1),11068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8396 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8507(a,2),11068(a,1,2))].">
      <j1 rule="para" parents="8507 11068"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8512(a,1),11068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8512 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(8690(a,1),11068(a,1,2))].">
      <j1 rule="para" parents="8690 11068"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(10730(a,2),11068(a,1,2))].">
      <j1 rule="para" parents="10730 11068"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10987(a,1),11068(a,1,2))].">
      <j1 rule="para" parents="10987 11068"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(11026(a,1),11068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11026 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      K(x,R(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(8708(a,1),11073(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8708 11073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(9349(a,1),11073(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9349 11073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(11010(a,2),11073(a,1,2))].">
      <j1 rule="para" parents="11010 11073"/>
    </justification>
  </clause>

  <clause id="11083">
    <literal><![CDATA[
      K(x,L(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(10737(a,1),11074(a,1,2))].">
      <j1 rule="para" parents="10737 11074"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11011(a,1),11074(a,1,2))].">
      <j1 rule="para" parents="11011 11074"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(11025(a,1),11074(a,1,2))].">
      <j1 rule="para" parents="11025 11074"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / z) = K(x,z \ L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),11070(a,1,2,1))].">
      <j1 rule="para" parents="25 11070"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      K(x,(y \ z) / y) = K(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[para(111(a,1),11070(a,1,2,1))].">
      <j1 rule="para" parents="111 11070"/>
    </justification>
  </clause>

  <clause id="11088">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3266(a,1),11070(a,1,2))].">
      <j1 rule="para" parents="3266 11070"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),y * (T(u,z) / z)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[para(11070(a,1),9259(a,1,1,2))].">
      <j1 rule="para" parents="11070 9259"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,5699,a,b,11088,a),flip(a)].">
      <j1 rule="hyper" parents="319 5699 11088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      T(x,y * T(z,z * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3295(a,1),11053(a,1,2,2))].">
      <j1 rule="para" parents="3295 11053"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,11059,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 11059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(11059(a,2),4117(a,1))].">
      <j1 rule="para" parents="11059 4117"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      K(a(x,y,x) \ z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8507(a,1),11092(a,1,1))].">
      <j1 rule="para" parents="8507 11092"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(8521(a,1),11092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8521 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(9349(a,1),11092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9349 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(11010(a,2),11092(a,1,1))].">
      <j1 rule="para" parents="11010 11092"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      K(x \ R(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(11015(a,1),11092(a,1,1))].">
      <j1 rule="para" parents="11015 11092"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(11028(a,1),11094(a,1,1))].">
      <j1 rule="para" parents="11028 11094"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(11032(a,2),11095(a,1,1))].">
      <j1 rule="para" parents="11032 11095"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(3414(a,1),11061(a,1,2,2))].">
      <j1 rule="para" parents="3414 11061"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5913(a,1),11061(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5913 11061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5976(a,1),11061(a,1,2,2))].">
      <j1 rule="para" parents="5976 11061"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      T(x,y / T(z,z \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(3414(a,1),11063(a,1,2,2))].">
      <j1 rule="para" parents="3414 11063"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5976(a,1),11063(a,1,2,2))].">
      <j1 rule="para" parents="5976 11063"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      K(x,y * T(z / u,z)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(3296(a,1),11071(a,1,2,2))].">
      <j1 rule="para" parents="3296 11071"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(10361(a,1),11071(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10361 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3295(a,1),11072(a,1,2,1))].">
      <j1 rule="para" parents="3295 11072"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(3296(a,1),11072(a,1,2,1))].">
      <j1 rule="para" parents="3296 11072"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10361(a,1),11072(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10361 11072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3414(a,1),11076(a,1,2,1))].">
      <j1 rule="para" parents="3414 11076"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3414(a,1),11080(a,1,2,1))].">
      <j1 rule="para" parents="3414 11080"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5976(a,1),11080(a,1,2,1))].">
      <j1 rule="para" parents="5976 11080"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(3296(a,1),11083(a,1,2,1))].">
      <j1 rule="para" parents="3296 11083"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(10361(a,1),11083(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10361 11083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5913(a,1),11101(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5913 11101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(3296(a,1),11102(a,1,1,2))].">
      <j1 rule="para" parents="3296 11102"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      T(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8335(a,1),11048(a,1,2))].">
      <j1 rule="para" parents="8335 11048"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      T(x,(y / z) * ((z * K(z \ y,z)) * (y / z))) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(5242(a,1),11051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5242 11051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2371(a,1),11069(a,1,2,2))].">
      <j1 rule="para" parents="2371 11069"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8335(a,1),11069(a,1,2))].">
      <j1 rule="para" parents="8335 11069"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(10736(a,1),11069(a,1,2))].">
      <j1 rule="para" parents="10736 11069"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      T(T(x,K(y,z \ (u / z))),y / ((z \ u) / z)) = T(x,((z \ u) / z) \ y)
    ]]></literal>
    <justification jstring="[para(11087(a,1),7110(a,1,1,2))].">
      <j1 rule="para" parents="11087 7110"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(11090(a,2),6354(a,1))].">
      <j1 rule="para" parents="11090 6354"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(8507(a,1),11093(a,1,1))].">
      <j1 rule="para" parents="8507 11093"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      K(T(x,y) / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8335(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="8335 11131"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(8335(a,1),11057(a,1,2,2))].">
      <j1 rule="para" parents="8335 11057"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(8685(a,1),11077(a,1,2,1))].">
      <j1 rule="para" parents="8685 11077"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      K(x,y * ((z * u) * z)) = K(x,y * (z * (u * z)))
    ]]></literal>
    <justification jstring="[para(85(a,1),11078(a,1,2,2))].">
      <j1 rule="para" parents="85 11078"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8328(a,1),11078(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8328 11078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(8335(a,1),11078(a,1,2,2))].">
      <j1 rule="para" parents="8335 11078"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8341(a,1),11078(a,1,2,2))].">
      <j1 rule="para" parents="8341 11078"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(8389(a,1),11078(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8389 11078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      K(x,y * (R(z,u,z) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(8690(a,1),11078(a,1,2,2))].">
      <j1 rule="para" parents="8690 11078"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(10987(a,1),11078(a,1,2,2))].">
      <j1 rule="para" parents="10987 11078"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(8332(a,1),11079(a,1,2,1))].">
      <j1 rule="para" parents="8332 11079"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8343(a,1),11079(a,1,2,1))].">
      <j1 rule="para" parents="8343 11079"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(8521(a,1),11079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8521 11079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(9349(a,1),11079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9349 11079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(10988(a,1),11079(a,1,2,1))].">
      <j1 rule="para" parents="10988 11079"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      K(x,(y \ R(z,u,z)) \ w) = K(x,(y \ z) \ w)
    ]]></literal>
    <justification jstring="[para(11015(a,1),11079(a,1,2,1))].">
      <j1 rule="para" parents="11015 11079"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      K(x,y \ (L(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(8521(a,1),11082(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8521 11082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(8685(a,1),11082(a,1,2,2))].">
      <j1 rule="para" parents="8685 11082"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(8681(a,1),11082(a,1,2,2))].">
      <j1 rule="para" parents="8681 11082"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      K(x,y * K(z \ u,z)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8305(a,1),11084(a,1,2,2))].">
      <j1 rule="para" parents="8305 11084"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(11023(a,2),11084(a,1,2))].">
      <j1 rule="para" parents="11023 11084"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(11028(a,1),11084(a,1,2,2))].">
      <j1 rule="para" parents="11028 11084"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      K(x,y \ K(z \ u,z)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(8305(a,1),11085(a,1,2,2))].">
      <j1 rule="para" parents="8305 11085"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(8344(a,1),11085(a,1,2,2))].">
      <j1 rule="para" parents="8344 11085"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8306(a,1),11100(a,1,1,2))].">
      <j1 rule="para" parents="8306 11100"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(8685(a,1),11100(a,1,1,2))].">
      <j1 rule="para" parents="8685 11100"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      K(K(x * y,x) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(8333(a,1),11105(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8333 11105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(8523(a,1),11105(a,1,1,1))].">
      <j1 rule="para" parents="8523 11105"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3266(a,1),11124(a,1,2))].">
      <j1 rule="para" parents="3266 11124"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2362(a,1),11126(a,1,2))].">
      <j1 rule="para" parents="2362 11126"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(11132,a,7197,a),flip(a)].">
      <j1 rule="hyper" parents="11132 7197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(11163(a,1),7920(a,2,2))].">
      <j1 rule="para" parents="11163 7920"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8305(a,1),11153(a,1,2,1))].">
      <j1 rule="para" parents="8305 11153"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(8523(a,1),11153(a,1,2,1))].">
      <j1 rule="para" parents="8523 11153"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (y / T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(11064(a,1),11161(a,1,2,2))].">
      <j1 rule="para" parents="11064 11161"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ u,w)) = K(x,w) * T(x * K(w,x),(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(131,a,11060,a(flip),b,7604,a),flip(a)].">
      <j1 rule="hyper" parents="131 11060 7604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11060(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11081(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) * K(y,(T(u * z,u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(11081(a,1),7295(a,1,1,2))].">
      <j1 rule="para" parents="11081 7295"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,11091,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 11091 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11099(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) * a(w,v5,K((z * y) \ u,x)) = K(x,L(T(y * z,y) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(11099(a,1),10106(a,1,2,3))].">
      <j1 rule="para" parents="11099 10106"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,5815,a(flip),b,11106,a),flip(a)].">
      <j1 rule="hyper" parents="319 5815 11106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7558,a(flip),b,11106,a),flip(a)].">
      <j1 rule="hyper" parents="64 7558 11106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),z / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,11178,a(flip),b,7604,a),flip(a)].">
      <j1 rule="hyper" parents="131 11178 7604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      T(x,(y * y) * (z \ T(u,z / (y * y)))) = T(x,u / (z / (y * y)))
    ]]></literal>
    <justification jstring="[para(414(a,1),11178(a,1,2))].">
      <j1 rule="para" parents="414 11178"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      T(x,y \ ((z * z) * T(u,(z * z) \ y))) = T(x,u / ((z * z) \ y))
    ]]></literal>
    <justification jstring="[para(638(a,1),11178(a,1,2))].">
      <j1 rule="para" parents="638 11178"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(3270(a,2),11178(a,1,2))].">
      <j1 rule="para" parents="3270 11178"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((z \ T(y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(11178(a,1),3627(a,1,1))].">
      <j1 rule="para" parents="11178 3627"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      K(x,T(y,z / u) * (u \ T(z,u))) = K(x,(u \ T(z,u)) * y)
    ]]></literal>
    <justification jstring="[para(11178(a,1),9306(a,1,2,1))].">
      <j1 rule="para" parents="11178 9306"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(318(a,1),11177(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="318 11177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = K(x,w) * T(x * K(w,x),y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,11107,a(flip),b,7604,a),flip(a)].">
      <j1 rule="hyper" parents="131 11107 7604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,672,a(flip),b,11108,a),flip(a)].">
      <j1 rule="hyper" parents="64 672 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) = T(x,y \ T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(6337(a,2),11108(a,1,2,2))].">
      <j1 rule="para" parents="6337 11108"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      T(x,y / T(z * K(u,z \ w),w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[para(5171(a,1),11110(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5171 11110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(6325(a,2),11110(a,1,2,2))].">
      <j1 rule="para" parents="6325 11110"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      T(x,y / (((z * K(u,w / z)) \ (z \ w)) \ (z \ w))) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[para(7098(a,1),11110(a,2,2,2))].">
      <j1 rule="para" parents="7098 11110"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,4359,a,b,11112,a),flip(a)].">
      <j1 rule="hyper" parents="319 4359 11112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3288(a,2),11112(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3288 11112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(10156,a,11113,a)].">
      <j1 rule="hyper" parents="10156 11113"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),y * K(z,z \ u)) * w) = K(x,T(y / ((z \ u) * z),u) * w)
    ]]></literal>
    <justification jstring="[para(8219(a,1),11113(a,1,2,1,2))].">
      <j1 rule="para" parents="8219 11113"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a(flip),b,11115,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 11115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      T(x,T(y,y \ z) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,11118,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11118 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(318(a,1),11118(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="318 11118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      K(x,T(y,y \ x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(11118(a,2),5869(a,1))].">
      <j1 rule="para" parents="11118 5869"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(10156,a,11119,a)].">
      <j1 rule="hyper" parents="10156 11119"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11118,a,b,11119,a)].">
      <j1 rule="hyper" parents="319 11118 11119"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a,b,11119,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 11119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(8544(a,1),11119(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8544 11119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      L(K(x,T(y,z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(11119(a,1),10202(a,1,1))].">
      <j1 rule="para" parents="11119 10202"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(129,a,11121,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11121 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(5110(a,2),11121(a,1,2,1))].">
      <j1 rule="para" parents="5110 11121"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      K(R(x / y,y,x \ T(z,z * u)) \ T(z,u),w) = K(y * (x \ T(z,z * u)),w)
    ]]></literal>
    <justification jstring="[para(517(a,1),11122(a,1,1)),flip(a)].">
      <j1 rule="para" parents="517 11122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = x * K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,11133,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 11133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      T(x,y * (z / T(u,z))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(3266(a,1),11133(a,1,2,2))].">
      <j1 rule="para" parents="3266 11133"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11135(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,y) / w) = K(x,(u * L(y,z,y)) / w)
    ]]></literal>
    <justification jstring="[para(5696(a,1),11135(a,1,2,1))].">
      <j1 rule="para" parents="5696 11135"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(3266(a,1),11138(a,1,2,2))].">
      <j1 rule="para" parents="3266 11138"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),(z * (u \ w)) \ z)) = K(x,y * K((u * (1 / z)) \ w,z))
    ]]></literal>
    <justification jstring="[para(9634(a,2),11139(a,2,2,2))].">
      <j1 rule="para" parents="9634 11139"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11143(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11144(a,1,2,1,1))].">
      <j1 rule="para" parents="10 11144"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11150(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(y,z \ y),u)
    ]]></literal>
    <justification jstring="[para(4243(a,1),11157(a,1,1,2))].">
      <j1 rule="para" parents="4243 11157"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = K(K(y,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(5930(a,1),11159(a,2,1,1))].">
      <j1 rule="para" parents="5930 11159"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(11165(a,1),8721(a,1,1,2))].">
      <j1 rule="para" parents="11165 8721"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a(flip),b,11166,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 11166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,11166,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11166 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(4510(a,1),11166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4510 11166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5057,a(flip),b,11171,a),flip(a)].">
      <j1 rule="hyper" parents="64 5057 11171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7560,a,11172,a),flip(a)].">
      <j1 rule="hyper" parents="7560 11172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(11172(a,1),7560(a,1))].">
      <j1 rule="para" parents="11172 7560"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,T(y,x) \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[para(11172(a,1),9242(a,1,2))].">
      <j1 rule="para" parents="11172 9242"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(3270(a,1),11224(a,1,2))].">
      <j1 rule="para" parents="3270 11224"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(11227(a,1),10096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11227 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(3270(a,1),11225(a,1,2))].">
      <j1 rule="para" parents="3270 11225"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      K(x,((y \ z) \ 1) \ T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ z) \ 1)) = w
    ]]></literal>
    <justification jstring="[para(5058(a,1),11229(a,1,2,2))].">
      <j1 rule="para" parents="5058 11229"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y \ z,z)) = w
    ]]></literal>
    <justification jstring="[para(6946(a,1),11229(a,1,2,2))].">
      <j1 rule="para" parents="6946 11229"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (T(y,z) \ z)) = w
    ]]></literal>
    <justification jstring="[para(11182(a,1),11229(a,1,2,2))].">
      <j1 rule="para" parents="11182 11229"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(11198(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11198 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / w) * (((z \ u) \ u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(((z \ u) \ u) / w) * y) = v5
    ]]></literal>
    <justification jstring="[para(11205(a,1),9330(a,1,2,1))].">
      <j1 rule="para" parents="11205 9330"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      K(x,y * (z / L(T(u,z),w,v5))) = K(x,y * (L(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[para(25(a,2),11212(a,1,2,2,2))].">
      <j1 rule="para" parents="25 11212"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / z) \ u)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4671(a,1),11214(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4671 11214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(206,a,11221,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 11221 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11238">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11221(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11239">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(u \ z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u \ z,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(11221(a,1),11225(a,1,2,1))].">
      <j1 rule="para" parents="11221 11225"/>
    </justification>
  </clause>

  <clause id="11240">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(206,a,11238,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 11238 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(8705(a,1),11038(a,1,3,2))].">
      <j1 rule="para" parents="8705 11038"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      K(x,y * (z * L(T(u,w),v5,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(9604(a,1),11140(a,1,2,2,2))].">
      <j1 rule="para" parents="9604 11140"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(5976(a,1),11141(a,1,2,2,1))].">
      <j1 rule="para" parents="5976 11141"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(3296(a,1),11149(a,1,2,2,1))].">
      <j1 rule="para" parents="3296 11149"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10361(a,1),11149(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10361 11149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5976(a,1),11151(a,1,2,2,2))].">
      <j1 rule="para" parents="5976 11151"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(3295(a,1),11154(a,1,2,2,2))].">
      <j1 rule="para" parents="3295 11154"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(3296(a,1),11154(a,1,2,2,2))].">
      <j1 rule="para" parents="3296 11154"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(11160(a,1),9462(a,1,1))].">
      <j1 rule="para" parents="11160 9462"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2312(a,1),11162(a,1,2,1))].">
      <j1 rule="para" parents="2312 11162"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = a(x,y,x) * T(z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),11014(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = a(y,z,y) * T(x,u)
    ]]></literal>
    <justification jstring="[para(8507(a,1),11252(a,1,1))].">
      <j1 rule="para" parents="8507 11252"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(762,a,11254,a)].">
      <j1 rule="hyper" parents="762 11254"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(8512(a,1),11255(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8512 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * v5))) = K(x,y * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(11029(a,1),11084(a,1,2,2))].">
      <j1 rule="para" parents="11029 11084"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      (a(x,y,x) \ z) * L(((u \ x) \ ((u \ L(x,y,x)) * z)) \ ((u \ L(x,y,x)) * z),w,v5) = L(u \ x,w,v5) * ((u \ x) \ ((u \ L(x,y,x)) * z))
    ]]></literal>
    <justification jstring="[para(11033(a,1),652(a,1,1))].">
      <j1 rule="para" parents="11033 652"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      L(x,y,x) \ (z \ L(x,y,x)) = x \ (z \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,11034,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 11034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,9247,a,b,11259,a),flip(a)].">
      <j1 rule="hyper" parents="39 9247 11259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ ((x * (z * y)) / x),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(3851(a,1),11260(a,1,1))].">
      <j1 rule="para" parents="3851 11260"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,(z \ 1) \ L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[para(3426(a,1),11086(a,1,2,1,1))].">
      <j1 rule="para" parents="3426 11086"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11174(a,2),4106(a,1))].">
      <j1 rule="para" parents="11174 4106"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(11196(a,2),4106(a,1))].">
      <j1 rule="para" parents="11196 4106"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(11208(a,2),4089(a,1))].">
      <j1 rule="para" parents="11208 4089"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(11220(a,2),4106(a,1))].">
      <j1 rule="para" parents="11220 4106"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = K(x,L(z / y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,10096,a(flip),b,11228,a),flip(a)].">
      <j1 rule="hyper" parents="319 10096 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(11237(a,2),4117(a,1))].">
      <j1 rule="para" parents="11237 4117"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(11240(a,2),4117(a,1))].">
      <j1 rule="para" parents="11240 4117"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11045,a(flip),b,11241,a)].">
      <j1 rule="hyper" parents="64 11045 11241"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),11273(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="11 11273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      L(x,y,((z * (1 / u)) * (z / (z * (1 / u)))) \ (z * (1 / u))) = L(x,y,K(z,u \ 1) / u)
    ]]></literal>
    <justification jstring="[para(4182(a,2),11273(a,2,3))].">
      <j1 rule="para" parents="4182 11273"/>
    </justification>
  </clause>

  <clause id="11276">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(4279(a,1),11273(a,1,3))].">
      <j1 rule="para" parents="4279 11273"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(78(a,1),11276(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="78 11276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11278">
    <literal><![CDATA[
      L(x,y,y \ (y / z)) = L(x,y,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9665,a,11277,a),flip(a)].">
      <j1 rule="hyper" parents="9665 11277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ T(u,z \ 1),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[para(3423(a,1),11270(a,1,2,1,2))].">
      <j1 rule="para" parents="3423 11270"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z \ 1),w,v5)) = K(x,L(u / ((y * z) \ y),w,v5))
    ]]></literal>
    <justification jstring="[para(5057(a,1),11270(a,1,2,1,2))].">
      <j1 rule="para" parents="5057 11270"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6698,a,10955,a),flip(a)].">
      <j1 rule="hyper" parents="6698 10955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4934(a,1),11282(a,2,2))].">
      <j1 rule="para" parents="4934 11282"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11283(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(6106(a,1),11285(a,1,2,2))].">
      <j1 rule="para" parents="6106 11285"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(6113(a,1),11286(a,1,2))].">
      <j1 rule="para" parents="6113 11286"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,T(u,z)),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(11287(a,1),11065(a,1,2,2,1))].">
      <j1 rule="para" parents="11287 11065"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10964,a(flip),b,10965,a)].">
      <j1 rule="hyper" parents="64 10964 10965"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) = L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(11006(a,1),10781(a,1,3))].">
      <j1 rule="para" parents="11006 10781"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      K(x,y \ K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11006(a,1),11069(a,1,2))].">
      <j1 rule="para" parents="11006 11069"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(11006(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="11006 11131"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      K(x,y * (z * (L(u,w,u) \ v5))) = K(x,y * (z * (u \ v5)))
    ]]></literal>
    <justification jstring="[para(8401(a,1),11142(a,1,2,2,2))].">
      <j1 rule="para" parents="8401 11142"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      K(x,y * (K(z,z * u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(8404(a,1),11142(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8404 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(11006(a,1),11142(a,1,2,2,2))].">
      <j1 rule="para" parents="11006 11142"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(8331(a,1),11147(a,1,2,1,2))].">
      <j1 rule="para" parents="8331 11147"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(110(a,2),11267(a,1,2,1))].">
      <j1 rule="para" parents="110 11267"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(10754,a,11289,a),flip(a)].">
      <j1 rule="hyper" parents="10754 11289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(11289(a,1),10754(a,1))].">
      <j1 rule="para" parents="11289 10754"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),11300(a,1,2,2))].">
      <j1 rule="para" parents="7 11300"/>
    </justification>
  </clause>

  <clause id="11304">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(11300(a,1),8529(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11300 8529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10963,a,b,11303,a)].">
      <j1 rule="hyper" parents="64 10963 11303"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      a(x,((y * (z * (u * K(w,w \ 1)))) \ ((y * z) * u)) \ 1,x) = a(x,K(w,w \ 1) / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9071(a,1),11305(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9071 11305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      a(x,y \ (z * T(y,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(u,y) \ z,x) = w
    ]]></literal>
    <justification jstring="[para(4021(a,1),11301(a,1,2,1))].">
      <j1 rule="para" parents="4021 11301"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(10987(a,1),11005(a,1,1,2))].">
      <j1 rule="para" parents="10987 11005"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      ((x * (y * (z * a(u,w,u)))) \ ((x * y) * z)) * a(u,w,u) = a(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(713,a,11007,a),flip(a)].">
      <j1 rule="hyper" parents="713 11007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(18(a,2),11007(a,2,1))].">
      <j1 rule="para" parents="18 11007"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11192(a,2),4377(a,1))].">
      <j1 rule="para" parents="11192 4377"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(110(a,2),11311(a,1,2,2))].">
      <j1 rule="para" parents="110 11311"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11202(a,2),5187(a,1))].">
      <j1 rule="para" parents="11202 5187"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(110(a,2),11313(a,1,2,1))].">
      <j1 rule="para" parents="110 11313"/>
    </justification>
  </clause>

  <clause id="11315">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,11233,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 11233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11233(a,2),5187(a,1))].">
      <j1 rule="para" parents="11233 5187"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(78(a,1),11315(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 11315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(110(a,2),11317(a,1,1,1))].">
      <j1 rule="para" parents="110 11317"/>
    </justification>
  </clause>

  <clause id="11319">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(11317(a,2),5866(a,1))].">
      <j1 rule="para" parents="11317 5866"/>
    </justification>
  </clause>

  <clause id="11320">
    <literal><![CDATA[
      K(((x \ K(y,y * z)) \ K(y,y * z)) \ u,w) = K(T(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(6735(a,1),11317(a,2,1,1))].">
      <j1 rule="para" parents="6735 11317"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      K(T(x * y,y) \ ((x * y) * z),u) = K(K(y * x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9335,a(flip),b,11318,a),flip(a)].">
      <j1 rule="hyper" parents="64 9335 11318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(208(a,1),11316(a,1,1,1))].">
      <j1 rule="para" parents="208 11316"/>
    </justification>
  </clause>

  <clause id="11323">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),11294(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11324">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (K(u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(4512(a,2),11323(a,1,2,2))].">
      <j1 rule="para" parents="4512 11323"/>
    </justification>
  </clause>

  <clause id="11325">
    <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(64,a,9745,a(flip),b,10993,a),flip(a)].">
      <j1 rule="hyper" parents="64 9745 10993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,y \ z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(10130,a,11204,a)].">
      <j1 rule="hyper" parents="10130 11204"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      K(x,y * (z * T(T(u / w,u),v5))) = K(x,y * (z * T(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(3368(a,1),11242(a,1,2,2,2))].">
      <j1 rule="para" parents="3368 11242"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(3486(a,1),11293(a,1,2,2,2))].">
      <j1 rule="para" parents="3486 11293"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,L(x,w,v5)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10043,a(flip),b,11046,a),flip(a)].">
      <j1 rule="hyper" parents="64 10043 11046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11330">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,x) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(477(a,1),11329(a,1,2,3))].">
      <j1 rule="para" parents="477 11329"/>
    </justification>
  </clause>

  <clause id="11331">
    <literal><![CDATA[
      (x \ L(y,z,u)) * a(y,w,y) = x \ L(R(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(11330(a,1),10990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11330 10990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (z \ u)) = T(x,(u / T(z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11209,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="64 11209 11067"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      T(x,(y / T(z,y)) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(9318,a,11332,a),flip(a)].">
      <j1 rule="hyper" parents="9318 11332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(3266(a,2),11333(a,1,2,1))].">
      <j1 rule="para" parents="3266 11333"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / (z / y)) * u) = T(x,((z / y) \ y) * u)
    ]]></literal>
    <justification jstring="[para(3274(a,1),11334(a,1,2,1,1))].">
      <j1 rule="para" parents="3274 11334"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7603,a(flip),b,11179,a),flip(a)].">
      <j1 rule="hyper" parents="319 7603 11179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(11194(a,2),10156(a,1))].">
      <j1 rule="para" parents="11194 10156"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(11200(a,2),10156(a,1))].">
      <j1 rule="para" parents="11200 10156"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11135,a(flip),b,11206,a),flip(a)].">
      <j1 rule="hyper" parents="319 11135 11206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = L(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8529,a(flip),b,11304,a),flip(a)].">
      <j1 rule="hyper" parents="319 8529 11304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10957,a(flip),b,10953,a),flip(a)].">
      <j1 rule="hyper" parents="64 10957 10953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11340,a(flip),b,11341,a),flip(a)].">
      <j1 rule="hyper" parents="64 11340 11341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),11343(a,2,2))].">
      <j1 rule="para" parents="9 11343"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(10987(a,1),11310(a,1,2,2))].">
      <j1 rule="para" parents="10987 11310"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(489,a,11346,a)].">
      <j1 rule="hyper" parents="489 11346"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      a(x,y,x) \ L(a(x,y,x) * z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,3936,a,b,11347,a(flip))].">
      <j1 rule="hyper" parents="36 3936 11347"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,3938,a(flip),b,11347,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3938 11347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      L(x,y,z) \ L(a(u,w,u) * x,y,z) = a(u,w,u)
    ]]></literal>
    <justification jstring="[para(11348(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="11348 8514"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      L(K(x,y),z,u) \ L(K(x,x \ y),z,u) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(8340(a,1),11350(a,1,2,1))].">
      <j1 rule="para" parents="8340 11350"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      L(x,y,z) \ L(u * (T(x,u) / u),y,z) = a(u,u \ x,u)
    ]]></literal>
    <justification jstring="[para(8711(a,1),11350(a,1,2,1))].">
      <j1 rule="para" parents="8711 11350"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      L(K(x,y / ((x \ z) * u)),w,v5) \ L(K(x,x \ (y / ((z / x) * u))),w,v5) = a(x,x \ (y / ((z / x) * u)),x)
    ]]></literal>
    <justification jstring="[para(7532(a,1),11351(a,1,1,1))].">
      <j1 rule="para" parents="7532 11351"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      a(x,x \ L(y,z,u),x) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8719,a(flip),b,11352,a)].">
      <j1 rule="hyper" parents="64 8719 11352"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      a(x,x \ ((y * z) \ u),x) = a(x,x \ (z \ (y \ u)),x)
    ]]></literal>
    <justification jstring="[para(302(a,1),11354(a,1,2,2))].">
      <j1 rule="para" parents="302 11354"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      a(x,x \ ((y \ z) \ u),x) = a(x,x \ (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(504(a,1),11354(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="504 11354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      a(x,x \ y,x) \ y = (L(x,z,u) \ y) * T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(10335(a,1),10982(a,1,1))].">
      <j1 rule="para" parents="10335 10982"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      (L(x,y,z) \ u) * T(L(x,y,z),u) = (x \ u) * T(x,u)
    ]]></literal>
    <justification jstring="[hyper(8671,a,11358,a),flip(a)].">
      <j1 rule="hyper" parents="8671 11358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(T(x,u),y,z) = (x \ u) * T(x,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),11359(a,1,2))].">
      <j1 rule="para" parents="25 11359"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      T(x,(y / z) * y) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(3990(a,1),11125(a,1,2,2))].">
      <j1 rule="para" parents="3990 11125"/>
    </justification>
  </clause>

  <clause id="11363">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(3270(a,2),11183(a,2,2,1))].">
      <j1 rule="para" parents="3270 11183"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,y \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[para(5849(a,1),11226(a,1,2))].">
      <j1 rule="para" parents="5849 11226"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      K(K(x * y,y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y * x,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11321(a,1),4472(a,1))].">
      <j1 rule="para" parents="11321 4472"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11183,a(flip),b,11363,a),flip(a)].">
      <j1 rule="hyper" parents="64 11183 11363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) = L(y,K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11219(a,1,1))].">
      <j1 rule="para" parents="9 11219"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(7080,a,11369,a)].">
      <j1 rule="hyper" parents="7080 11369"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(81(a,1),11370(a,1,2,1))].">
      <j1 rule="para" parents="81 11370"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8072,a,11372,a)].">
      <j1 rule="hyper" parents="8072 11372"/>
    </justification>
  </clause>

  <clause id="11374">
    <literal><![CDATA[
      T(x,x * K(y,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9605,a(flip),b,11372,a)].">
      <j1 rule="hyper" parents="64 9605 11372"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      T(x * K(y,z),L(x,K(y,z),x)) = x \ (x * (K(y,z) * x))
    ]]></literal>
    <justification jstring="[para(11372(a,1),472(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11372 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      T(K(x,y) \ z,z) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(4356(a,2),11373(a,1,1))].">
      <j1 rule="para" parents="4356 11373"/>
    </justification>
  </clause>

  <clause id="11379">
    <literal><![CDATA[
      K(K(x,y) * z,z) * (((K(x,y) * z) * u) * z) = ((z * K(x,y)) * u) * z
    ]]></literal>
    <justification jstring="[para(11373(a,1),5717(a,2,1,1))].">
      <j1 rule="para" parents="11373 5717"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      K(x * K(y,z),x) = T(x,K(y,z)) \ x
    ]]></literal>
    <justification jstring="[para(11374(a,1),4001(a,2,1))].">
      <j1 rule="para" parents="11374 4001"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      T(T(K(x,y) \ z,u),z) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(11377(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11377 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4001,a,b,11380,a),flip(a)].">
      <j1 rule="hyper" parents="319 4001 11380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11383">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6757,a(flip),b,11382,a),flip(a)].">
      <j1 rule="hyper" parents="319 6757 11382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6705,a(flip),b,11382,a),flip(a)].">
      <j1 rule="hyper" parents="319 6705 11382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * K(y,z),L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11383(a,1),10130(a,1,1))].">
      <j1 rule="para" parents="11383 10130"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      K(K(x,y) * z,z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5865,a,11384,a)].">
      <j1 rule="hyper" parents="5865 11384"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      T(T(x,T(K(y,z) \ x,u)),x \ T(K(y,z) \ x,u)) = (x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(11381(a,1),6342(a,2,1,2))].">
      <j1 rule="para" parents="11381 6342"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      (x \ T(K(y,z) \ x,u)) * ((x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)) = (x * T(K(y,z) \ x,u)) / x
    ]]></literal>
    <justification jstring="[para(11381(a,1),8118(a,1,2,1,2))].">
      <j1 rule="para" parents="11381 8118"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      T(x * K(y,z),L(x,K(y,z),x)) = x \ (x * (K(z,y) \ x))
    ]]></literal>
    <justification jstring="[para(4356(a,2),11375(a,2,2,2))].">
      <j1 rule="para" parents="4356 11375"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      T(x * K(y,z),L(x,K(y,z),x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,9,a(flip),b,11390,a),flip(a)].">
      <j1 rule="hyper" parents="319 9 11390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      T(x * K(y,z),x) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(5723,a,11391,a)].">
      <j1 rule="hyper" parents="5723 11391"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      (x * (K(y,z) \ x)) / x = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(279,a,11392,a)].">
      <j1 rule="hyper" parents="279 11392"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      (x * T(K(y,z) \ x,u)) / x = T(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(11392(a,1),277(a,1,1,2,1))].">
      <j1 rule="para" parents="11392 277"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11392(a,1),9264(a,1,2))].">
      <j1 rule="para" parents="11392 9264"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      T(x,K(y,z) \ x) = K(y,z) * (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,11394,a(flip),b,3118,a),flip(a)].">
      <j1 rule="hyper" parents="131 11394 3118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      T(x,y * (T(y,z) \ u)) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4101(a,2),11397(a,1,2))].">
      <j1 rule="para" parents="4101 11397"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      T(x,K(y,z) \ x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6801,a(flip),b,11398,a),flip(a)].">
      <j1 rule="hyper" parents="319 6801 11398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z * y) \ u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11169(a,2),7605(a,1))].">
      <j1 rule="para" parents="11169 7605"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,7603,a(flip),b,11186,a),flip(a)].">
      <j1 rule="hyper" parents="319 7603 11186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      K(x,K(y,z)) * (((K(x,y) * z) * u) * z) = ((z * K(x,y)) * u) * z
    ]]></literal>
    <justification jstring="[para(11386(a,1),11379(a,1,1))].">
      <j1 rule="para" parents="11386 11379"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(10804(a,1),11043(a,1,1))].">
      <j1 rule="para" parents="10804 11043"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ (K(x,y) * ((x \ y) * (z * u))) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(10804(a,1),11405(a,1,2))].">
      <j1 rule="para" parents="10804 11405"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(801,a,11406,a)].">
      <j1 rule="hyper" parents="801 11406"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),10952(a,2,2))].">
      <j1 rule="para" parents="14 10952"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11345,a(flip),b,11408,a)].">
      <j1 rule="hyper" parents="64 11345 11408"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,a(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(11409(a,1),10927(a,1,2))].">
      <j1 rule="para" parents="11409 10927"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(4777,a,11411,a)].">
      <j1 rule="hyper" parents="4777 11411"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(4194(a,1),11325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4194 11325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11415">
    <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(8338,a,11414,a)].">
      <j1 rule="hyper" parents="8338 11414"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(10981(a,1),11415(a,1,1))].">
      <j1 rule="para" parents="10981 11415"/>
    </justification>
  </clause>

  <clause id="11417">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10963,a(flip),b,11416,a),flip(a)].">
      <j1 rule="hyper" parents="319 10963 11416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),11417(a,2,2))].">
      <j1 rule="para" parents="18 11417"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10994,a,11419,a),flip(a)].">
      <j1 rule="hyper" parents="10994 11419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      a(x,L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(11419(a,1),10994(a,1))].">
      <j1 rule="para" parents="11419 10994"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a,b,11420,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(302(a,1),11420(a,1,2))].">
      <j1 rule="para" parents="302 11420"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      a(x,(y \ z) \ u,x) = a(x,z \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(504(a,1),11420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      a(x,(y * z) \ (z * u),x) = a(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(508(a,1),11420(a,1,2))].">
      <j1 rule="para" parents="508 11420"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(11420(a,1),8393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11420 8393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (a(x,y,x) \ w) = K(x,x * L(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(11420(a,1),8532(a,1,2,1))].">
      <j1 rule="para" parents="11420 8532"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8320,a,11423,a)].">
      <j1 rule="hyper" parents="8320 11423"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,u) = T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,11429,a(flip),b,3292,a)].">
      <j1 rule="hyper" parents="131 11429 3292"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      R(x,(y * z) \ u,x) = R(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(302(a,1),11429(a,1,2))].">
      <j1 rule="para" parents="302 11429"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8393,a(flip),b,11427,a),flip(a)].">
      <j1 rule="hyper" parents="319 8393 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1568(a,2),11432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1568 11432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ (y \ u),x) = w
    ]]></literal>
    <justification jstring="[para(302(a,1),11421(a,1,2))].">
      <j1 rule="para" parents="302 11421"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      a(x,y \ (z \ (u * y)),x) = a(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(11301,a,11424,a),flip(a)].">
      <j1 rule="hyper" parents="11301 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,z \ (u / y),x)
    ]]></literal>
    <justification jstring="[para(12(a,1),11435(a,1,2,2,2))].">
      <j1 rule="para" parents="12 11435"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      K(x \ (y / z),u) \ K((x \ (y / z)) * u,u) = a(u,z \ (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,8330,a,b,11436,a)].">
      <j1 rule="hyper" parents="319 8330 11436"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      K(x,x * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11430(a,1),8696(a,1,2))].">
      <j1 rule="para" parents="11430 8696"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      a(x,y \ (z \ (y * u)),x) = a(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11424,a(flip),b,11426,a)].">
      <j1 rule="hyper" parents="64 11424 11426"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      a(x,T(y,z) \ (z \ u),x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),11439(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 11439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      T(K(x,x * y) * (x * L(y,z,u)),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5920,a,b,11438,a)].">
      <j1 rule="hyper" parents="64 5920 11438"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4081(a,1),11441(a,1,1))].">
      <j1 rule="para" parents="4081 11441"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3519,a(flip),b,11442,a)].">
      <j1 rule="hyper" parents="64 3519 11442"/>
    </justification>
  </clause>

  <clause id="11444">
    <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(127,a,11443,a(flip),b,4019,a(flip))].">
      <j1 rule="hyper" parents="127 11443 4019"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (a(x,y,x) \ w) != v5 * w
    ]]></literal>
    <literal><![CDATA[
      K(x,x * L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(11428(a,2),45(a,1))].">
      <j1 rule="para" parents="11428 45"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(8302,a,11444,a),flip(a)].">
      <j1 rule="hyper" parents="8302 11444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,10139,a(flip),b,11446,a),flip(a)].">
      <j1 rule="hyper" parents="319 10139 11446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <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),11447(a,1,1))].">
      <j1 rule="para" parents="12 11447"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5599,a(flip),b,11448,a)].">
      <j1 rule="hyper" parents="64 5599 11448"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10085(a,1),11449(a,2,3))].">
      <j1 rule="para" parents="10085 11449"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,10289,a(flip),b,11450,a),flip(a)].">
      <j1 rule="hyper" parents="319 10289 11450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8798,a,11451,a)].">
      <j1 rule="hyper" parents="8798 11451"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      (x * K(L(y,z,u) \ y,x)) \ L(x,L(y,z,u) \ y,x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8668,a,b,11453,a)].">
      <j1 rule="hyper" parents="64 8668 11453"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ y),x) = a(u,z,K(x / (L(y,z,u) \ y),y))
    ]]></literal>
    <justification jstring="[para(12(a,1),11453(a,1,2))].">
      <j1 rule="para" parents="12 11453"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      K((L(x,y,z) \ x) \ u,u) = a(z,y,K(u / (L(x,y,z) \ x),x))
    ]]></literal>
    <justification jstring="[hyper(5251,a,11455,a)].">
      <j1 rule="hyper" parents="5251 11455"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x / (L(y,z,u) \ y),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8779,a(flip),b,11456,a)].">
      <j1 rule="hyper" parents="64 8779 11456"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(10066(a,1),11457(a,2,3))].">
      <j1 rule="para" parents="10066 11457"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(81(a,1),11458(a,2,3,1))].">
      <j1 rule="para" parents="81 11458"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(11459(a,1),4359(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11459 4359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,8644,a(flip),b,11462,a),flip(a)].">
      <j1 rule="hyper" parents="319 8644 11462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,11463,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 11463 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = a(x,y,a(v5,w,K(u,z)))
    ]]></literal>
    <justification jstring="[para(11463(a,1),10301(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11463 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10308,a,b,11465,a)].">
      <j1 rule="hyper" parents="64 10308 11465"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) * K(v5,L(y \ L(y,w,u),y,x)) = K(v5,y \ L(y,w,u))
    ]]></literal>
    <justification jstring="[para(11465(a,1),10164(a,1,1))].">
      <j1 rule="para" parents="11465 10164"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      K(a(x,y,z),u) * a(x * y,z,a(x,y,K(z,u))) = K(L(z,y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11466(a,1),8621(a,1,2))].">
      <j1 rule="para" parents="11466 8621"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      (x * K(L(y,z,u) \ y,x)) \ L(x,a(u,z,y),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11433(a,1),11454(a,1,2))].">
      <j1 rule="para" parents="11433 11454"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) * (x \ L(x,a(u,z,y),x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(4777,a,11469,a)].">
      <j1 rule="hyper" parents="4777 11469"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(10396(a,1),11468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10396 11468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a(flip),b,11471,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 11471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = T((x \ 1) \ 1,w) / ((T(x,w) \ 1) \ K(a(u,z,y),x))
    ]]></literal>
    <justification jstring="[para(11472(a,1),7991(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11472 7991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,7991,a(flip),b,11474,a),flip(a)].">
      <j1 rule="hyper" parents="319 7991 11474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11475,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11475 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      K(x,K(y,z \ L(z,u,w))) = K(x,K(y,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(11475(a,1),7037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11475 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(11012(a,1),11019(a,1,2,1))].">
      <j1 rule="para" parents="11012 11019"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),(z \ w) \ 1))
    ]]></literal>
    <justification jstring="[para(5083(a,1),11213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5083 11213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(5084(a,1),11479(a,2,2,2))].">
      <j1 rule="para" parents="5084 11479"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(9634(a,1),11481(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9634 11481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11483">
    <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(11308(a,1),11309(a,1,1))].">
      <j1 rule="para" parents="11308 11309"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(10728,a,11478,a),flip(a)].">
      <j1 rule="hyper" parents="10728 11478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,10905,a(flip),b,11484,a),flip(a)].">
      <j1 rule="hyper" parents="64 10905 11484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      a(x,a(y,z,y) \ u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11485(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      a(x,y * a(z,u,z),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(8507(a,1),11485(a,1,2))].">
      <j1 rule="para" parents="8507 11485"/>
    </justification>
  </clause>

  <clause id="11489">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8685(a,1),11485(a,1,2))].">
      <j1 rule="para" parents="8685 11485"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      a(x,y * (T(z,y) / y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8711(a,1),11485(a,1,2))].">
      <j1 rule="para" parents="8711 11485"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      a(x,((y \ 1) * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2370(a,1),11487(a,1,2,1))].">
      <j1 rule="para" parents="2370 11487"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(8393(a,1),11487(a,1,2))].">
      <j1 rule="para" parents="8393 11487"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      a(x,y / (T(y,z) / z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(3487(a,1),11492(a,1,2))].">
      <j1 rule="para" parents="3487 11492"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      a(x,y \ (z * a(u,w,u)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(10990(a,2),11488(a,1,2))].">
      <j1 rule="para" parents="10990 11488"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      a(x,y * z,x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(10969,a,11489,a)].">
      <j1 rule="hyper" parents="10969 11489"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      K(x,y * z) * K(x * (y * z),x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(8322,a,11495,a)].">
      <j1 rule="hyper" parents="8322 11495"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      a(x,y * (z / y),x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),11495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      a(x,y \ T(z,y \ 1),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(3041(a,2),11498(a,1,2))].">
      <j1 rule="para" parents="3041 11498"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      a(x,y * (((y \ T(z,y)) * T(y,u)) / y),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(6638(a,1),11490(a,1,2,2,1))].">
      <j1 rule="para" parents="6638 11490"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9652(a,1),11491(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9652 11491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      (x * y) / a(T(x,x \ z) / z,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(11496(a,1),3396(a,1,2))].">
      <j1 rule="para" parents="11496 3396"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      a(x,T(y \ z,u) \ T(w,T(z \ y,u)),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[para(7555(a,1),11499(a,1,2,2))].">
      <j1 rule="para" parents="7555 11499"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      a(x,y \ (T(z * u,z) / z),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(8323(a,2),11494(a,1,2,2))].">
      <j1 rule="para" parents="8323 11494"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      a(x,y \ T(z * u,z),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(8682(a,1),11494(a,1,2,2))].">
      <j1 rule="para" parents="8682 11494"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      a(x,y \ (z * (T(u,z) / z)),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(8709(a,1),11494(a,1,2,2))].">
      <j1 rule="para" parents="8709 11494"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      a(x,y \ (z * ((1 / z) * u)),w) = a(x,y \ L(u,1 / z,z),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),11501(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 11501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      a(x,y \ (z \ T(y * u,y)),x) = a(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11436,a,b,11504,a)].">
      <j1 rule="hyper" parents="64 11436 11504"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      a(x,T(y,z) \ T(y * u,y),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(4304(a,1),11508(a,1,2))].">
      <j1 rule="para" parents="4304 11508"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      K(x,y * z) * K(x * (y * z),x) = x \ R(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a,b,11497,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 11497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      R(x,y * z,x) = R(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(4577,a,11510,a(flip))].">
      <j1 rule="hyper" parents="4577 11510"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      R(x,y \ (T(y,z) * u),x) = R(x,(y \ u) * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(1010(a,2),11511(a,1,2))].">
      <j1 rule="para" parents="1010 11511"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      R(x,K(y,z) \ ((y \ u) * y),x) = R(x,y * (y \ (K(y,z) \ u)),x)
    ]]></literal>
    <justification jstring="[para(6449(a,2),11511(a,1,2))].">
      <j1 rule="para" parents="6449 11511"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      a(x,y \ (z * ((1 / z) * u)),w) = a(x,y \ L(u,z \ 1,z),w)
    ]]></literal>
    <justification jstring="[para(1762(a,1),11507(a,2,2,2))].">
      <j1 rule="para" parents="1762 11507"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      a(x,y * ((y \ T(z,y)) * K(y,u)),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(4915(a,1),11500(a,1,2,2))].">
      <j1 rule="para" parents="4915 11500"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      a(x,y * (y \ (T(z,y) * K(y,u))),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(5622(a,2),11515(a,1,2,2))].">
      <j1 rule="para" parents="5622 11515"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      a(x,y * (y \ (y \ (z * T(y,u)))),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(6089(a,2),11516(a,1,2,2,2))].">
      <j1 rule="para" parents="6089 11516"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      a(x,y \ (z * T(y,u)),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11517(a,1,2))].">
      <j1 rule="para" parents="10 11517"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(11030,a,11483,a),flip(a)].">
      <j1 rule="hyper" parents="11030 11483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,14,a,b,11520,a),flip(a)].">
      <j1 rule="hyper" parents="319 14 11520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      a(x,y,T(z * u,z)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(8682(a,1),11521(a,1,3))].">
      <j1 rule="para" parents="8682 11521"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / (y * (z * a(u,w,u))) = R(R(x,y,z),y * z,a(u,w,u))
    ]]></literal>
    <justification jstring="[para(10987(a,1),10997(a,1,2))].">
      <j1 rule="para" parents="10987 10997"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10397(a,1),11467(a,1,1))].">
      <j1 rule="para" parents="10397 11467"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,11524,a)].">
      <j1 rule="hyper" parents="133 11524"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5347,a(flip),b,11525,a)].">
      <j1 rule="hyper" parents="64 5347 11525"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11527,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11527 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,x * (u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[para(11529(a,2),611(a,1,1))].">
      <j1 rule="para" parents="11529 611"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,11464,a(flip),b,11530,a),flip(a)].">
      <j1 rule="hyper" parents="319 11464 11530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11532">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(11523(a,1),531(a,1))].">
      <j1 rule="para" parents="11523 531"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(11532,a,10996,a)].">
      <j1 rule="hyper" parents="11532 10996"/>
    </justification>
  </clause>

  <clause id="11534">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(3735,a,11533,a)].">
      <j1 rule="hyper" parents="3735 11533"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(8512(a,1),11533(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8512 11533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      R(x,y,z \ L(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(11028(a,1),11535(a,1,3))].">
      <j1 rule="para" parents="11028 11535"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      R(x,y,z \ T(u,u * w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(3295(a,1),11537(a,1,3,2))].">
      <j1 rule="para" parents="3295 11537"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(10361(a,1),11537(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10361 11537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      K(R(x / y,y,x \ T(z,u)) \ T(z,u),w) = K(y * (x \ T(z,z * u)),w)
    ]]></literal>
    <justification jstring="[para(11538(a,1),11207(a,1,1,1))].">
      <j1 rule="para" parents="11538 11207"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(517(a,1),11540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="517 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(x,(y * z) \ u) * a(w,v5,K((y * z) \ u,x)) = K(x,L(T(z * y,z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(11081(a,1),11176(a,1,1))].">
      <j1 rule="para" parents="11081 11176"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((z * y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(11542(a,1),10155(a,1))].">
      <j1 rule="para" parents="11542 10155"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(7389(a,1),11275(a,1,3,1))].">
      <j1 rule="para" parents="7389 11275"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(9186(a,1),11544(a,1,3))].">
      <j1 rule="para" parents="9186 11544"/>
    </justification>
  </clause>

  <clause id="11546">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(4785(a,1),11545(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4785 11545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10884(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 10884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,1133,a,b,11547,a)].">
      <j1 rule="hyper" parents="40 1133 11547"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(3297,a,11548,a)].">
      <j1 rule="hyper" parents="3297 11548"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,11409,a(flip),b,11549,a)].">
      <j1 rule="hyper" parents="64 11409 11549"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(3513,a,11550,a)].">
      <j1 rule="hyper" parents="3513 11550"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(1653,a,11550,a)].">
      <j1 rule="hyper" parents="1653 11550"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,11550,a,b,8386,a),flip(a)].">
      <j1 rule="hyper" parents="126 11550 8386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,11433,a,b,11550,a)].">
      <j1 rule="hyper" parents="64 11433 11550"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(11550(a,1),3370(a,1,1,1))].">
      <j1 rule="para" parents="11550 3370"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1906,a(flip),b,11551,a)].">
      <j1 rule="hyper" parents="64 1906 11551"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      x * a(y,a(z,u,w),y) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,11554,a,b,68,a)].">
      <j1 rule="hyper" parents="131 11554 68"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(1653,a,11555,a)].">
      <j1 rule="hyper" parents="1653 11555"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      T(x,x * (L(y,z,u) \ y)) = T(x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9605,a(flip),b,11555,a)].">
      <j1 rule="hyper" parents="64 9605 11555"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(130,a,11558,a(flip),b,8676,a)].">
      <j1 rule="hyper" parents="130 11558 8676"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      a(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(11558(a,1),137(a,1)),flip(a)].">
      <j1 rule="para" parents="11558 137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11552(a,1),333(a,1,1))].">
      <j1 rule="para" parents="11552 333"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(14(a,1),11557(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14 11557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11470,a(flip),b,11562,a),flip(a)].">
      <j1 rule="hyper" parents="64 11470 11562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11412,a(flip),b,11562,a)].">
      <j1 rule="hyper" parents="64 11412 11562"/>
    </justification>
  </clause>

  <clause id="11568">
    <literal><![CDATA[
      x \ T((x / a(y,z,u)) * a(y,z,u),x / a(y,z,u)) = K(a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(127,a,11556,a,b,4244,a)].">
      <j1 rule="hyper" parents="127 11556 4244"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11475,a(flip),b,11566,a),flip(a)].">
      <j1 rule="hyper" parents="64 11475 11566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a(flip),b,11570,a)].">
      <j1 rule="hyper" parents="319 4012 11570"/>
    </justification>
  </clause>

  <clause id="11572">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,11570,a,b,4947,a)].">
      <j1 rule="hyper" parents="131 11570 4947"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,11570,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 11570 4012"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(130,a,11570,a,b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 11570 4011"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      K(x,a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5632,a(flip),b,11570,a),flip(a)].">
      <j1 rule="hyper" parents="64 5632 11570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      K(x,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,4967,a(flip),b,11570,a),flip(a)].">
      <j1 rule="hyper" parents="64 4967 11570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11570(a,2),4089(a,1,2))].">
      <j1 rule="para" parents="11570 4089"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = K(u,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(11570(a,1),8643(a,2,1))].">
      <j1 rule="para" parents="11570 8643"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      T(x,a(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,11575,a)].">
      <j1 rule="hyper" parents="57 11575"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      T(x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,11576,a)].">
      <j1 rule="hyper" parents="57 11576"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,11579,a)].">
      <j1 rule="hyper" parents="55 11579"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(9695(a,1),11580(a,1,2))].">
      <j1 rule="para" parents="9695 11580"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      T(a(x,y,y \ 1),z) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(55,a,11582,a)].">
      <j1 rule="hyper" parents="55 11582"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(11571(a,1),4106(a,1))].">
      <j1 rule="para" parents="11571 4106"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(5644(a,1),11573(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5644 11573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14(a,1),11564(a,1,1,1))].">
      <j1 rule="para" parents="14 11564"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6249,a,11578,a),flip(a)].">
      <j1 rule="hyper" parents="6249 11578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) * u = a(x,y,z) * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4418,a,11578,a)].">
      <j1 rule="hyper" parents="4418 11578"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = T(K(a(x,y,z),u),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,6099,a(flip),b,11589,a),flip(a)].">
      <j1 rule="hyper" parents="319 6099 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,11589,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 11589 4012"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      K(a(x,y,z),y) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,4967,a(flip),b,11589,a),flip(a)].">
      <j1 rule="hyper" parents="64 4967 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(11589(a,2),4130(a,1,1,2))].">
      <j1 rule="para" parents="11589 4130"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u,a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(11589(a,2),4322(a,1,1))].">
      <j1 rule="para" parents="11589 4322"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(57,a,11594,a)].">
      <j1 rule="hyper" parents="57 11594"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      (x * a(y,x,z)) / x = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(279,a,11597,a)].">
      <j1 rule="hyper" parents="279 11597"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      T(x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,11597,a)].">
      <j1 rule="hyper" parents="55 11597"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = T(a(x,y,K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(11589(a,2),11592(a,2,1))].">
      <j1 rule="para" parents="11589 11592"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11597,a(flip),b,11600,a),flip(a)].">
      <j1 rule="hyper" parents="319 11597 11600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      (x \ 1) * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10306(a,1),11577(a,1,2))].">
      <j1 rule="para" parents="10306 11577"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(11586(a,2),11577(a,1))].">
      <j1 rule="para" parents="11586 11577"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(6712(a,1),11593(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6712 11593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11605">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a(flip),b,11604,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 11604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(6982,a,11605,a)].">
      <j1 rule="hyper" parents="6982 11605"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,11606,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 11606 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ x)) = T(x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8799,a,b,11561,a)].">
      <j1 rule="hyper" parents="64 8799 11561"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11581,a,b,11565,a),flip(a)].">
      <j1 rule="hyper" parents="64 11581 11565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10324,a(flip),b,11607,a),flip(a)].">
      <j1 rule="hyper" parents="64 10324 11607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(10708(a,1),11610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10708 11610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,8341,a(flip),b,11611,a),flip(a)].">
      <j1 rule="hyper" parents="319 8341 11611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      K(x,K(y,R(y,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(11611(a,2),11068(a,1,2))].">
      <j1 rule="para" parents="11611 11068"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(8073,a,11612,a),flip(a)].">
      <j1 rule="hyper" parents="8073 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      K(x,x \ ((x * y) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(194(a,1),11612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="194 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) = K(x / y,(x / y) \ z)
    ]]></literal>
    <justification jstring="[para(538(a,1),11612(a,1,2,1))].">
      <j1 rule="para" parents="538 11612"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(519(a,1),11612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="519 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11619">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(521(a,1),11612(a,1,2))].">
      <j1 rule="para" parents="521 11612"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) * K(x,K(y,R(x / y,u,w) \ z)) = K(y \ x,R(x / y,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(11612(a,1),7310(a,1,1))].">
      <j1 rule="para" parents="11612 7310"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(9210,a,11616,a)].">
      <j1 rule="hyper" parents="9210 11616"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      K(x,y * (x \ (y \ (z * u)))) = K(x,(x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(8242,a,11618,a)].">
      <j1 rule="hyper" parents="8242 11618"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(8138,a,11618,a),flip(a)].">
      <j1 rule="hyper" parents="8138 11618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 11621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(11621(a,1),11157(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11621 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,11623,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11623 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11624(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5872,a,11626,a)].">
      <j1 rule="hyper" parents="5872 11626"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      K(x,K(y,R(x \ y,z,u) \ w)) = K(x,K(x \ y,w))
    ]]></literal>
    <justification jstring="[hyper(6979,a,11614,a)].">
      <j1 rule="hyper" parents="6979 11614"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      K(x,y * (x \ T(z,y))) = K(x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),11622(a,1,2,2,2))].">
      <j1 rule="para" parents="22 11622"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      x * K(y \ z,y * (z \ x)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(131,a,11627,a(flip),b,4242,a)].">
      <j1 rule="hyper" parents="131 11627 4242"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9158,a(flip),b,11615,a)].">
      <j1 rule="hyper" parents="64 9158 11615"/>
    </justification>
  </clause>

  <clause id="11633">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10387,a(flip),b,11632,a)].">
      <j1 rule="hyper" parents="64 10387 11632"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10515,a,b,11633,a)].">
      <j1 rule="hyper" parents="64 10515 11633"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10519,a(flip),b,11633,a)].">
      <j1 rule="hyper" parents="64 10519 11633"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8976,a(flip),b,11633,a)].">
      <j1 rule="hyper" parents="64 8976 11633"/>
    </justification>
  </clause>

  <clause id="11639">
    <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(64,a,9881,a(flip),b,11636,a),flip(a)].">
      <j1 rule="hyper" parents="64 9881 11636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) = K(x,(u / (y * z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10514,a(flip),b,11635,a)].">
      <j1 rule="hyper" parents="64 10514 11635"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,8783,a(flip),b,11637,a),flip(a)].">
      <j1 rule="hyper" parents="319 8783 11637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      K(x,K(y,R(x \ y,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6832,a(flip),b,11629,a),flip(a)].">
      <j1 rule="hyper" parents="319 6832 11629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x,K(y,R(y \ x,z,u) \ w)) = K(y,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(6744,a,11645,a)].">
      <j1 rule="hyper" parents="6744 11645"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      K(x,K(y,R(y \ x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6742,a,b,11646,a),flip(a)].">
      <j1 rule="hyper" parents="319 6742 11646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      T(a(x,y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11609(a,1),11587(a,1))].">
      <j1 rule="para" parents="11609 11587"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1961(a,2),11648(a,1,1))].">
      <j1 rule="para" parents="1961 11648"/>
    </justification>
  </clause>

  <clause id="11650">
    <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(64,a,9911,a(flip),b,11639,a)].">
      <j1 rule="hyper" parents="64 9911 11639"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3171(a,1),11650(a,1,1))].">
      <j1 rule="para" parents="3171 11650"/>
    </justification>
  </clause>

  <clause id="11655">
    <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(11651(a,1),7877(a,1,1,1,2))].">
      <j1 rule="para" parents="11651 7877"/>
    </justification>
  </clause>

  <clause id="11656">
    <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(9875,a,11655,a)].">
      <j1 rule="hyper" parents="9875 11655"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(215,a,11656,a),flip(a)].">
      <j1 rule="hyper" parents="215 11656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11656(a,1),215(a,1))].">
      <j1 rule="para" parents="11656 215"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11651,a(flip),b,11657,a)].">
      <j1 rule="hyper" parents="64 11651 11657"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,11657,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 11657 20"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(266(a,2),11657(a,2,2)),flip(a)].">
      <j1 rule="para" parents="266 11657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11657(a,1),10539(a,1,2))].">
      <j1 rule="para" parents="11657 10539"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      a(K(x,R(y,z,u) \ 1),w,v5) = a(K(y,R(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11660(a,1),10924(a,2,1))].">
      <j1 rule="para" parents="11660 10924"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11660(a,1),10930(a,2,1))].">
      <j1 rule="para" parents="11660 10930"/>
    </justification>
  </clause>

  <clause id="11670">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10546,a(flip),b,11666,a)].">
      <j1 rule="hyper" parents="64 10546 11666"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x)
    ]]></literal>
    <justification jstring="[para(11666(a,1),9798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11666 9798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,K(x,y) * K(R(y,z,u),x)) = v5
    ]]></literal>
    <justification jstring="[para(11666(a,1),9838(a,1,1))].">
      <j1 rule="para" parents="11666 9838"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(11661(a,1),4448(a,1,2))].">
      <j1 rule="para" parents="11661 4448"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(9278,a,11662,a)].">
      <j1 rule="hyper" parents="9278 11662"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(4022(a,2),11674(a,1,2,1))].">
      <j1 rule="para" parents="4022 11674"/>
    </justification>
  </clause>

  <clause id="11677">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(3310,a,11676,a)].">
      <j1 rule="hyper" parents="3310 11676"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,27,a(flip),b,11677,a(flip))].">
      <j1 rule="hyper" parents="41 27 11677"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      R(x,y,z) * (T(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,11678,a(flip),b,238,a)].">
      <j1 rule="hyper" parents="130 11678 238"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * (K(x,y) * z)) = R(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,9180,a(flip),b,11680,a)].">
      <j1 rule="hyper" parents="128 9180 11680"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      (T(x,y) * z) * K(R(y,x,z),T(x,y) * z) = ((x * y) * z) / R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,11680,a(flip),b,4095,a),flip(a)].">
      <j1 rule="hyper" parents="128 11680 4095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,7590,a(flip),b,11675,a),flip(a)].">
      <j1 rule="hyper" parents="64 7590 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11658,a,11687,a)].">
      <j1 rule="hyper" parents="11658 11687"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(538(a,1),11688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="538 11688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11690">
    <literal><![CDATA[
      R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(x,R(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10574,a,b,11668,a)].">
      <j1 rule="hyper" parents="64 10574 11668"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      R(K(a(K(x,y),z,u),w),K(K(x,w),v5),v6) * v7 = K(y,K(x,w)) * (R(K(K(x,w),y),z,u) * v7)
    ]]></literal>
    <justification jstring="[para(11671(a,1),9931(a,1,1,1))].">
      <j1 rule="para" parents="11671 9931"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4317(a,1),11685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4317 11685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,11692,a),flip(a)].">
      <j1 rule="hyper" parents="319 20 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      R(x,y,K(x,y) \ z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11693(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 11693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(10926(a,1),11690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10926 11690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11697">
    <literal><![CDATA[
      a(K(x,R(y,x * R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,10769,a(flip),b,11696,a),flip(a)].">
      <j1 rule="hyper" parents="319 10769 11696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      a(K(x,R(y,R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11669,a(flip),b,11697,a)].">
      <j1 rule="hyper" parents="64 11669 11697"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,u / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),11568(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 11568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11700">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3116(a,1),11699(a,2,2))].">
      <j1 rule="para" parents="3116 11699"/>
    </justification>
  </clause>

  <clause id="11701">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11700(a,2),4106(a,1))].">
      <j1 rule="para" parents="11700 4106"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(11701,a,11589,a(flip))].">
      <j1 rule="hyper" parents="11701 11589"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v5) = K(a(K(y,x),u,w),z) * v5
    ]]></literal>
    <justification jstring="[para(365(a,1),11691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="365 11691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,7519,a(flip),b,11703,a),flip(a)].">
      <j1 rule="hyper" parents="319 7519 11703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11705">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(y,K(z,x)),u,w) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(6705(a,1),11704(a,1,2,1,1))].">
      <j1 rule="para" parents="6705 11704"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,K(z,R(x,u,w))) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7464(a,1),11705(a,1,2,1))].">
      <j1 rule="para" parents="7464 11705"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(z,R(x,u,w))) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(4022(a,2),11706(a,1,2))].">
      <j1 rule="para" parents="4022 11706"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      T(K(x,K(y,z)) * y,K(x,R(z,u,w))) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8655,a,b,11707,a)].">
      <j1 rule="hyper" parents="64 8655 11707"/>
    </justification>
  </clause>

  <clause id="11709">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,R(z,u,w))) = x * K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6751(a,1),11708(a,1,1))].">
      <j1 rule="para" parents="6751 11708"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = x * K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(9806,a,11709,a)].">
      <j1 rule="hyper" parents="9806 11709"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10547,a(flip),b,11710,a),flip(a)].">
      <j1 rule="hyper" parents="64 10547 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,4019,a(flip),b,11711,a),flip(a)].">
      <j1 rule="hyper" parents="35 4019 11711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(y,a(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(11672,a,11712,a)].">
      <j1 rule="hyper" parents="11672 11712"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(11713(a,1),10556(a,1,2))].">
      <j1 rule="para" parents="11713 10556"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,11714,a),flip(a)].">
      <j1 rule="hyper" parents="133 11714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11716">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,11712,a,b,11715,a),flip(a)].">
      <j1 rule="hyper" parents="319 11712 11715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(6742(a,1),11715(a,1,1))].">
      <j1 rule="para" parents="6742 11715"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6742(a,1),11716(a,1,1))].">
      <j1 rule="para" parents="6742 11716"/>
    </justification>
  </clause>

  <clause id="11719">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(11670(a,2),11716(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11670 11716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11567(a,1),11717(a,2,2))].">
      <j1 rule="para" parents="11567 11717"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11718,a,b,11719,a)].">
      <j1 rule="hyper" parents="64 11718 11719"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11721,a(flip),b,11720,a),flip(a)].">
      <j1 rule="hyper" parents="64 11721 11720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11723">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,8230,a,b,11722,a)].">
      <j1 rule="hyper" parents="64 8230 11722"/>
    </justification>
  </clause>

  <clause id="11724">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(6748(a,2),11723(a,2,1))].">
      <j1 rule="para" parents="6748 11723"/>
    </justification>
  </clause>

  <clause id="11725">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(8416,a,11724,a)].">
      <j1 rule="hyper" parents="8416 11724"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(R(y,z,u),z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,7940,a(flip),b,11725,a)].">
      <j1 rule="hyper" parents="64 7940 11725"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,R(y,z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(6758(a,1),11726(a,2,1))].">
      <j1 rule="para" parents="6758 11726"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(9137(a,1),11727(a,2,1,2))].">
      <j1 rule="para" parents="9137 11727"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,v5))) = a(K(x,K(y,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(7960,a,11728,a)].">
      <j1 rule="hyper" parents="7960 11728"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T(w,y * (z * u)))) = a(K(x,K(y,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8920,a(flip),b,11729,a)].">
      <j1 rule="hyper" parents="64 8920 11729"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      a(((x * ((x / y) / x)) \ T(x,y \ 1)) \ T(x,y \ 1),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[para(3805(a,1),10920(a,2,1))].">
      <j1 rule="para" parents="3805 10920"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),T(x,y \ 1)),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10913,a(flip),b,11734,a)].">
      <j1 rule="hyper" parents="64 10913 11734"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(w,L(y,a(z,u,z),x),x * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(11012(a,1),11021(a,1,2))].">
      <j1 rule="para" parents="11012 11021"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      L(x,L(y,a(z,u,z),w),w * a(z,u,z)) = L(x,a(z,u,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,10717,a(flip),b,11737,a),flip(a)].">
      <j1 rule="hyper" parents="64 10717 11737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(11017(a,1),11738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11017 11738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11740">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,10781,a(flip),b,11739,a),flip(a)].">
      <j1 rule="hyper" parents="319 10781 11739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8319(a,1),11740(a,1,2))].">
      <j1 rule="para" parents="8319 11740"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8327(a,1),11740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8327 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11745">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8332(a,1),11740(a,1,2))].">
      <j1 rule="para" parents="8332 11740"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      L(x,y * a(z,u,z),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(8507(a,1),11740(a,1,2))].">
      <j1 rule="para" parents="8507 11740"/>
    </justification>
  </clause>

  <clause id="11747">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8685(a,1),11740(a,1,2))].">
      <j1 rule="para" parents="8685 11740"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      L(x,R(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(8708(a,1),11740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8708 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11749">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(3414(a,1),11743(a,1,2))].">
      <j1 rule="para" parents="3414 11743"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5976(a,1),11743(a,1,2))].">
      <j1 rule="para" parents="5976 11743"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8305(a,1),11742(a,1,2))].">
      <j1 rule="para" parents="8305 11742"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      L(x,y / (z * a(u,w,u)),v5) = L(x,y / z,v5)
    ]]></literal>
    <justification jstring="[para(11035(a,2),11742(a,1,2))].">
      <j1 rule="para" parents="11035 11742"/>
    </justification>
  </clause>

  <clause id="11754">
    <literal><![CDATA[
      L(x,y / R(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(11036(a,1),11742(a,1,2))].">
      <j1 rule="para" parents="11036 11742"/>
    </justification>
  </clause>

  <clause id="11755">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(8380(a,1),11746(a,1,2))].">
      <j1 rule="para" parents="8380 11746"/>
    </justification>
  </clause>

  <clause id="11756">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(8705(a,1),11746(a,1,2))].">
      <j1 rule="para" parents="8705 11746"/>
    </justification>
  </clause>

  <clause id="11757">
    <literal><![CDATA[
      L(x,R(y,z,y) / u,w) = L(x,y / u,w)
    ]]></literal>
    <justification jstring="[para(10736(a,1),11746(a,1,2))].">
      <j1 rule="para" parents="10736 11746"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(6533(a,1),11744(a,2,2))].">
      <j1 rule="para" parents="6533 11744"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(9225,a,11747,a),flip(a)].">
      <j1 rule="hyper" parents="9225 11747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11760">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      L(x,T(y,z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(11749(a,1),3647(a,1))].">
      <j1 rule="para" parents="11749 3647"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(5057(a,1),11749(a,1,2))].">
      <j1 rule="para" parents="5057 11749"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(11223(a,1),11749(a,1,2))].">
      <j1 rule="para" parents="11223 11749"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,T(y * z,y),z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(11750(a,1),5292(a,1,2))].">
      <j1 rule="para" parents="11750 5292"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(3448,a,11751,a),flip(a)].">
      <j1 rule="hyper" parents="3448 11751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      L(x,K(y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(9627,a,11765,a)].">
      <j1 rule="hyper" parents="9627 11765"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      (x / y) * (K(x,y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(11765(a,1),8069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11765 8069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,11766,a)].">
      <j1 rule="hyper" parents="64 302 11766"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(3304(a,1),11756(a,1,2))].">
      <j1 rule="para" parents="3304 11756"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(3157(a,1),11760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3157 11760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      L(x,T((y / T(z,y)) * z,y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11747,a,b,11769,a)].">
      <j1 rule="hyper" parents="64 11747 11769"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      L(x,(y \ T(z,y \ z)) \ u,w) = L(x,(z / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3401(a,1),11748(a,1,2,1))].">
      <j1 rule="para" parents="3401 11748"/>
    </justification>
  </clause>

  <clause id="11773">
    <literal><![CDATA[
      L(x,y / T(z,z \ u),w) = L(x,y / T(z,u),w)
    ]]></literal>
    <justification jstring="[para(3414(a,1),11754(a,1,2,2))].">
      <j1 rule="para" parents="3414 11754"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(553(a,1),11755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="553 11755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      L(x,T(y,y \ z) / u,w) = L(x,T(y,z) / u,w)
    ]]></literal>
    <justification jstring="[para(3414(a,1),11757(a,1,2,1))].">
      <j1 rule="para" parents="3414 11757"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      ((x * y) / T(x,y)) * (K(x * y,T(x,y)) * z) = (K(x * y,x) * y) * z
    ]]></literal>
    <justification jstring="[para(6184(a,1),11767(a,2,1))].">
      <j1 rule="para" parents="6184 11767"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      L(x,y / T(z * (u / z),z),w) = L(x,y / u,w)
    ]]></literal>
    <justification jstring="[para(8705(a,1),11753(a,1,2,2))].">
      <j1 rule="para" parents="8705 11753"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11747,a(flip),b,11762,a),flip(a)].">
      <j1 rule="hyper" parents="319 11747 11762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),u * z,(u * z) \ z)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11778(a,1),10176(a,1,2))].">
      <j1 rule="para" parents="11778 10176"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(5624(a,2),11768(a,1,1))].">
      <j1 rule="para" parents="5624 11768"/>
    </justification>
  </clause>

  <clause id="11781">
    <literal><![CDATA[
      L(x,y / T(z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(270(a,1),11773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="270 11773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      L(x,(y * (z / y)) \ y,u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11781,a(flip),b,11777,a)].">
      <j1 rule="hyper" parents="64 11781 11777"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      L(x,y / (z * y),u) = L(x,(y * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),11782(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 11782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * ((x \ y) \ z) = u
    ]]></literal>
    <justification jstring="[para(11780(a,2),4384(a,1))].">
      <j1 rule="para" parents="11780 4384"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(3263(a,1),11771(a,1,2,1))].">
      <j1 rule="para" parents="3263 11771"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      L(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,u),x) = z
    ]]></literal>
    <justification jstring="[para(11785(a,1),10959(a,1))].">
      <j1 rule="para" parents="11785 10959"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(11064(a,1),11785(a,1,2))].">
      <j1 rule="para" parents="11064 11785"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,w),x) = u
    ]]></literal>
    <justification jstring="[para(8718(a,2),11786(a,1))].">
      <j1 rule="para" parents="8718 11786"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11763,a,b,11787,a)].">
      <j1 rule="hyper" parents="64 11763 11787"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(9225,a,11789,a)].">
      <j1 rule="hyper" parents="9225 11789"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11787,a(flip),b,11790,a),flip(a)].">
      <j1 rule="hyper" parents="64 11787 11790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11770,a(flip),b,11790,a)].">
      <j1 rule="hyper" parents="64 11770 11790"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10233,a(flip),b,11772,a),flip(a)].">
      <j1 rule="hyper" parents="64 10233 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      K(x,y) * ((y \ x) \ (K(y,x) * z)) = (((y \ x) * y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(11784,a,10889,a)].">
      <j1 rule="hyper" parents="11784 10889"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      (((x \ y) * x) / x) \ z = K(y,x) * ((T(x,y) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(10851(a,1),11795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10851 11795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(11(a,1),11796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 11796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      L(x,K(y * z,R(y,z,z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(266(a,1),11758(a,1,2,2))].">
      <j1 rule="para" parents="266 11758"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(5585(a,1),11799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5585 11799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11745,a(flip),b,11800,a),flip(a)].">
      <j1 rule="hyper" parents="319 11745 11800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      x * (K(y * x,T(y,x)) * z) = (K(y * x,y) * x) * z
    ]]></literal>
    <justification jstring="[para(198(a,1),11776(a,1,1))].">
      <j1 rule="para" parents="198 11776"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      (K(x * y,x) * y) * z = y * (K(x * y,x) * z)
    ]]></literal>
    <justification jstring="[para(4354(a,1),11803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4354 11803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      K(x * y,x) * (y * z) = y * (K(x * y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(10800,a,11804,a)].">
      <j1 rule="hyper" parents="10800 11804"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,z * y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(11747(a,1),11764(a,1,2))].">
      <j1 rule="para" parents="11747 11764"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      a(x,((y * z) * u) \ (y * (z * (u * K(w,w \ 1)))),x) = a(x,K(w,w \ 1) / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(8801,a,11306,a)].">
      <j1 rule="hyper" parents="8801 11306"/>
    </justification>
  </clause>

  <clause id="11808">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ (z * (u * (y * K(w,w \ 1))))),x) = a(x,K(w,w \ 1) / a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(11434,a,11807,a)].">
      <j1 rule="hyper" parents="11434 11807"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      a(x,y \ L(y * K(z,z \ 1),u,w),x) = a(x,K(z,z \ 1) / a(w,u,y),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),11808(a,1,2,2))].">
      <j1 rule="para" parents="18 11808"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      a(x,(y \ L(y,z,u)) * K(w,w \ 1),x) = a(x,K(w,w \ 1) / a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(3967(a,1),11809(a,1,2))].">
      <j1 rule="para" parents="3967 11809"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = a(x,K(w,w \ 1) / a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9077,a(flip),b,11810,a)].">
      <j1 rule="hyper" parents="64 9077 11810"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      a(x,a(y,z,u) \ K(w,w \ 1),x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10963,a(flip),b,11811,a)].">
      <j1 rule="hyper" parents="319 10963 11811"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(214(a,1),11812(a,1,2,2))].">
      <j1 rule="para" parents="214 11812"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,u * (a(x,y,z) \ 1)),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(11814(a,1),8809(a,1,1,2))].">
      <j1 rule="para" parents="11814 8809"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      L(K(x,y / ((x \ z) * u)),w,v5) \ L(K(x,x \ (y / ((x \ z) * u))),w,v5) = a(x,x \ (y / ((z / x) * u)),x)
    ]]></literal>
    <justification jstring="[para(10246(a,1),11353(a,1,2,1))].">
      <j1 rule="para" parents="10246 11353"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (y / ((x \ z) * u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11351,a(flip),b,11817,a),flip(a)].">
      <j1 rule="hyper" parents="64 11351 11817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w) = ((x * y) * (a(z,u,z) \ w)) / ((y / a(z,u,z)) * w)
    ]]></literal>
    <justification jstring="[para(8677(a,1),11024(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8677 11024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w) = ((x * y) * (a(z,u,z) \ w)) / (y * (a(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(11020(a,1),11819(a,2,2))].">
      <j1 rule="para" parents="11020 11819"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,11820,a),flip(a)].">
      <j1 rule="hyper" parents="319 20 11820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      R(x,y * (a(z,u,z) \ 1),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(11534(a,1),11821(a,1,1))].">
      <j1 rule="para" parents="11534 11821"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      R(x,y / a(z,u,z),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(8677(a,1),11822(a,1,2))].">
      <j1 rule="para" parents="8677 11822"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      R(x,y * a(z,u,z),a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),11823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 11823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      R(x,y * a(z,u,z),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11535,a(flip),b,11824,a)].">
      <j1 rule="hyper" parents="64 11535 11824"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      R(x,a(y,z,y) \ u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[para(8512(a,1),11825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8512 11825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      R(x,((y \ 1) * y) \ z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2370(a,1),11827(a,1,2,1))].">
      <j1 rule="para" parents="2370 11827"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      R(x,((y \ 1) * y) \ (((z \ 1) \ 1) \ u),w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,8950,a(flip),b,11828,a),flip(a)].">
      <j1 rule="hyper" parents="319 8950 11828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      R(x,((y \ 1) \ ((z \ 1) * z)) \ u,w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9664(a,1),11829(a,1,2))].">
      <j1 rule="para" parents="9664 11829"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      R(x,(y / ((z \ 1) \ 1)) \ u,w) = R(x,(y / z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,9967,a(flip),b,11830,a)].">
      <j1 rule="hyper" parents="64 9967 11830"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      a(((x * y) \ x) \ 1,z,((x * y) \ x) \ 1) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(8595(a,1),10967(a,1,1))].">
      <j1 rule="para" parents="8595 10967"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L((a(y,w,y) \ v5) \ ((x \ L(y,w,y)) * v5),z,u)
    ]]></literal>
    <justification jstring="[para(11033(a,1),11258(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11033 11258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L((v5 \ ((x \ L(y,w,y)) * v5)) * a(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(11032(a,1),11836(a,2,2,1))].">
      <j1 rule="para" parents="11032 11836"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T((x \ L(y,w,y)) * a(y,w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(11008(a,1),11837(a,2,2,1))].">
      <j1 rule="para" parents="11008 11837"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T(x \ L(R(y,w,y),w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(11331(a,1),11839(a,2,2,1,1))].">
      <j1 rule="para" parents="11331 11839"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T(x \ y,v5),z,u)
    ]]></literal>
    <justification jstring="[para(3290(a,1),11840(a,2,2,1,1,2))].">
      <j1 rule="para" parents="3290 11840"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * (a(y,w,y) \ L(T(x \ y,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11023,a(flip),b,11841,a),flip(a)].">
      <j1 rule="hyper" parents="319 11023 11841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(a(y,w,y) \ T(x \ y,v5),z,u)
    ]]></literal>
    <justification jstring="[para(11349(a,2),11842(a,2,2))].">
      <j1 rule="para" parents="11349 11842"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(T(a(y,w,y) \ (x \ y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(11256(a,2),11843(a,2,2,1))].">
      <j1 rule="para" parents="11256 11843"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(T(x \ L(y,w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(11028(a,1),11844(a,2,2,1,1))].">
      <j1 rule="para" parents="11028 11844"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[hyper(319,a,242,a(flip),b,11845,a),flip(a)].">
      <j1 rule="hyper" parents="319 242 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      L(x \ y,z,u) * (a(y,w,y) \ v5) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[para(11033(a,1),11846(a,1,2))].">
      <j1 rule="para" parents="11033 11846"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,a(x,y,z) \ u),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(1453(a,1),11815(a,2,1))].">
      <j1 rule="para" parents="1453 11815"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,10996,a(flip),b,11849,a),flip(a)].">
      <j1 rule="hyper" parents="319 10996 11849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * R(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8675(a,1),11850(a,1,1))].">
      <j1 rule="para" parents="8675 11850"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(9685,a,11852,a)].">
      <j1 rule="hyper" parents="9685 11852"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11531,a(flip),b,11853,a),flip(a)].">
      <j1 rule="hyper" parents="64 11531 11853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      T(K(x,y \ ((z * u) * (u \ 1))),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(4691(a,1),7105(a,1,1))].">
      <j1 rule="para" parents="4691 7105"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(266(a,1),11855(a,1,1,2,2))].">
      <j1 rule="para" parents="266 11855"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((1 / L(y,z,u)) * ((x * (1 / (1 / L(y,z,u)))) / x))
    ]]></literal>
    <justification jstring="[para(3729(a,1),7977(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3729 7977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((1 / L(y,z,u)) * (1 / (1 / ((x * L(y,z,u)) / x))))
    ]]></literal>
    <justification jstring="[para(2393(a,1),11857(a,2,2,2))].">
      <j1 rule="para" parents="2393 11857"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((T(L(y,z,u),x) \ 1) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10561(a,1),11858(a,2,2))].">
      <j1 rule="para" parents="10561 11858"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(y,1 / y) * ((T(L(y,z,u),x) \ 1) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a(flip),b,11860,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 11860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5528,a(flip),b,11861,a),flip(a)].">
      <j1 rule="hyper" parents="319 5528 11861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ (1 / L(y,z,u)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3729(a,1),11862(a,1,2,2,2))].">
      <j1 rule="para" parents="3729 11862"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      K(x,1 / (K(y,1 / y) * (1 / L(y,z,u)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(4356(a,1),11863(a,1,2,2))].">
      <j1 rule="para" parents="4356 11863"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,1 / (1 / (1 / (1 / L(x,y,z)))))
    ]]></literal>
    <justification jstring="[para(8844(a,1),11865(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8844 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,T(L(x,y,z),1))
    ]]></literal>
    <justification jstring="[hyper(319,a,9174,a(flip),b,11866,a),flip(a)].">
      <j1 rule="hyper" parents="319 9174 11866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(208(a,1),11867(a,2,2))].">
      <j1 rule="para" parents="208 11867"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,L(x,u,w) * (1 / x)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3964(a,1),7994(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="3964 7994"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3759(a,1),11869(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3759 11869"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(6742(a,1),11870(a,1,2,1))].">
      <j1 rule="para" parents="6742 11870"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,T(z,L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8040(a,1),11871(a,1,2,1,2))].">
      <j1 rule="para" parents="8040 11871"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(6281(a,1),11872(a,1,2,1,2))].">
      <j1 rule="para" parents="6281 11872"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(7042(a,1),11873(a,1,2,1))].">
      <j1 rule="para" parents="7042 11873"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,L(x,u,w) * (1 / x))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3964(a,1),11875(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="3964 11875"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L(x,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3759(a,1),11876(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="3759 11876"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,x \ L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(6705(a,1),11877(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6705 11877"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8004(a,1),11878(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="8004 11878"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(z,x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(6140(a,1),11879(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="6140 11879"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(7032(a,1),11880(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7032 11880"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(4068(a,2),11882(a,1,2,2,1))].">
      <j1 rule="para" parents="4068 11882"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      (x \ 1) * T(K(x,K(y,z)) * L(T(x,K(y,z)),u,w),x \ 1) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(6686(a,2),11883(a,1,2))].">
      <j1 rule="para" parents="6686 11883"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      K(x,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6663,a(flip),b,11884,a)].">
      <j1 rule="hyper" parents="64 6663 11884"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z))
    ]]></literal>
    <justification jstring="[para(1196(a,1),11885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1196 11885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6785,a(flip),b,11886,a),flip(a)].">
      <j1 rule="hyper" parents="319 6785 11886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(T(x,K(y,z)),u,w) = T(x \ L(x,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(1063(a,1),11887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1063 11887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = T(x \ L(x,y,z),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10504,a,b,11888,a)].">
      <j1 rule="hyper" parents="64 10504 11888"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      T(x \ L(x,y,z),K(u,w * x)) = T(x \ L(x,y,z),K(u,w))
    ]]></literal>
    <justification jstring="[para(1063(a,1),11889(a,1,1))].">
      <j1 rule="para" parents="1063 11889"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(w * x,u))
    ]]></literal>
    <justification jstring="[para(11890(a,1),10601(a,1,2))].">
      <j1 rule="para" parents="11890 10601"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(x \ L(x,y,z),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(10602,a,11891,a),flip(a)].">
      <j1 rule="hyper" parents="10602 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,x \ L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(11892(a,2),6780(a,1))].">
      <j1 rule="para" parents="11892 6780"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      K(x,K(y * z,y \ L(y,u,w))) = K(z,K(x,y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(11893,a,10494,a),flip(a)].">
      <j1 rule="hyper" parents="11893 10494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      K(x,K(y * z,y \ L(y,u,w))) = K(x,K(z,y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6742,a,b,11894,a),flip(a)].">
      <j1 rule="hyper" parents="319 6742 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      K(x,K(y * z,z \ L(z,u,w))) = K(x,K(y,z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(10495,a,11895,a)].">
      <j1 rule="hyper" parents="10495 11895"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K(y * z,u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10496,a,b,11896,a)].">
      <j1 rule="hyper" parents="64 10496 11896"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,11477,a(flip),b,11897,a),flip(a)].">
      <j1 rule="hyper" parents="319 11477 11897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(6978,a,11898,a)].">
      <j1 rule="hyper" parents="6978 11898"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = w
    ]]></literal>
    <justification jstring="[para(11898(a,1),6978(a,1))].">
      <j1 rule="para" parents="11898 6978"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,6739,a,b,11899,a)].">
      <j1 rule="hyper" parents="64 6739 11899"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(u,K(x * y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10645,a,b,11901,a)].">
      <j1 rule="hyper" parents="64 10645 11901"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T((y * z) * u,y * (z * u)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(7607,a,11902,a)].">
      <j1 rule="hyper" parents="7607 11902"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      a(K(x,K(y,(y * z) * u)),z,u) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11732,a(flip),b,11903,a)].">
      <j1 rule="hyper" parents="64 11732 11903"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7583(a,1),11904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7583 11904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,10462,a(flip),b,11905,a),flip(a)].">
      <j1 rule="hyper" parents="319 10462 11905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(11900,a,11906,a)].">
      <j1 rule="hyper" parents="11900 11906"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(11907(a,1),7845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11907 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a(flip),b,11910,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 11910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7675,a,b,11911,a)].">
      <j1 rule="hyper" parents="64 7675 11911"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      R(a(K(x,y),z * y,u),R(y,z,u),z * u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11567(a,2),11913(a,1,1))].">
      <j1 rule="para" parents="11567 11913"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      a(K(x,R(y,R(y,z,u),z * u)),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11696,a,b,11914,a)].">
      <j1 rule="hyper" parents="64 11696 11914"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11698,a(flip),b,11915,a)].">
      <j1 rule="hyper" parents="64 11698 11915"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11670,a(flip),b,11916,a)].">
      <j1 rule="hyper" parents="64 11670 11916"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11567,a(flip),b,11916,a)].">
      <j1 rule="hyper" parents="64 11567 11916"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11570,a,b,11918,a),flip(a)].">
      <j1 rule="hyper" parents="319 11570 11918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      a(K(x,y),z,z) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,11576,a(flip),b,11918,a),flip(a)].">
      <j1 rule="hyper" parents="319 11576 11918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      L(x,x,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,11921,a)].">
      <j1 rule="hyper" parents="53 11921"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      L(x \ 1,x,K(y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9570,a(flip),b,11922,a)].">
      <j1 rule="hyper" parents="64 9570 11922"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(206,a,11922,a(flip),b,9562,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 11922 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      (K(x,y) * z) * z = K(x,y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,11922,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="131 11922 18"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(512,a,11923,a)].">
      <j1 rule="hyper" parents="512 11923"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(206,a,11923,a(flip),b,224,a(flip))].">
      <j1 rule="hyper" parents="206 11923 224"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,8777,a(flip),b,11920,a),flip(a)].">
      <j1 rule="hyper" parents="319 8777 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3153,a(flip),b,11920,a),flip(a)].">
      <j1 rule="hyper" parents="64 3153 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(K(z,w),u,v5)
    ]]></literal>
    <justification jstring="[para(11920(a,1),10553(a,1,1,2))].">
      <j1 rule="para" parents="11920 10553"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(10213,a,11931,a)].">
      <j1 rule="hyper" parents="10213 11931"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,1957,a,b,11931,a)].">
      <j1 rule="hyper" parents="64 1957 11931"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      K(a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,11589,a(flip),b,11931,a)].">
      <j1 rule="hyper" parents="64 11589 11931"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,11931,a)].">
      <j1 rule="hyper" parents="53 11931"/>
    </justification>
  </clause>

  <clause id="11937">
    <literal><![CDATA[
      T(a(x,x,y),z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(57,a,11935,a)].">
      <j1 rule="hyper" parents="57 11935"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      a(K(x,y * z),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,10924,a(flip),b,11930,a)].">
      <j1 rule="hyper" parents="64 10924 11930"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      L(x,y,K(y * x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,11930,a)].">
      <j1 rule="hyper" parents="53 11930"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      K(x,L(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10130,a,11936,a)].">
      <j1 rule="hyper" parents="10130 11936"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9601,a,11936,a)].">
      <j1 rule="hyper" parents="9601 11936"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      K(L(x,y,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10129,a(flip),b,11936,a)].">
      <j1 rule="hyper" parents="64 10129 11936"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      K(x,(y * y) \ z) = K(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10117,a(flip),b,11936,a)].">
      <j1 rule="hyper" parents="64 10117 11936"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5275,a(flip),b,11936,a),flip(a)].">
      <j1 rule="hyper" parents="64 5275 11936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,11936,a(flip),b,1895,a),flip(a)].">
      <j1 rule="hyper" parents="127 11936 1895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11949">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,11936,a(flip),b,461,a)].">
      <j1 rule="hyper" parents="127 11936 461"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,11938,a)].">
      <j1 rule="hyper" parents="53 11938"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),11939(a,1,3,1))].">
      <j1 rule="para" parents="10 11939"/>
    </justification>
  </clause>

  <clause id="11953">
    <literal><![CDATA[
      T(x,L(y,z,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,11942,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11942 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      T(x,L(y,z,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,11942,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 11942 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(466(a,1),11942(a,1,2))].">
      <j1 rule="para" parents="466 11942"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(469(a,1),11942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 11942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1584(a,1),11942(a,1,2))].">
      <j1 rule="para" parents="1584 11942"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1584(a,2),11942(a,1,2))].">
      <j1 rule="para" parents="1584 11942"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(466(a,1),11945(a,1,1))].">
      <j1 rule="para" parents="466 11945"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      K((x * x) \ y,z) = K(x \ (x \ y),z)
    ]]></literal>
    <justification jstring="[para(302(a,1),11945(a,1,1))].">
      <j1 rule="para" parents="302 11945"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(469(a,1),11945(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 11945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),11950(a,1,3,2))].">
      <j1 rule="para" parents="10 11950"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[para(9271(a,1),11950(a,1,3))].">
      <j1 rule="para" parents="9271 11950"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      T(x,(((y * y) \ y) * ((y * y) \ y)) * z) = T(T(x,z),y \ ((y * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1049,a,b,11953,a)].">
      <j1 rule="hyper" parents="64 1049 11953"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(466(a,1),11953(a,1,2))].">
      <j1 rule="para" parents="466 11953"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      T(x,(y * y) \ z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(302(a,1),11953(a,1,2))].">
      <j1 rule="para" parents="302 11953"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(469(a,1),11953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),11963(a,1,3,2))].">
      <j1 rule="para" parents="10 11963"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      L(x,x \ T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(6158(a,1),11968(a,1,3))].">
      <j1 rule="para" parents="6158 11968"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      T(x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,11937,a)].">
      <j1 rule="hyper" parents="55 11937"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[para(1960(a,2),11970(a,1,2))].">
      <j1 rule="para" parents="1960 11970"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(6413,a,11971,a),flip(a)].">
      <j1 rule="hyper" parents="6413 11971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5520,a,11943,a)].">
      <j1 rule="hyper" parents="5520 11943"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10220,a(flip),b,11943,a),flip(a)].">
      <j1 rule="hyper" parents="64 10220 11943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,4123,a(flip),b,11952,a)].">
      <j1 rule="hyper" parents="64 4123 11952"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(206,a,11952,a(flip),b,4123,a(flip))].">
      <j1 rule="hyper" parents="206 11952 4123"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,11952,a(flip),b,4123,a(flip))].">
      <j1 rule="hyper" parents="131 11952 4123"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      T(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(11954(a,2),4089(a,1))].">
      <j1 rule="para" parents="11954 4089"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(620(a,1),11957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="620 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(621(a,1),11957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="621 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11688,a,b,11958,a)].">
      <j1 rule="hyper" parents="64 11688 11958"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11687,a,b,11958,a)].">
      <j1 rule="hyper" parents="64 11687 11958"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11689,a(flip),b,11958,a)].">
      <j1 rule="hyper" parents="64 11689 11958"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(10856,a,11962,a)].">
      <j1 rule="hyper" parents="10856 11962"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,11962,a(flip),b,2837,a(flip))].">
      <j1 rule="hyper" parents="131 11962 2837"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,11981,a,b,11982,a),flip(a)].">
      <j1 rule="hyper" parents="319 11981 11982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,11958,a,b,11982,a),flip(a)].">
      <j1 rule="hyper" parents="319 11958 11982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(4374,a,11924,a)].">
      <j1 rule="hyper" parents="4374 11924"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,11924,a(flip),b,9181,a)].">
      <j1 rule="hyper" parents="131 11924 9181"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(11924(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="11924 5822"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (K(z,z \ u) / w)))
    ]]></literal>
    <justification jstring="[para(11924(a,1),4809(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11924 4809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      (T(x,y) * z) \ K(x,y) = (x * z) \ 1
    ]]></literal>
    <justification jstring="[para(4081(a,1),11926(a,1,1))].">
      <j1 rule="para" parents="4081 11926"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),11926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ (K(x,y) / (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(11926(a,1),4148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11926 4148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4292(a,1),11926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4292 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(z,y) = (x * K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(4367(a,1),11926(a,1,1))].">
      <j1 rule="para" parents="4367 11926"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      ((x * y) \ z) \ K(y,x) = ((y * x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(9187(a,1),11926(a,1,1))].">
      <j1 rule="para" parents="9187 11926"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,4314,a(flip),b,11929,a)].">
      <j1 rule="hyper" parents="130 4314 11929"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(7152,a,11948,a),flip(a)].">
      <j1 rule="hyper" parents="7152 11948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      x * ((y \ 1) * K(z,u)) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,11948,a,b,9,a)].">
      <j1 rule="hyper" parents="131 11948 9"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      (x \ 1) * (y * K(z,y)) = (x \ K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(130,a,11948,a(flip),b,7623,a),flip(a)].">
      <j1 rule="hyper" parents="130 11948 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,11948,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="130 11948 4915"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(11948(a,1),627(a,1))].">
      <j1 rule="para" parents="11948 627"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (u \ 1),u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(11948(a,1),708(a,2,2))].">
      <j1 rule="para" parents="11948 708"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(11948(a,1),3778(a,2,2,2))].">
      <j1 rule="para" parents="11948 3778"/>
    </justification>
  </clause>

  <clause id="12018">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(11948(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="11948 5176"/>
    </justification>
  </clause>

  <clause id="12020">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(11948(a,1),5175(a,1,1))].">
      <j1 rule="para" parents="11948 5175"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,L(w,L(x,y,z) \ 1,x)) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[para(11948(a,1),10179(a,2,2))].">
      <j1 rule="para" parents="11948 10179"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[hyper(206,a,5172,a(flip),b,11949,a),flip(a)].">
      <j1 rule="hyper" parents="206 5172 11949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      K(x * ((y \ 1) \ K(z,u)),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(11949(a,1),3903(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11949 3903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4604,a(flip),b,11955,a),flip(a)].">
      <j1 rule="hyper" parents="64 4604 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4601,a(flip),b,11955,a)].">
      <j1 rule="hyper" parents="64 4601 11955"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(11230,a,11956,a),flip(a)].">
      <j1 rule="hyper" parents="11230 11956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,9269,a,b,11956,a)].">
      <j1 rule="hyper" parents="319 9269 11956"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,z * L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11263,a,b,11956,a)].">
      <j1 rule="hyper" parents="64 11263 11956"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(11956(a,1),10096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11956 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(11956(a,1),11162(a,1))].">
      <j1 rule="para" parents="11956 11162"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      (1 / x) \ K(y,z * u) = x * K(y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11956(a,1),11949(a,1,2))].">
      <j1 rule="para" parents="11956 11949"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3874,a(flip),b,11959,a),flip(a)].">
      <j1 rule="hyper" parents="64 3874 11959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3871,a(flip),b,11959,a)].">
      <j1 rule="hyper" parents="64 3871 11959"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,9720,a(flip),b,11961,a)].">
      <j1 rule="hyper" parents="64 9720 11961"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(11961(a,1),4259(a,1,1,2))].">
      <j1 rule="para" parents="11961 4259"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11961(a,1),4983(a,2,2))].">
      <j1 rule="para" parents="11961 4983"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11961(a,1),4988(a,1,2,2))].">
      <j1 rule="para" parents="11961 4988"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11961(a,1),5127(a,1,1,2))].">
      <j1 rule="para" parents="11961 5127"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(11961(a,1),6671(a,1,1,2))].">
      <j1 rule="para" parents="11961 6671"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(11961(a,1),7483(a,1))].">
      <j1 rule="para" parents="11961 7483"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(11961(a,1),10789(a,1,3))].">
      <j1 rule="para" parents="11961 10789"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(11961(a,1),11751(a,1,2))].">
      <j1 rule="para" parents="11961 11751"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3751,a(flip),b,11965,a),flip(a)].">
      <j1 rule="hyper" parents="64 3751 11965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12053">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3748,a(flip),b,11965,a)].">
      <j1 rule="hyper" parents="64 3748 11965"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      T(1 / (1 / x),x \ y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3347,a(flip),b,11965,a),flip(a)].">
      <j1 rule="hyper" parents="64 3347 11965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      T(x,((y \ 1) \ y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(816(a,1),11967(a,1,2))].">
      <j1 rule="para" parents="816 11967"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(206,a,81,a(flip),b,11975,a),flip(a)].">
      <j1 rule="hyper" parents="206 81 11975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4041(a,1),11975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4041 11975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      (T(x,y) * z) \ T(x,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(4081(a,1),11975(a,1,1))].">
      <j1 rule="para" parents="4081 11975"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(4356(a,2),11975(a,1,1))].">
      <j1 rule="para" parents="4356 11975"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),11975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 11975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(10806(a,1),11975(a,1,1))].">
      <j1 rule="para" parents="10806 11975"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      R(x,y,z \ T(K(u,w) * v5,T(u,w))) = R(x,y,z \ ((v5 \ u) \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(11975(a,1),11539(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="11975 11539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[para(11924(a,1),11975(a,1,1))].">
      <j1 rule="para" parents="11924 11975"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(3841,a,11976,a)].">
      <j1 rule="hyper" parents="3841 11976"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      T(x,y) / ((y \ z) \ x) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(319,a,4314,a(flip),b,11976,a),flip(a)].">
      <j1 rule="hyper" parents="319 4314 11976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,4314,a(flip),b,11976,a)].">
      <j1 rule="hyper" parents="130 4314 11976"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * x) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,11976,a(flip),b,3798,a)].">
      <j1 rule="hyper" parents="131 11976 3798"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      L(x,T(y,z) / (u \ y),w) = L(x,K(y,y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(11976(a,1),11775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11976 11775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      a(T(T(x,y),K(x,y) * z),u,w) = a((z \ x) * (K(x,y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(11977(a,1),10906(a,1,1,1))].">
      <j1 rule="para" parents="11977 10906"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      a(x,y,T(T(z,u),K(z,u) * w)) = a(x,y,(w \ z) * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(11977(a,1),11522(a,1,3,1))].">
      <j1 rule="para" parents="11977 11522"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      T(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(466(a,1),11978(a,1,2))].">
      <j1 rule="para" parents="466 11978"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(302(a,1),11978(a,1,2))].">
      <j1 rule="para" parents="302 11978"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,11983,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11983 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4594,a,b,11983,a)].">
      <j1 rule="hyper" parents="64 4594 11983"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4596,a(flip),b,11983,a),flip(a)].">
      <j1 rule="hyper" parents="64 4596 11983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),11983(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 11983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,192,a(flip),b,11991,a),flip(a)].">
      <j1 rule="hyper" parents="64 192 11991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(11991(a,1),4375(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11991 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,u) * w)) \ v5) = L(x,y,(w \ K(u,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(11997(a,1),2552(a,2,3,1))].">
      <j1 rule="para" parents="11997 2552"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      L(x,y,z / (1 / (K(u,w) * v5))) = L(x,y,z / (v5 \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(11997(a,1),2723(a,2,3,2))].">
      <j1 rule="para" parents="11997 2723"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      K(x,y / (((z \ K(u,w)) \ 1) * v5)) = K(x,y / ((K(w,u) * z) * v5))
    ]]></literal>
    <justification jstring="[para(11997(a,1),4686(a,1,2,2,1,1))].">
      <j1 rule="para" parents="11997 4686"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      T(x,y \ ((1 / (K(z,u) * w)) \ v5)) = T(x,y \ ((w \ K(u,z)) \ v5))
    ]]></literal>
    <justification jstring="[para(11997(a,1),4792(a,2,2,2,1))].">
      <j1 rule="para" parents="11997 4792"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      (x * y) \ K(z,T(y,x)) = (x * T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(7092(a,1),11997(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7092 11997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(11997(a,1),11983(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11997 11983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(12018(a,1),343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12018 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      (x \ K(y,z * (y \ u))) \ (x \ 1) = K((y \ z) * u,y)
    ]]></literal>
    <justification jstring="[para(11623(a,1),12018(a,1,1,2))].">
      <j1 rule="para" parents="11623 12018"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(12023(a,1),111(a,1,1))].">
      <j1 rule="para" parents="12023 111"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(12023(a,1),4612(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12023 4612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      K(x,y) / (1 / y) = 1 / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(4916(a,1),12023(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4916 12023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(12023(a,1),5344(a,1,2,1,2,2))].">
      <j1 rule="para" parents="12023 5344"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(6055(a,2),12023(a,1,2))].">
      <j1 rule="para" parents="6055 12023"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),12026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[para(4288(a,1),12026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4288 12026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(12026(a,1),10096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12026 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      K(x,y \ L(x,z,u)) = K(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,10075,a(flip),b,12027,a),flip(a)].">
      <j1 rule="hyper" parents="64 10075 12027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,9290,a,b,12037,a),flip(a)].">
      <j1 rule="hyper" parents="319 9290 12037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(9296,a,12038,a),flip(a)].">
      <j1 rule="hyper" parents="9296 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,9298,a(flip),b,12038,a),flip(a)].">
      <j1 rule="hyper" parents="64 9298 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12038(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      T(T(x,(y \ 1) * z),K(y \ z,u)) = T(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(12038(a,1),6392(a,1,2))].">
      <j1 rule="para" parents="12038 6392"/>
    </justification>
  </clause>

  <clause id="12111">
    <literal><![CDATA[
      T(x,y \ L(z,y,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1899(a,2),12053(a,1,2))].">
      <j1 rule="para" parents="1899 12053"/>
    </justification>
  </clause>

  <clause id="12113">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,y \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(12053(a,1),6989(a,1,2))].">
      <j1 rule="para" parents="12053 6989"/>
    </justification>
  </clause>

  <clause id="12115">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(4393,a,12057,a)].">
      <j1 rule="hyper" parents="4393 12057"/>
    </justification>
  </clause>

  <clause id="12116">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(4374,a,12057,a)].">
      <j1 rule="hyper" parents="4374 12057"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      (x / y) \ (T(x,z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,12057,a(flip),b,7156,a)].">
      <j1 rule="hyper" parents="127 12057 7156"/>
    </justification>
  </clause>

  <clause id="12119">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(12057(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="12057 5822"/>
    </justification>
  </clause>

  <clause id="12120">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(12057(a,1),9203(a,1,1))].">
      <j1 rule="para" parents="12057 9203"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12057(a,1),11397(a,2,2))].">
      <j1 rule="para" parents="12057 11397"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(206,a,12060,a(flip),b,10945,a(flip))].">
      <j1 rule="hyper" parents="206 12060 10945"/>
    </justification>
  </clause>

  <clause id="12123">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(3108(a,1),12060(a,1,1))].">
      <j1 rule="para" parents="3108 12060"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(429,a,xx,b,12061,a)].">
      <j1 rule="hyper" parents="429 12061"/>
    </justification>
  </clause>

  <clause id="12126">
    <literal><![CDATA[
      T((x \ T(y,z)) \ T(y,x),y) = ((K(z,y) * x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(12061(a,1),5817(a,1,1,1))].">
      <j1 rule="para" parents="12061 5817"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(9295(a,1),12061(a,1,1))].">
      <j1 rule="para" parents="9295 12061"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(9581(a,1),12061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9581 12061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3753,a,b,12075,a)].">
      <j1 rule="hyper" parents="64 3753 12075"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12053,a(flip),b,12075,a),flip(a)].">
      <j1 rule="hyper" parents="64 12053 12075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      T(x,y * ((z * z) * (u \ 1))) = T(x,(y * (z * z)) / u)
    ]]></literal>
    <justification jstring="[para(34(a,1),12075(a,1,2))].">
      <j1 rule="para" parents="34 12075"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),12075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 12075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      T(x,y / ((z * z) \ u)) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(591(a,1),12075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="591 12075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      T(x,y * ((z * z) * (u \ 1))) = T(x,y / (u / (z * z)))
    ]]></literal>
    <justification jstring="[para(414(a,1),12075(a,1,2,2))].">
      <j1 rule="para" parents="414 12075"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(12075(a,1),646(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12075 646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(11997(a,1),12075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11997 12075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(6890,a,12076,a),flip(a)].">
      <j1 rule="hyper" parents="6890 12076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12139">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(12076(a,1),6861(a,1,2,2))].">
      <j1 rule="para" parents="12076 6861"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12077,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12077 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(12077(a,1),4361(a,1,1))].">
      <j1 rule="para" parents="12077 4361"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(12077(a,1),10096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12077 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(12023(a,1),12078(a,1,2,2))].">
      <j1 rule="para" parents="12023 12078"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      1 / (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) / x = u
    ]]></literal>
    <justification jstring="[para(12087(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12087 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(12087(a,1),8911(a,1,1,1,2))].">
      <j1 rule="para" parents="12087 8911"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,u * ((1 / u) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,11957,a,b,12096,a)].">
      <j1 rule="hyper" parents="319 11957 12096"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,3872,a,b,12108,a),flip(a)].">
      <j1 rule="hyper" parents="319 3872 12108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ 1) = T(x,(y / u) \ K(z,y))
    ]]></literal>
    <justification jstring="[para(12115(a,1),5058(a,1,2,1))].">
      <j1 rule="para" parents="12115 5058"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      K(x,T(y,z)) \ ((z * (y / z)) / u) = T(z * (y / z),x) / u
    ]]></literal>
    <justification jstring="[para(9282(a,1),12115(a,1,1))].">
      <j1 rule="para" parents="9282 12115"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(110(a,1),12116(a,1,2,1))].">
      <j1 rule="para" parents="110 12116"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(12116(a,1),4375(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12116 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(12116(a,1),5870(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12116 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(12079(a,1),12130(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12079 12130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z / (1 / u))) = T(x,(z / (1 / u)) * y)
    ]]></literal>
    <justification jstring="[para(12133(a,1),9307(a,1,2,1))].">
      <j1 rule="para" parents="12133 9307"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(12140(a,1),7150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12140 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      K(x,R(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,11661,a,b,11925,a(flip))].">
      <j1 rule="hyper" parents="36 11661 11925"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      K(R(x,y,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11660,a,b,12161,a)].">
      <j1 rule="hyper" parents="64 11660 12161"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4784(a,1),12163(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4784 12163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,11961,a,b,12164,a),flip(a)].">
      <j1 rule="hyper" parents="319 11961 12164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3876,a(flip),b,12164,a)].">
      <j1 rule="hyper" parents="64 3876 12164"/>
    </justification>
  </clause>

  <clause id="12167">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),12164(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 12164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12168">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),12166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 12166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),12166(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="81 12166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      K((x \ 1) / y,z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12038,a(flip),b,12167,a),flip(a)].">
      <j1 rule="hyper" parents="64 12038 12167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y * (x * (y \ 1)),z) = K(x,z) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12168(a,1),9295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12168 9295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11947,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11947 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      T(x,y \ ((z * z) * T(u,z \ (z \ y)))) = T(x,u / ((z * z) \ y))
    ]]></literal>
    <justification jstring="[para(11966(a,1),11181(a,1,2,2,2))].">
      <j1 rule="para" parents="11966 11181"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,11973,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 11973 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(11319,a,11974,a),flip(a)].">
      <j1 rule="hyper" parents="11319 11974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      K(x \ ((x / y) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(81(a,1),11974(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="81 11974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(356,a,11985,a)].">
      <j1 rule="hyper" parents="356 11985"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(11991(a,1),11985(a,1,1))].">
      <j1 rule="para" parents="11991 11985"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      T(x,(y \ z) \ K(y,u)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(11999(a,1),5058(a,1,2))].">
      <j1 rule="para" parents="11999 5058"/>
    </justification>
  </clause>

  <clause id="12181">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(11999(a,1),5247(a,1,1))].">
      <j1 rule="para" parents="11999 5247"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(11999(a,1),11983(a,1,2,2))].">
      <j1 rule="para" parents="11999 11983"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(((y \ z) \ 1) / x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12002(a,1),9274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12002 9274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[para(6845(a,1),12003(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6845 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      K(x,y * z) * (z \ 1) = z \ K(x,z * y)
    ]]></literal>
    <justification jstring="[para(9275(a,1),12003(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9275 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(12009(a,2),12038(a,1,1))].">
      <j1 rule="para" parents="12009 12038"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(12029(a,1),9328(a,1))].">
      <j1 rule="para" parents="12029 9328"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,12043,a(flip),b,3797,a)].">
      <j1 rule="hyper" parents="130 12043 3797"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(12043(a,1),509(a,1,1))].">
      <j1 rule="para" parents="12043 509"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(12043(a,2),5176(a,1,1))].">
      <j1 rule="para" parents="12043 5176"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(12043(a,2),5187(a,1,1))].">
      <j1 rule="para" parents="12043 5187"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9290(a,1),12043(a,2,2))].">
      <j1 rule="para" parents="9290 12043"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(10180,a,12044,a)].">
      <j1 rule="hyper" parents="10180 12044"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,12198,a(flip),b,472,a),flip(a)].">
      <j1 rule="hyper" parents="206 12198 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,12198,a(flip),b,472,a)].">
      <j1 rule="hyper" parents="131 12198 472"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      T(x * y,(x * y) \ z) = T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(302(a,1),12198(a,1,2))].">
      <j1 rule="para" parents="302 12198"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3560,a,b,12054,a)].">
      <j1 rule="hyper" parents="64 3560 12054"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3103(a,1),12058(a,1,1))].">
      <j1 rule="para" parents="3103 12058"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      (T(K(x,y),z * K(x,y)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6800(a,1),12058(a,2,2))].">
      <j1 rule="para" parents="6800 12058"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ T(y,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u) * z,T(y,u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(12059(a,1),11267(a,1,2,1,1))].">
      <j1 rule="para" parents="12059 11267"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) \ K(y,T(z,x)) = (x \ u) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,6099,a,b,12067,a)].">
      <j1 rule="hyper" parents="127 6099 12067"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(12092(a,1),4402(a,1,1))].">
      <j1 rule="para" parents="12092 4402"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(12102(a,2),9296(a,1))].">
      <j1 rule="para" parents="12102 9296"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(12103(a,1),6984(a,1))].">
      <j1 rule="para" parents="12103 6984"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,(x / z) \ (T(x,y) / z)) = (K(x,T(y,z)) * (x / z)) \ 1
    ]]></literal>
    <justification jstring="[para(12118(a,1),9212(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12118 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a(flip),b,12122,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 12122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      T(K(x,(y * K(z \ u,z)) * w),w \ T(w * (y * K(z \ u,z)),x)) = (w \ T(w * (y * K(z \ u,z)),x)) \ ((y / (u / z)) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(417,a,5233,a,b,12141,a)].">
      <j1 rule="hyper" parents="417 5233 12141"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      T(K(x,(y * K(z,z \ u)) * w),w \ T(w * (y * K(z,z \ u)),x)) = (w \ T(w * (y * K(z,z \ u)),x)) \ ((y / z) * ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(417,a,4935,a,b,12141,a)].">
      <j1 rule="hyper" parents="417 4935 12141"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      T(K(x,K(y \ (z * (u \ 1)),w) * v5),v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) = (v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) \ K(y \ (z * (1 / u)),w)
    ]]></literal>
    <justification jstring="[hyper(417,a,3907,a,b,12141,a)].">
      <j1 rule="hyper" parents="417 3907 12141"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(10088,a,12175,a),flip(a)].">
      <j1 rule="hyper" parents="10088 12175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),12175(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),12177(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[para(4097(a,1),12178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4097 12178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      T(K(x,y) * (y / T(z,K(x,y))),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(12178(a,1),5157(a,1,1))].">
      <j1 rule="para" parents="12178 5157"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),12191(a,1,1,2,1))].">
      <j1 rule="para" parents="12 12191"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(131,a,12209,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 12209 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(199,a,12213,a)].">
      <j1 rule="hyper" parents="199 12213"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(81(a,1),12213(a,1,2)),flip(a)].">
      <j1 rule="para" parents="81 12213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = (x * y) / a(y / z,z,x)
    ]]></literal>
    <justification jstring="[para(87(a,1),12213(a,1,2)),flip(a)].">
      <j1 rule="para" parents="87 12213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8780,a(flip),b,12217,a),flip(a)].">
      <j1 rule="hyper" parents="64 8780 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      K((1 / x) \ ((x * y) \ z),L(y,x,x \ 1)) = K(L(y,x,x \ 1) \ z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1594(a,1),12218(a,1,1,2,1))].">
      <j1 rule="para" parents="1594 12218"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),12219(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      K((x \ 1) \ ((y * x) \ z),R(y,x,x \ 1)) = K(R(y,x,x \ 1) \ z,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(419(a,1),12219(a,1,1,2,1))].">
      <j1 rule="para" parents="419 12219"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,3585,a(flip),b,12224,a),flip(a)].">
      <j1 rule="hyper" parents="40 3585 12224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      (T(x,y) / z) \ (x * y) = (x / z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(12057(a,1),12224(a,1,1))].">
      <j1 rule="para" parents="12057 12224"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(12225(a,1),11926(a,1,1))].">
      <j1 rule="para" parents="12225 11926"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(12225(a,1),11975(a,1,1))].">
      <j1 rule="para" parents="12225 11975"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(7354,a,12227,a)].">
      <j1 rule="hyper" parents="7354 12227"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(198(a,1),12235(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="198 12235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4508,a(flip),b,11984,a)].">
      <j1 rule="hyper" parents="64 4508 11984"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(3270(a,1),11984(a,2,2))].">
      <j1 rule="para" parents="3270 11984"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (z \ K(y,x)) * K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(12079(a,1),12012(a,1,1))].">
      <j1 rule="para" parents="12079 12012"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4601(a,2),12034(a,1))].">
      <j1 rule="para" parents="4601 12034"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,z) / y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(12087(a,1),12034(a,1,2,1))].">
      <j1 rule="para" parents="12087 12034"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3871(a,2),12049(a,1))].">
      <j1 rule="para" parents="3871 12049"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12009(a,2),12049(a,1,1))].">
      <j1 rule="para" parents="12009 12049"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3748(a,1),12072(a,1))].">
      <j1 rule="para" parents="3748 12072"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(4023(a,2),12080(a,1,2))].">
      <j1 rule="para" parents="4023 12080"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      K(x,y \ L(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4489,a(flip),b,12099,a),flip(a)].">
      <j1 rule="hyper" parents="319 4489 12099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      1 / x != y
    ]]></literal>
    <literal><![CDATA[
      K(z,u) / (x * K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(5172(a,1),12145(a,1,2))].">
      <j1 rule="para" parents="5172 12145"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = u
    ]]></literal>
    <justification jstring="[para(3267(a,1),12154(a,1,2))].">
      <j1 rule="para" parents="3267 12154"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4602(a,2),12190(a,1))].">
      <j1 rule="para" parents="4602 12190"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9360(a,2),12190(a,1))].">
      <j1 rule="para" parents="9360 12190"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(11368(a,2),12190(a,1,2))].">
      <j1 rule="para" parents="11368 12190"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(130,a,12200,a,b,5146,a),flip(a)].">
      <j1 rule="hyper" parents="130 12200 5146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = L(y,K(z,T(u,y)),x)
    ]]></literal>
    <justification jstring="[para(6839(a,1),12200(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6839 12200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,12201,a(flip),b,10264,a),flip(a)].">
      <j1 rule="hyper" parents="128 12201 10264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(12201(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12201 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      L(K(x,y),z / y,u) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(5163(a,1),12201(a,2,2))].">
      <j1 rule="para" parents="5163 12201"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,3327,a(flip),b,12203,a),flip(a)].">
      <j1 rule="hyper" parents="319 3327 12203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(3873(a,1),12210(a,1))].">
      <j1 rule="para" parents="3873 12210"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z \ K(y,x)) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(12079(a,1),12210(a,1,1,1))].">
      <j1 rule="para" parents="12079 12210"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      K(x * (y * K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / (K(u,z) / y),w) = v5
    ]]></literal>
    <justification jstring="[para(12087(a,1),12211(a,1,1,2))].">
      <j1 rule="para" parents="12087 12211"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ K(z,y)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(12079(a,1),12240(a,1,2,1))].">
      <j1 rule="para" parents="12079 12240"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z \ K(y,x)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(12079(a,1),12242(a,1,1,1))].">
      <j1 rule="para" parents="12079 12242"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(11967(a,2),12244(a,1))].">
      <j1 rule="para" parents="11967 12244"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(12247,a,11559,a)].">
      <j1 rule="hyper" parents="12247 11559"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      K(x,L((y * z) \ y,u,w) * z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1786(a,1),12249(a,1,2))].">
      <j1 rule="para" parents="1786 12249"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      T(L(x,x,x),(1 / x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1904,a,b,12260,a)].">
      <j1 rule="hyper" parents="64 1904 12260"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(12165(a,2),12261(a,1))].">
      <j1 rule="para" parents="12165 12261"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      T(L(x,x,x),x \ y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(12072,a,12269,a)].">
      <j1 rule="hyper" parents="12072 12269"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      (L(x,x,x) \ y) \ y = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9418,a(flip),b,12271,a)].">
      <j1 rule="hyper" parents="64 9418 12271"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      (L(x / y,x / y,x / y) \ y) \ y = T(x / y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),12272(a,2,2))].">
      <j1 rule="para" parents="12 12272"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      K(x / (K(y,z) / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (u * K(z,y)),w) = v5
    ]]></literal>
    <justification jstring="[para(12023(a,1),12270(a,1,1,2))].">
      <j1 rule="para" parents="12023 12270"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (u \ K(z,y)),w) = v5
    ]]></literal>
    <justification jstring="[para(12079(a,1),12270(a,1,1,2))].">
      <j1 rule="para" parents="12079 12270"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11989(a,1),536(a,1))].">
      <j1 rule="para" parents="11989 536"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(538(a,1),12276(a,1,2))].">
      <j1 rule="para" parents="538 12276"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(625(a,1),12276(a,1,2))].">
      <j1 rule="para" parents="625 12276"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11688(a,1),12276(a,1))].">
      <j1 rule="para" parents="11688 12276"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1589(a,1),12281(a,1,2))].">
      <j1 rule="para" parents="1589 12281"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(9663(a,1),12283(a,1,2))].">
      <j1 rule="para" parents="9663 12283"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(10133(a,2),12283(a,1))].">
      <j1 rule="para" parents="10133 12283"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      K(K(x,y \ 1) * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y \ 1,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(9663(a,1),12285(a,1,1))].">
      <j1 rule="para" parents="9663 12285"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(4024(a,1),12279(a,1,2,2))].">
      <j1 rule="para" parents="4024 12279"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      K(x,y * (K(z,y) * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = w
    ]]></literal>
    <justification jstring="[para(4526(a,1),12279(a,1,2))].">
      <j1 rule="para" parents="4526 12279"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(4594(a,2),12279(a,1))].">
      <j1 rule="para" parents="4594 12279"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(11999(a,1),12279(a,1,2,2))].">
      <j1 rule="para" parents="11999 12279"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(12023(a,1),12289(a,1,2,2))].">
      <j1 rule="para" parents="12023 12289"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10478,a(flip),b,11994,a)].">
      <j1 rule="hyper" parents="64 10478 11994"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(11994(a,1),10479(a,1,1))].">
      <j1 rule="para" parents="11994 10479"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(11994(a,1),11111(a,1,2,2))].">
      <j1 rule="para" parents="11994 11111"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(12023(a,2),11994(a,1,1))].">
      <j1 rule="para" parents="12023 11994"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(111(a,1),12294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 12294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),1 / u,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(12294(a,2),708(a,2,2))].">
      <j1 rule="para" parents="12294 708"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      (x / ((y \ x) * y)) \ ((((y \ x) * y) \ 1) \ (((y \ x) * y) \ x)) = R((y \ x) * y,((y \ x) * y) \ 1,((y * (y \ x)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(12001(a,1),4896(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12001 4896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5128,a(flip),b,12008,a),flip(a)].">
      <j1 rule="hyper" parents="64 5128 12008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      T(x,y) \ K(x * y,x \ 1) = T(y,x) / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(12042(a,1),12066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12042 12066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      T(T(x,y * x) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(3334(a,1),12045(a,1,1,2,1))].">
      <j1 rule="para" parents="3334 12045"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(12045(a,1),6102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12045 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9290(a,1),12045(a,1,1,2))].">
      <j1 rule="para" parents="9290 12045"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      T(x,(y / z) * ((y / z) * (z * u))) = T(x,(((y / z) \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[para(963(a,1),12055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="963 12055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      a(T((x \ y) * x,z),u,T((x \ y) * x,z)) \ (K(y,z) * x) = (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z))
    ]]></literal>
    <justification jstring="[para(12065(a,1),11028(a,1,2))].">
      <j1 rule="para" parents="12065 11028"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(12107(a,2),7180(a,1))].">
      <j1 rule="para" parents="12107 7180"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      T(x,K(y,T(y,z) \ z) \ ((T(y,z) \ z) / u)) = T(x,(((y \ T(z,y)) \ z) \ z) / u)
    ]]></literal>
    <justification jstring="[para(6326(a,2),12121(a,2,2,1))].">
      <j1 rule="para" parents="6326 12121"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(23(a,1),12155(a,1,2,1,1))].">
      <j1 rule="para" parents="23 12155"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      K(x,L(T(1 / y,(K(z,u) / y) \ z) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(12179(a,1),10160(a,2,2,1))].">
      <j1 rule="para" parents="12179 10160"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(12223(a,1),4683(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12223 4683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ T(K(y,z),x)) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(12233(a,1),6581(a,2,2,1))].">
      <j1 rule="para" parents="12233 6581"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(3103(a,1),12234(a,2,1,1))].">
      <j1 rule="para" parents="3103 12234"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = w
    ]]></literal>
    <justification jstring="[para(415(a,1),12073(a,1,2))].">
      <j1 rule="para" parents="415 12073"/>
    </justification>
  </clause>

  <clause id="12318">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(12148(a,1),5681(a,1))].">
      <j1 rule="para" parents="12148 5681"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (K(1 / y,z) * u)) = w
    ]]></literal>
    <justification jstring="[para(4452(a,1),12318(a,1,2,2))].">
      <j1 rule="para" parents="4452 12318"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5429,a(flip),b,12231,a)].">
      <j1 rule="hyper" parents="64 5429 12231"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      T(x,((((y \ 1) \ 1) \ z) / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2411(a,2),12266(a,1,2,1))].">
      <j1 rule="para" parents="2411 12266"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(2751(a,1),12266(a,1,2,1))].">
      <j1 rule="para" parents="2751 12266"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      K(x,L((y / z) * z,T((y / z) \ 1,y),u)) = K(x,L(((y / z) \ 1) \ z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10148,a(flip),b,11980,a),flip(a)].">
      <j1 rule="hyper" parents="64 10148 11980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) = K(x,L((1 / T(y,z)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(2310(a,1),11980(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2310 11980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12033(a,2),10130(a,1))].">
      <j1 rule="para" parents="12033 10130"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      x * K(y,(z \ 1) \ (z \ u)) = (1 / x) \ K(y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12035(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 12035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3975,a(flip),b,12048,a),flip(a)].">
      <j1 rule="hyper" parents="36 3975 12048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10875,a(flip),b,12050,a),flip(a)].">
      <j1 rule="hyper" parents="64 10875 12050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      L(x,y,K(z \ 1,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(3883(a,1),12328(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3883 12328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      L(x,y,K(((z * u) \ z) * w,u)) = L(x,y,K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10871,a(flip),b,12330,a),flip(a)].">
      <j1 rule="hyper" parents="64 10871 12330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11801,a(flip),b,12051,a),flip(a)].">
      <j1 rule="hyper" parents="64 11801 12051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(3883(a,1),12333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3883 12333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12336">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(6988,a,12335,a),flip(a)].">
      <j1 rule="hyper" parents="6988 12335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(3301,a,12062,a)].">
      <j1 rule="hyper" parents="3301 12062"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,11045,a(flip),b,12337,a)].">
      <j1 rule="hyper" parents="64 11045 12337"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(206,a,11045,a(flip),b,12337,a(flip))].">
      <j1 rule="hyper" parents="206 11045 12337"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,96,a(flip),b,12338,a)].">
      <j1 rule="hyper" parents="64 96 12338"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(206,a,12336,a(flip),b,12338,a(flip))].">
      <j1 rule="hyper" parents="206 12336 12338"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),12339(a,1,2,1))].">
      <j1 rule="para" parents="9 12339"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12098(a,2),10130(a,1))].">
      <j1 rule="para" parents="12098 10130"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      T(x,(y / z) * (u * u)) = T(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(688(a,1),12134(a,1,2))].">
      <j1 rule="para" parents="688 12134"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(6890,a,12138,a),flip(a)].">
      <j1 rule="hyper" parents="6890 12138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(12138(a,1),6890(a,1))].">
      <j1 rule="para" parents="12138 6890"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(78(a,1),12346(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 12346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12142(a,2),10130(a,1))].">
      <j1 rule="para" parents="12142 10130"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(12150(a,2),5833(a,1))].">
      <j1 rule="para" parents="12150 5833"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      K(x \ T((x \ 1) \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K((x \ 1) \ y,z),u) = w
    ]]></literal>
    <justification jstring="[para(4940(a,1),12350(a,1,1,2))].">
      <j1 rule="para" parents="4940 12350"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3424,a(flip),b,12151,a),flip(a)].">
      <j1 rule="hyper" parents="64 3424 12151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(78(a,1),12352(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 12352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      T(x * y,y \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) \ z) \ z = u
    ]]></literal>
    <justification jstring="[para(12202(a,1),404(a,1))].">
      <j1 rule="para" parents="12202 404"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(y,x) * z,x * y) = w
    ]]></literal>
    <justification jstring="[para(9180(a,1),12258(a,1,2,1))].">
      <j1 rule="para" parents="9180 12258"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7141,a(flip),b,12297,a)].">
      <j1 rule="hyper" parents="64 7141 12297"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) = K(x,y) / (K(w,u) * z)
    ]]></literal>
    <justification jstring="[para(12356(a,1),11924(a,1,2))].">
      <j1 rule="para" parents="12356 11924"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5272,a,12326,a),flip(a)].">
      <j1 rule="hyper" parents="5272 12326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(12012,a,12358,a)].">
      <j1 rule="hyper" parents="12012 12358"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(127,a,12358,a(flip),b,11949,a(flip))].">
      <j1 rule="hyper" parents="127 12358 11949"/>
    </justification>
  </clause>

  <clause id="12363">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5185,a,12359,a)].">
      <j1 rule="hyper" parents="5185 12359"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(627,a,12359,a),flip(a)].">
      <j1 rule="hyper" parents="627 12359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12365">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(244,a,12359,a,b,4363,a)].">
      <j1 rule="hyper" parents="244 12359 4363"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(206,a,202,a(flip),b,12359,a(flip))].">
      <j1 rule="hyper" parents="206 202 12359"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,12359,a(flip),b,5147,a),flip(a)].">
      <j1 rule="hyper" parents="128 12359 5147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      ((x \ T(y,z)) * T(K(z,y),u)) * K(z,y) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[para(12359(a,1),1272(a,2,1))].">
      <j1 rule="para" parents="12359 1272"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12359(a,1),5176(a,1,1))].">
      <j1 rule="para" parents="12359 5176"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(12359(a,1),6029(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12359 6029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(627,a,12363,a),flip(a)].">
      <j1 rule="hyper" parents="627 12363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7155,a,b,12363,a)].">
      <j1 rule="hyper" parents="64 7155 12363"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,202,a(flip),b,12363,a(flip))].">
      <j1 rule="hyper" parents="131 202 12363"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,12363,a(flip),b,7155,a)].">
      <j1 rule="hyper" parents="128 12363 7155"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      (x \ T(y,z)) / T(K(y,z),u) = (x \ y) * K(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,12363,a(flip),b,5159,a)].">
      <j1 rule="hyper" parents="128 12363 5159"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),12363(a,1,1))].">
      <j1 rule="para" parents="22 12363"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(L(y,z,u),w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),12363(a,2,2))].">
      <j1 rule="para" parents="25 12363"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      (x \ (y * (z / y))) * K(y * (z / y),u) = x \ (y * (T(z,u) / y))
    ]]></literal>
    <justification jstring="[para(3795(a,1),12363(a,2,2))].">
      <j1 rule="para" parents="3795 12363"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(12363(a,1),9203(a,2,1))].">
      <j1 rule="para" parents="12363 9203"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      (x \ T(y,z)) \ K(u,T(K(y,z),x \ y)) = ((x \ y) * T(K(y,z),u)) \ 1
    ]]></literal>
    <justification jstring="[para(12363(a,1),12085(a,1,1))].">
      <j1 rule="para" parents="12363 12085"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      T(x,y) / (z / (y \ 1)) = x / (z / (T(y,x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(206,a,8483,a(flip),b,12364,a),flip(a)].">
      <j1 rule="hyper" parents="206 8483 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      T(x,y) / (z * T(x,y)) = x / (z * x)
    ]]></literal>
    <justification jstring="[hyper(206,a,5144,a(flip),b,12364,a),flip(a)].">
      <j1 rule="hyper" parents="206 5144 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(206,a,4916,a(flip),b,12364,a),flip(a)].">
      <j1 rule="hyper" parents="206 4916 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      (x * y) / (z * K(u,y * x)) = K(x,y) * (T(y * x,u) / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,12364,a(flip),b,12224,a)].">
      <j1 rule="hyper" parents="206 12364 12224"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      (x \ y) * K(y \ x,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(5069(a,1),12364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5069 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(5113(a,1),12364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5113 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      (x * y) / (z * K(u,y * x)) = T(x * y,T(u,x)) / z
    ]]></literal>
    <justification jstring="[para(9271(a,1),12366(a,1,2,2))].">
      <j1 rule="para" parents="9271 12366"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      T(x,y) \ (y \ T(x * y,z)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),12370(a,1,1))].">
      <j1 rule="para" parents="22 12370"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(5207,a,12372,a)].">
      <j1 rule="hyper" parents="5207 12372"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(206,a,12372,a(flip),b,12061,a)].">
      <j1 rule="hyper" parents="206 12372 12061"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = (K(x,z) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11977,a,b,12378,a),flip(a)].">
      <j1 rule="hyper" parents="319 11977 12378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(206,a,12374,a(flip),b,6151,a)].">
      <j1 rule="hyper" parents="206 12374 6151"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(6845(a,1),12374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6845 12374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      K(x / y,z) * (y \ (y \ x)) = y \ T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(6850(a,1),12374(a,1,1))].">
      <j1 rule="para" parents="6850 12374"/>
    </justification>
  </clause>

  <clause id="12408">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9290,a(flip),b,12379,a),flip(a)].">
      <j1 rule="hyper" parents="319 9290 12379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      T((x * K(y,z)) / (u / K(z,y)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(417,a,5175,a(flip),b,12400,a)].">
      <j1 rule="hyper" parents="417 5175 12400"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      K(x,y) * (y / (z / x)) = y / (z / T(x,y))
    ]]></literal>
    <justification jstring="[para(5163(a,1),12403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5163 12403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) \ 1) = K(x,(u / z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(12403(a,1),5041(a,1,2,1))].">
      <j1 rule="para" parents="12403 5041"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      T(x,T((K(y,z) * (z / u)) \ 1,w)) = T(x,T((u / z) * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(12403(a,1),7704(a,1,2,1,1))].">
      <j1 rule="para" parents="12403 7704"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      K(x,y) * (y / (z \ 1)) = y / (z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(11948(a,1),12403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11948 12403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u \ y),w) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(T(y,T(z,u)) / u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12406(a,1),9322(a,1,2,1,1))].">
      <j1 rule="para" parents="12406 9322"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,12382,a(flip),b,7623,a),flip(a)].">
      <j1 rule="hyper" parents="130 12382 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      ((x * (y / x)) \ x) * y = (y \ x) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(12394(a,1),8895(a,1,1))].">
      <j1 rule="para" parents="12394 8895"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(10153,a,12340,a),flip(a)].">
      <j1 rule="hyper" parents="10153 12340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(4356(a,1),12341(a,1,2))].">
      <j1 rule="para" parents="4356 12341"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(244,a,12404,a(flip),b,3643,a)].">
      <j1 rule="hyper" parents="244 12404 3643"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),12408(a,1,2))].">
      <j1 rule="para" parents="22 12408"/>
    </justification>
  </clause>

  <clause id="12422">
    <literal><![CDATA[
      R(K(x * y,z),T(y,x),T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = u
    ]]></literal>
    <justification jstring="[para(12421(a,1),545(a,1,1))].">
      <j1 rule="para" parents="12421 545"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,7851,a,b,12420,a)].">
      <j1 rule="hyper" parents="319 7851 12420"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      K((x \ y) \ K(x,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,1 / z),u) = w
    ]]></literal>
    <justification jstring="[para(3886(a,1),12181(a,1,1,2))].">
      <j1 rule="para" parents="3886 12181"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      T(x / y,x) = ((1 / (1 / (x / y))) \ y) \ y
    ]]></literal>
    <justification jstring="[para(645(a,1),12273(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="645 12273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      (R(1 / (x / y),1 / (x / y),y) * y) \ y = T(x / y,x)
    ]]></literal>
    <justification jstring="[para(3468(a,2),12425(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3468 12425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),(x \ y) * (L(x \ y,z,u) \ (x * L(x \ y,z,u)))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(12354,a,11608,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12354 11608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / u) * (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(12418(a,1),293(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12418 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12077,a(flip),b,12028,a),flip(a)].">
      <j1 rule="hyper" parents="319 12077 12028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (z \ y)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(187(a,1),12429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 12429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(11976(a,1),12069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11976 12069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(4751,a,12088,a),flip(a)].">
      <j1 rule="hyper" parents="4751 12088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12433">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8261,a,b,12432,a)].">
      <j1 rule="hyper" parents="319 8261 12432"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),12433(a,2,1,1))].">
      <j1 rule="para" parents="9 12433"/>
    </justification>
  </clause>

  <clause id="12435">
    <literal><![CDATA[
      K(x,y \ K((z \ u) * w,z)) = K(x,y \ K(u * w,z))
    ]]></literal>
    <justification jstring="[para(12433(a,1),11155(a,1,2,2))].">
      <j1 rule="para" parents="12433 11155"/>
    </justification>
  </clause>

  <clause id="12436">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9209,a,b,12434,a)].">
      <j1 rule="hyper" parents="64 9209 12434"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      K((x \ y) \ (y * z),x \ y) = K(x * z,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),12436(a,1,1,2,1))].">
      <j1 rule="para" parents="10 12436"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),12437(a,1,1,2))].">
      <j1 rule="para" parents="10 12437"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8180,a(flip),b,12438,a)].">
      <j1 rule="hyper" parents="64 8180 12438"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(12438(a,1),10289(a,1,3))].">
      <j1 rule="para" parents="12438 10289"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(8265,a,12439,a)].">
      <j1 rule="hyper" parents="8265 12439"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(2917(a,1),12097(a,2,2,1))].">
      <j1 rule="para" parents="2917 12097"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),T(x * y,K(y,z)) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[para(4946(a,1),12124(a,1,2,1))].">
      <j1 rule="para" parents="4946 12124"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      T((x \ T(y,z)) \ T(y,x),y) = (x \ T(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(12061(a,1),12126(a,2,1))].">
      <j1 rule="para" parents="12061 12126"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      T(x,(y * (z * z)) / u) = T(x,y / (u / (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12132,a(flip),b,12135,a)].">
      <j1 rule="hyper" parents="64 12132 12135"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      R(x,y,z \ T(T(u,K(w,v5)) \ v6,K(w,T(v5,u)))) = R(x,y,z \ (((u \ v6) \ K(w,v5)) \ K(w,T(v5,u))))
    ]]></literal>
    <justification jstring="[para(12207(a,1),11539(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="12207 11539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12447">
    <literal><![CDATA[
      K(x,(T(T(y * z,x),z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[para(5062(a,1),12312(a,2,2,1,1))].">
      <j1 rule="para" parents="5062 12312"/>
    </justification>
  </clause>

  <clause id="12448">
    <literal><![CDATA[
      L(x,y,K(((z * u) \ z) * w,u)) = L(x,y,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12330,a(flip),b,12331,a),flip(a)].">
      <j1 rule="hyper" parents="319 12330 12331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * z) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6981,a,12357,a),flip(a)].">
      <j1 rule="hyper" parents="6981 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      (x \ T(y,z)) / K(y,T(z,u)) = (x \ y) * K(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6099(a,2),12380(a,1,2))].">
      <j1 rule="para" parents="6099 12380"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12411(a,1),5257(a,1))].">
      <j1 rule="para" parents="12411 5257"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,T(y,u)) = (x \ y) * K(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6169,a,12450,a)].">
      <j1 rule="hyper" parents="6169 12450"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,T(y,u)) = (x \ y) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6748(a,2),12452(a,2,2))].">
      <j1 rule="para" parents="6748 12452"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,T(y,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12363,a(flip),b,12453,a),flip(a)].">
      <j1 rule="hyper" parents="319 12363 12453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4159(a,1),12238(a,1,3))].">
      <j1 rule="para" parents="4159 12238"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,4422,a(flip),b,12455,a)].">
      <j1 rule="hyper" parents="64 4422 12455"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      K(x * ((y \ 1) \ K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / (K(u,z) / y),w) = v5
    ]]></literal>
    <justification jstring="[para(12025(a,2),12263(a,1))].">
      <j1 rule="para" parents="12025 12263"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      K(x,L(y / T((z \ u) \ 1,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(8484(a,1),12349(a,1,2,1,2))].">
      <j1 rule="para" parents="8484 12349"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      (R(1 / (x / y),x / y,y) * y) \ y = T(x / y,x)
    ]]></literal>
    <justification jstring="[para(8432(a,1),12426(a,1,1,1))].">
      <j1 rule="para" parents="8432 12426"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      T(x / y,x) = ((y / x) * y) \ y
    ]]></literal>
    <justification jstring="[para(383(a,1),12459(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="383 12459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      (1 / (1 / (x / y))) \ y = (y / x) * y
    ]]></literal>
    <justification jstring="[hyper(40,a,12425,a(flip),b,12460,a(flip))].">
      <j1 rule="hyper" parents="40 12425 12460"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      T(x,(T(y,1 / (1 / (z / y))) / (1 / (1 / (z / y)))) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(12461(a,1),11334(a,2,2,1))].">
      <j1 rule="para" parents="12461 11334"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(12261,a,12041,a),flip(a)].">
      <j1 rule="hyper" parents="12261 12041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,5237,a(flip),b,12463,a),flip(a)].">
      <j1 rule="hyper" parents="319 5237 12463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,10402,a,b,12464,a)].">
      <j1 rule="hyper" parents="64 10402 12464"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(12465(a,1),9440(a,1,1,1))].">
      <j1 rule="para" parents="12465 9440"/>
    </justification>
  </clause>

  <clause id="12468">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,7494,a(flip),b,12467,a),flip(a)].">
      <j1 rule="hyper" parents="64 7494 12467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),12468(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12 12468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(z \ K(u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(12356(a,1),12081(a,1,3,1))].">
      <j1 rule="para" parents="12356 12081"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (u \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(12356(a,1),12082(a,1,3,2))].">
      <j1 rule="para" parents="12356 12082"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      T(T(x,y \ z),K(y \ z,u)) = T(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(12053(a,1),12109(a,1,1))].">
      <j1 rule="para" parents="12053 12109"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(6394,a,12473,a),flip(a)].">
      <j1 rule="hyper" parents="6394 12473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(6705(a,1),12120(a,1,2))].">
      <j1 rule="para" parents="6705 12120"/>
    </justification>
  </clause>

  <clause id="12476">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(6821(a,1),12123(a,2,1))].">
      <j1 rule="para" parents="6821 12123"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(12139(a,2),12347(a,1))].">
      <j1 rule="para" parents="12139 12347"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,z \ y) = T(z * (y / z),x) / y
    ]]></literal>
    <justification jstring="[para(4261(a,1),12152(a,1,2))].">
      <j1 rule="para" parents="4261 12152"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,z \ y) = (z * (T(y,x) / z)) / y
    ]]></literal>
    <justification jstring="[para(3795(a,1),12478(a,2,1))].">
      <j1 rule="para" parents="3795 12478"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u / (1 / z))) = T(x,(u / (1 / z)) * T(y,K(u,z)))
    ]]></literal>
    <justification jstring="[para(9259(a,1),12159(a,1,2,1))].">
      <j1 rule="para" parents="9259 12159"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      T(K(x,y) * T(y / z,K(x,y)),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(7319(a,1),12221(a,1,1,2))].">
      <j1 rule="para" parents="7319 12221"/>
    </justification>
  </clause>

  <clause id="12482">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(12327(a,1),5992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12327 5992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(8262(a,1),12327(a,1,2))].">
      <j1 rule="para" parents="8262 12327"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),12483(a,1,2,1))].">
      <j1 rule="para" parents="9 12483"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(627,a,12484,a),flip(a)].">
      <j1 rule="hyper" parents="627 12484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12487">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(206,a,202,a(flip),b,12484,a(flip))].">
      <j1 rule="hyper" parents="206 202 12484"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      (x \ (y * z)) * T(z,y) = (x \ (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,12484,a(flip),b,5158,a)].">
      <j1 rule="hyper" parents="130 12484 5158"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12484(a,1,1,2))].">
      <j1 rule="para" parents="10 12484"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(194(a,1),12484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="194 12484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(206,a,12486,a(flip),b,12224,a)].">
      <j1 rule="hyper" parents="206 12486 12224"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(12486(a,1),322(a,1,2))].">
      <j1 rule="para" parents="12486 322"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(109(a,1),12487(a,1,1))].">
      <j1 rule="para" parents="109 12487"/>
    </justification>
  </clause>

  <clause id="12495">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(4167(a,1),12493(a,1,2,2))].">
      <j1 rule="para" parents="4167 12493"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(5178(a,1),12495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5178 12495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(4162(a,1),12494(a,1,2,2))].">
      <j1 rule="para" parents="4162 12494"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,12492,a(flip),b,12497,a)].">
      <j1 rule="hyper" parents="64 12492 12497"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4922,a(flip),b,12490,a),flip(a)].">
      <j1 rule="hyper" parents="319 4922 12490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12500">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,11643,a(flip),b,12482,a),flip(a)].">
      <j1 rule="hyper" parents="319 11643 12482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12501">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (w * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7336,a,b,12482,a)].">
      <j1 rule="hyper" parents="64 7336 12482"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12504">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) = K(x,x * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(105(a,1),12500(a,1,2,2))].">
      <j1 rule="para" parents="105 12500"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      K(x,(x * y) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(194(a,1),12503(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="194 12503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(9208,a,12506,a)].">
      <j1 rule="hyper" parents="9208 12506"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      K(x,y \ ((z * u) * x)) = K(x,y \ ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,8773,a,b,12504,a)].">
      <j1 rule="hyper" parents="319 8773 12504"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5881,a,b,12501,a)].">
      <j1 rule="hyper" parents="64 5881 12501"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,11643,a(flip),b,12509,a),flip(a)].">
      <j1 rule="hyper" parents="319 11643 12509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(6705(a,1),12386(a,1,2))].">
      <j1 rule="para" parents="6705 12386"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      K(x,y) * (T(y * x,z) / u) = T(x * y,T(z,x)) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,12396,a(flip),b,12393,a),flip(a)].">
      <j1 rule="hyper" parents="64 12396 12393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,4022,a(flip),b,12423,a)].">
      <j1 rule="hyper" parents="36 4022 12423"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (1 / (x / y)) \ R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(12470(a,1),8533(a,2,2))].">
      <j1 rule="para" parents="12470 8533"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7021(a,1),12475(a,1,2))].">
      <j1 rule="para" parents="7021 12475"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * T(K(z,x),y))
    ]]></literal>
    <justification jstring="[para(109(a,1),12481(a,1,1))].">
      <j1 rule="para" parents="109 12481"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * K(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(6099(a,2),12517(a,2,2,2))].">
      <j1 rule="para" parents="6099 12517"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7017(a,1),12512(a,1,2))].">
      <j1 rule="para" parents="7017 12512"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      ((x \ y) \ K(z,y)) * K(y,K(z,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(12239,a,12519,a)].">
      <j1 rule="hyper" parents="12239 12519"/>
    </justification>
  </clause>

  <clause id="12521">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(8629,a,11932,a),flip(a)].">
      <j1 rule="hyper" parents="8629 11932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12522">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(11932(a,1),8629(a,1))].">
      <j1 rule="para" parents="11932 8629"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11920,a(flip),b,12521,a),flip(a)].">
      <j1 rule="hyper" parents="64 11920 12521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11918,a(flip),b,12521,a),flip(a)].">
      <j1 rule="hyper" parents="64 11918 12521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / a(x,z,K(u,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(206,a,12521,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="206 12521 14"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(131,a,12521,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="131 12521 14"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(11585,a,12524,a),flip(a)].">
      <j1 rule="hyper" parents="11585 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(10290,a,12524,a)].">
      <j1 rule="hyper" parents="10290 12524"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(10210,a,12524,a)].">
      <j1 rule="hyper" parents="10210 12524"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10166,a,12524,a)].">
      <j1 rule="hyper" parents="10166 12524"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(10161,a,12524,a)].">
      <j1 rule="hyper" parents="10161 12524"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12521,a,b,12524,a)].">
      <j1 rule="hyper" parents="319 12521 12524"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,11601,a,b,12524,a)].">
      <j1 rule="hyper" parents="319 11601 12524"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11566,a,b,12524,a)].">
      <j1 rule="hyper" parents="319 11566 12524"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11463,a,b,12524,a)].">
      <j1 rule="hyper" parents="319 11463 12524"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,10303,a,b,12524,a)].">
      <j1 rule="hyper" parents="319 10303 12524"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,10306,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="319 10306 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,10197,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="319 10197 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,8781,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="319 8781 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,12524,a,b,11571,a)].">
      <j1 rule="hyper" parents="131 12524 11571"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(u,y,K(z,x)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(130,a,12524,a,b,8644,a)].">
      <j1 rule="hyper" parents="130 12524 8644"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10309,a,b,12524,a)].">
      <j1 rule="hyper" parents="64 10309 12524"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10308,a,b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="64 10308 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10303,a,b,12524,a)].">
      <j1 rule="hyper" parents="64 10303 12524"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      a(x,L(x,y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9731,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="64 9731 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,8858,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="64 8858 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,8774,a(flip),b,12524,a),flip(a)].">
      <j1 rule="hyper" parents="64 8774 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,12524,a(flip),b,11571,a)].">
      <j1 rule="hyper" parents="131 12524 11571"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      a(x,y,K(z * (u / T(w,x)),v5)) = a(v5,y,K(x,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(6067(a,1),12524(a,2,3))].">
      <j1 rule="para" parents="6067 12524"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(6416(a,1),12524(a,2,3))].">
      <j1 rule="para" parents="6416 12524"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,z,K(u,y)) = v5
    ]]></literal>
    <justification jstring="[para(12524(a,2),8628(a,1,2))].">
      <j1 rule="para" parents="12524 8628"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(12524(a,2),8643(a,1,1))].">
      <j1 rule="para" parents="12524 8643"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12524(a,1),10106(a,1,2))].">
      <j1 rule="para" parents="12524 10106"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12524(a,2),10106(a,1,2))].">
      <j1 rule="para" parents="12524 10106"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(12524(a,2),10126(a,1,1))].">
      <j1 rule="para" parents="12524 10126"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12524(a,1),10155(a,1,2))].">
      <j1 rule="para" parents="12524 10155"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12524(a,2),10155(a,1,2))].">
      <j1 rule="para" parents="12524 10155"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(12524(a,1),11574(a,1,1))].">
      <j1 rule="para" parents="12524 11574"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(12524(a,2),11574(a,1,1))].">
      <j1 rule="para" parents="12524 11574"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(12524(a,1),11577(a,1,2))].">
      <j1 rule="para" parents="12524 11577"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12524(a,2),11577(a,1,2))].">
      <j1 rule="para" parents="12524 11577"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(12524(a,1),11854(a,2,2))].">
      <j1 rule="para" parents="12524 11854"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      a(L(x,y,y),z,K(u,w)) = a(u,z,K(w,x))
    ]]></literal>
    <justification jstring="[para(11942(a,1),12524(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11942 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      L(K(x * y,z),x,y) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,12541,a)].">
      <j1 rule="hyper" parents="53 12541"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      a(x,y,K(x * y,z)) = 1
    ]]></literal>
    <justification jstring="[para(9288(a,1),12541(a,1,3))].">
      <j1 rule="para" parents="9288 12541"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      a(x,y,K(z,x * (y * z))) = 1
    ]]></literal>
    <justification jstring="[hyper(10213,a,12550,a)].">
      <j1 rule="hyper" parents="10213 12550"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      L(K(x * y,z),y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,12569,a)].">
      <j1 rule="hyper" parents="53 12569"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      L(K(x,y),L(z,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,12548,a)].">
      <j1 rule="hyper" parents="53 12548"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      L(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,12549,a)].">
      <j1 rule="hyper" parents="53 12549"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(12549(a,1),10106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12549 10106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,11589,a(flip),b,12570,a)].">
      <j1 rule="hyper" parents="64 11589 12570"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      a(x,y,z) = 1 * (((x * y) * z) / (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(12575(a,1),4208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12575 4208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,11919,a,b,12525,a)].">
      <j1 rule="hyper" parents="319 11919 12525"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x * w) = T(x,a(u,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,12525,a,b,4070,a)].">
      <j1 rule="hyper" parents="130 12525 4070"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,12525,a,b,4263,a)].">
      <j1 rule="hyper" parents="128 12525 4263"/>
    </justification>
  </clause>

  <clause id="12581">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) != x * v5
    ]]></literal>
    <literal><![CDATA[
      T(y,a(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12525(a,2),4951(a,1,2))].">
      <j1 rule="para" parents="12525 4951"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * T(y,a(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12525(a,2),4976(a,1,2))].">
      <j1 rule="para" parents="12525 4976"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(12525(a,2),10096(a,1,1))].">
      <j1 rule="para" parents="12525 10096"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(12525(a,1),11570(a,2,2))].">
      <j1 rule="para" parents="12525 11570"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,12528,a,b,12370,a)].">
      <j1 rule="hyper" parents="131 12528 12370"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,12528,a,b,4070,a)].">
      <j1 rule="hyper" parents="130 12528 4070"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(12528(a,2),4063(a,1,1))].">
      <j1 rule="para" parents="12528 4063"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11589,a(flip),b,12533,a),flip(a)].">
      <j1 rule="hyper" parents="319 11589 12533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(w,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,12533,a,b,9,a)].">
      <j1 rule="hyper" parents="131 12533 9"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10130,a,12572,a)].">
      <j1 rule="hyper" parents="10130 12572"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10130,a,12573,a)].">
      <j1 rule="hyper" parents="10130 12573"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w) \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9560(a,2),12590(a,1,2))].">
      <j1 rule="para" parents="9560 12590"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(10130,a,12571,a)].">
      <j1 rule="hyper" parents="10130 12571"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      K(x * y,(x * y) \ z) = K(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10117,a(flip),b,12571,a)].">
      <j1 rule="hyper" parents="64 10117 12571"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12524,a(flip),b,12529,a)].">
      <j1 rule="hyper" parents="64 12524 12529"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(12530(a,1),10212(a,1))].">
      <j1 rule="para" parents="12530 10212"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(8153(a,1),12537(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8153 12537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a(flip),b,12539,a),flip(a)].">
      <j1 rule="hyper" parents="319 12524 12539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1960,a(flip),b,12539,a)].">
      <j1 rule="hyper" parents="64 1960 12539"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(12539(a,1),10106(a,1,2))].">
      <j1 rule="para" parents="12539 10106"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a,b,12599,a)].">
      <j1 rule="hyper" parents="319 12524 12599"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12521,a,b,12599,a)].">
      <j1 rule="hyper" parents="319 12521 12599"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12528,a(flip),b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="319 12528 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12525,a(flip),b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="319 12525 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a(flip),b,12599,a)].">
      <j1 rule="hyper" parents="319 12524 12599"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12599(a,1),10106(a,1,2))].">
      <j1 rule="para" parents="12599 10106"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[para(12603(a,1),12603(a,2,2))].">
      <j1 rule="para" parents="12603 12603"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,12604,a,b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 12604 4012"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a,b,12540,a),flip(a)].">
      <j1 rule="hyper" parents="319 12524 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(10301(a,1),12543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10301 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) = T(x,a(v5,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11589(a,2),12543(a,1,2,3))].">
      <j1 rule="para" parents="11589 12543"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) = T(x,a(a(v5,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(12525(a,2),12543(a,1,2,3))].">
      <j1 rule="para" parents="12525 12543"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(12530(a,1),12543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12530 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      a(x \ y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,12524,a(flip),b,12547,a)].">
      <j1 rule="hyper" parents="64 12524 12547"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10171,a,12551,a)].">
      <j1 rule="hyper" parents="10171 12551"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(z \ 1,x)) = T(L(x,y,z),a(z \ 1,w,u))
    ]]></literal>
    <justification jstring="[para(5652(a,1),12551(a,1,2,3))].">
      <j1 rule="para" parents="5652 12551"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12551(a,1),10200(a,1,1))].">
      <j1 rule="para" parents="12551 10200"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(12551(a,1),11595(a,1,1))].">
      <j1 rule="para" parents="12551 11595"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(w,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(12624(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="12624 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ x = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8643,a,b,12563,a)].">
      <j1 rule="hyper" parents="64 8643 12563"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(12574(a,2),138(a,1)),flip(b)].">
      <j1 rule="para" parents="12574 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,11933,a(flip),b,12577,a),flip(a)].">
      <j1 rule="hyper" parents="319 11933 12577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) * 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,12628,a(flip),b,4001,a(flip))].">
      <j1 rule="hyper" parents="131 12628 4001"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),12595(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 12595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(12087(a,1),12598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12087 12598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),12615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),12620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 12620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5644(a,1),12620(a,1,3))].">
      <j1 rule="para" parents="5644 12620"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(410,a,12623,a)].">
      <j1 rule="hyper" parents="410 12623"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,12623,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 12623 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(12624(a,1),12623(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12624 12623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(12630(a,1),12543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12630 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),12632(a,1,3))].">
      <j1 rule="para" parents="6748 12632"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(12633(a,1),12543(a,1,2))].">
      <j1 rule="para" parents="12633 12543"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      T(T(x,x * y),a(y,z,u)) = L(T(x,L(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(12635(a,1),613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12635 613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      T(x,a(a(y,x,z),u,w)) = T(x,L(a(y,x,z),u,w))
    ]]></literal>
    <justification jstring="[para(11599(a,1),12635(a,1,1))].">
      <j1 rule="para" parents="11599 12635"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      K(L(x,y,z) * T(u,a(z,y,x)),w) = K(T(u,x) * L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(12637(a,1),9316(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12637 9316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(12533(a,1),12522(a,1))].">
      <j1 rule="para" parents="12533 12522"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(12602(a,1),12522(a,1))].">
      <j1 rule="para" parents="12602 12522"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      a(L(x,y,y),z,K(u,L(w,v5,v6))) = a(u,z,K(w,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(10133(a,1),12567(a,2,3))].">
      <j1 rule="para" parents="10133 12567"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(12521(a,2),12596(a,1))].">
      <j1 rule="para" parents="12521 12596"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12529(a,2),12596(a,1))].">
      <j1 rule="para" parents="12529 12596"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12540(a,2),12596(a,1))].">
      <j1 rule="para" parents="12540 12596"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(12595(a,2),12596(a,1))].">
      <j1 rule="para" parents="12595 12596"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(12615(a,2),12596(a,1))].">
      <j1 rule="para" parents="12615 12596"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,K(w,z))) = v5
    ]]></literal>
    <justification jstring="[para(6743(a,1),12644(a,1,3))].">
      <j1 rule="para" parents="6743 12644"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(10125(a,2),12644(a,1))].">
      <j1 rule="para" parents="10125 12644"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(11459(a,2),12644(a,1))].">
      <j1 rule="para" parents="11459 12644"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      T(x,y) * a(x,z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,12531,a(flip),b,4442,a)].">
      <j1 rule="hyper" parents="131 12531 4442"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(12531(a,1),5181(a,1,1))].">
      <j1 rule="para" parents="12531 5181"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      K(x,y) * (K(y,L(x,z,u)) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(12531(a,1),8452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12531 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(L(x,y,z) \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(12531(a,1),12495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12531 12495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) * a(y,z,K(x,u)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,12536,a(flip),b,8329,a)].">
      <j1 rule="hyper" parents="131 12536 8329"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = K(z,L(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,10126,a,b,12544,a),flip(a)].">
      <j1 rule="hyper" parents="35 10126 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) * w = v5
    ]]></literal>
    <justification jstring="[para(12544(a,1),330(a,1,2))].">
      <j1 rule="para" parents="12544 330"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      (a(x,y,K(z,u)) \ T(w,a(u,y,K(z,x)) * v5)) / (a(u,y,K(z,x)) * w) = K(w,v5 * a(u,y,K(z,x)))
    ]]></literal>
    <justification jstring="[hyper(128,a,12556,a,b,9256,a)].">
      <j1 rule="hyper" parents="128 12556 9256"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8626,a,12557,a)].">
      <j1 rule="hyper" parents="8626 12557"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(8974(a,1),12557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8974 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y \ (u / w),y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(9367(a,1),12557(a,1,2,3))].">
      <j1 rule="para" parents="9367 12557"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,y \ u))
    ]]></literal>
    <justification jstring="[para(10289(a,1),12557(a,1,2))].">
      <j1 rule="para" parents="10289 12557"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(10307(a,1),12557(a,1,2))].">
      <j1 rule="para" parents="10307 12557"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(u \ 1) * w))
    ]]></literal>
    <justification jstring="[para(12038(a,1),12557(a,1,2,3))].">
      <j1 rule="para" parents="12038 12557"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(12166(a,1),12557(a,1,2,3))].">
      <j1 rule="para" parents="12166 12557"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(u * (w \ y),y))
    ]]></literal>
    <justification jstring="[para(12371(a,1),12557(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="12371 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[para(12615(a,1),12557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12615 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(12667(a,2),138(a,1)),flip(b)].">
      <j1 rule="para" parents="12667 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u / (w * v5))) = K(x,L(y,z,u / (T(w,x) * v5)))
    ]]></literal>
    <justification jstring="[para(7526(a,1),12558(a,1,2,3))].">
      <j1 rule="para" parents="7526 12558"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) = K(x,y) * a(y,z,1)
    ]]></literal>
    <justification jstring="[para(8859(a,1),12558(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="8859 12558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(y,z,K(x,x \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(10191(a,1),12558(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10191 12558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u * (w * K(v5,v6)))) = K(x,L(y,z,u / (K(v6,v5) / w)))
    ]]></literal>
    <justification jstring="[para(12144(a,1),12558(a,1,2,3))].">
      <j1 rule="para" parents="12144 12558"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(4105,a,12566,a)].">
      <j1 rule="hyper" parents="4105 12566"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11702,a(flip),b,12680,a)].">
      <j1 rule="hyper" parents="64 11702 12680"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,8619,a(flip),b,12589,a)].">
      <j1 rule="hyper" parents="127 8619 12589"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5 * a(w,u,K(z,y))
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(12589(a,1),45(a,2))].">
      <j1 rule="para" parents="12589 45"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,z,a(w,u,v5)))
    ]]></literal>
    <justification jstring="[para(12603(a,2),12606(a,1,2,3))].">
      <j1 rule="para" parents="12603 12606"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12543,a(flip),b,12616,a),flip(a)].">
      <j1 rule="hyper" parents="319 12543 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),12685(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11573,a(flip),b,12619,a),flip(a)].">
      <j1 rule="hyper" parents="319 11573 12619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12619(a,2),11577(a,1))].">
      <j1 rule="para" parents="12619 11577"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12543,a(flip),b,12638,a),flip(a)].">
      <j1 rule="hyper" parents="319 12543 12638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),12689(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12691">
    <literal><![CDATA[
      T(T(x,x * y),a((x * (x * y)) / x,z,u)) = T(T(x,x * y),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(3107(a,2),12689(a,1,2,1))].">
      <j1 rule="para" parents="3107 12689"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12521(a,2),12655(a,1,2))].">
      <j1 rule="para" parents="12521 12655"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,10096,a,b,12656,a),flip(a)].">
      <j1 rule="hyper" parents="319 10096 12656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      K(x,L(y,z,u * L(u \ 1,u,w))) = a(y,z,1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8594(a,1),12661(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="8594 12661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      a(K(x,y),z,u) \ T(y,x) = T(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(12682(a,1),10121(a,1,1))].">
      <j1 rule="para" parents="12682 10121"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) = x * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,12692,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 12692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(u,w)) = K(u,K(w,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,10131,a(flip),b,12693,a),flip(a)].">
      <j1 rule="hyper" parents="319 10131 12693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      L(K(x,y),z,u) != w * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(12693(a,1),45(a,1))].">
      <j1 rule="para" parents="12693 45"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(12693(a,2),10138(a,1))].">
      <j1 rule="para" parents="12693 10138"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,12576,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="130 12576 7"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      (x * (y * z)) / (y * (z * T(x,y * z))) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[hyper(128,a,109,a(flip),b,12701,a)].">
      <j1 rule="hyper" parents="128 109 12701"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(12701(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12701 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      a(x * (y / x),x,z) * (y * (T(x,y) * z)) = (y * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(10918(a,2),12701(a,1,1))].">
      <j1 rule="para" parents="10918 12701"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(u * z,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(10304(a,1),12587(a,1,1))].">
      <j1 rule="para" parents="10304 12587"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      a(x,y,K(z \ (u \ w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z \ w,u)) = v5
    ]]></literal>
    <justification jstring="[para(8216(a,2),12648(a,1,3))].">
      <j1 rule="para" parents="8216 12648"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(12651,a,12524,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12651 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,12709,a(flip),b,10125,a),flip(a)].">
      <j1 rule="hyper" parents="127 12709 10125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12711">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(12709(a,1),12543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12709 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(12709(a,1),12551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12709 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12543,a(flip),b,12711,a),flip(a)].">
      <j1 rule="hyper" parents="319 12543 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      T(T(x,y),a(z,x \ u,w)) = T(T(x,a(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(12713(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12713 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      T(x * K(y,z),a(u,K(z,y),w)) = T(x * K(y,z),a(u,x,w))
    ]]></literal>
    <justification jstring="[para(5176(a,1),12713(a,1,2,2))].">
      <j1 rule="para" parents="5176 12713"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12551,a(flip),b,12712,a),flip(a)].">
      <j1 rule="hyper" parents="319 12551 12712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),12716(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12718">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(12681(a,1),11590(a,1,1))].">
      <j1 rule="para" parents="12681 11590"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(12598(a,1),12580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12598 12580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,10395,a,b,12583,a)].">
      <j1 rule="hyper" parents="64 10395 12583"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      K(x * (y \ 1),(y \ 1) \ (x \ z)) = K(x / y,(x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(12211,a,12594,a),flip(a)].">
      <j1 rule="hyper" parents="12211 12594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,w,K(y,u)) = K(x,L(L(y,z,u),w,u \ 1))
    ]]></literal>
    <justification jstring="[para(5680(a,1),12600(a,1,2,3))].">
      <j1 rule="para" parents="5680 12600"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,z,a(v5,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(12525(a,2),12600(a,1,2,3))].">
      <j1 rule="para" parents="12525 12600"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,12629,a)].">
      <j1 rule="hyper" parents="139 12629"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),12639(a,2,3))].">
      <j1 rule="para" parents="6748 12639"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      K(x,L(y,z,y \ u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12557,a(flip),b,12669,a),flip(a)].">
      <j1 rule="hyper" parents="64 12557 12669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12600,a(flip),b,12670,a)].">
      <j1 rule="hyper" parents="64 12600 12670"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(10308(a,2),12670(a,1,2))].">
      <j1 rule="para" parents="10308 12670"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12557,a(flip),b,12674,a),flip(a)].">
      <j1 rule="hyper" parents="319 12557 12674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10122,a,12729,a),flip(a)].">
      <j1 rule="hyper" parents="10122 12729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,8164,a(flip),b,12729,a),flip(a)].">
      <j1 rule="hyper" parents="319 8164 12729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      T(x,L(y,z \ u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,12729,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12729 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),12729(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(504(a,1),12729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 12729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,L(y,R(z,u,u \ 1),z))
    ]]></literal>
    <justification jstring="[para(768(a,1),12729(a,1,2,2))].">
      <j1 rule="para" parents="768 12729"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,L(y,u,L(u,z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(1964(a,1),12729(a,1,2,2))].">
      <j1 rule="para" parents="1964 12729"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(9223(a,1),12729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9223 12729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(12729(a,1),10113(a,1,2))].">
      <j1 rule="para" parents="12729 10113"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(10122,a,12731,a)].">
      <j1 rule="hyper" parents="10122 12731"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12731,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12731 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(504(a,1),12731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 12731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9223(a,1),12731(a,1,2))].">
      <j1 rule="para" parents="9223 12731"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(504(a,1),12740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 12740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(12740(a,1),9306(a,1,2,1))].">
      <j1 rule="para" parents="12740 9306"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10097,a,12742,a)].">
      <j1 rule="hyper" parents="10097 12742"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      T(x,L(y,z * u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),12732(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),T(u,z))) = T(x,L(y,K(u * z,w),T(u,z)))
    ]]></literal>
    <justification jstring="[para(12399(a,1),12732(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12399 12732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = x \ T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a(flip),b,12733,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 12733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(9607(a,1),12733(a,1,2))].">
      <j1 rule="para" parents="9607 12733"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11759(a,2),12733(a,1,2))].">
      <j1 rule="para" parents="11759 12733"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(129,a,12739,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12739 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      K(x,T(y,y \ x) \ z) = K(x,x \ ((y \ x) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11201,a,b,12741,a)].">
      <j1 rule="hyper" parents="64 11201 12741"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      T(x,x \ ((y \ x) \ z)) = T(x,x \ (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8154,a(flip),b,12743,a)].">
      <j1 rule="hyper" parents="64 8154 12743"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(12743(a,1),4010(a,1,1,1))].">
      <j1 rule="para" parents="12743 4010"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      K(x,T(y,y \ ((z \ y) \ u)) * w) = K(x,T(y,y \ (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(12743(a,1),11117(a,2,2,1))].">
      <j1 rule="para" parents="12743 11117"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(12746(a,1),8182(a,1))].">
      <j1 rule="para" parents="12746 8182"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(12750(a,1),8184(a,1))].">
      <j1 rule="para" parents="12750 8184"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(9548(a,1),12737(a,2,2))].">
      <j1 rule="para" parents="9548 12737"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(9547(a,1),12737(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9547 12737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(12748(a,2),4106(a,1))].">
      <j1 rule="para" parents="12748 4106"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      T(x * (y / z),L(z,z \ y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * (y / z),z) = u
    ]]></literal>
    <justification jstring="[para(8247(a,1),12757(a,1,2))].">
      <j1 rule="para" parents="8247 12757"/>
    </justification>
  </clause>

  <clause id="12763">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) = K(x,z \ (y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12590,a(flip),b,12730,a),flip(a)].">
      <j1 rule="hyper" parents="64 12590 12730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12764">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(12675,a,12734,a)].">
      <j1 rule="hyper" parents="12675 12734"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6619,a,12738,a)].">
      <j1 rule="hyper" parents="6619 12738"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(571,a,12738,a)].">
      <j1 rule="hyper" parents="571 12738"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(10(a,1),12761(a,1,2,2))].">
      <j1 rule="para" parents="10 12761"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(9607(a,1),12761(a,1,2))].">
      <j1 rule="para" parents="9607 12761"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      x \ ((1 / y) * K(z,y)) = (x \ (1 / y)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(5378(a,1),12766(a,1,2,2))].">
      <j1 rule="para" parents="5378 12766"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[para(5382(a,1),12766(a,1,2,2))].">
      <j1 rule="para" parents="5382 12766"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4016(a,2),12770(a,1,2))].">
      <j1 rule="para" parents="4016 12770"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[para(4097(a,1),12770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4097 12770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      (x \ K(y,z)) * K(u,K(y,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6794(a,1),12770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6794 12770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      ((x * y) / x) / (z * K(x,y)) = y / z
    ]]></literal>
    <justification jstring="[hyper(206,a,202,a(flip),b,12773,a)].">
      <j1 rule="hyper" parents="206 202 12773"/>
    </justification>
  </clause>

  <clause id="12779">
    <literal><![CDATA[
      ((x * y) / x) / (y / x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(4933(a,1),12777(a,1,2))].">
      <j1 rule="para" parents="4933 12777"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(627,a,12774,a),flip(a)].">
      <j1 rule="hyper" parents="627 12774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(12774(a,1),7526(a,2,2,2))].">
      <j1 rule="para" parents="12774 7526"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      a(x / y,x / (T(x,y) / y),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(12779(a,1),9121(a,1,2))].">
      <j1 rule="para" parents="12779 9121"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(12781(a,1),12737(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="12781 12737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,10543,a(flip),b,12696,a(flip))].">
      <j1 rule="hyper" parents="35 10543 12696"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11658,a,12786,a)].">
      <j1 rule="hyper" parents="11658 12786"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(5596,a,12786,a)].">
      <j1 rule="hyper" parents="5596 12786"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(5570,a,12786,a),flip(a)].">
      <j1 rule="hyper" parents="5570 12786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,10096,a,b,12786,a),flip(a)].">
      <j1 rule="hyper" parents="319 10096 12786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11651,a(flip),b,12786,a)].">
      <j1 rule="hyper" parents="64 11651 12786"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5572,a(flip),b,12786,a),flip(a)].">
      <j1 rule="hyper" parents="64 5572 12786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      K(x / (y / z),L(u,x,z)) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5461,a(flip),b,12786,a),flip(a)].">
      <j1 rule="hyper" parents="64 5461 12786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4726,a(flip),b,12786,a)].">
      <j1 rule="hyper" parents="64 4726 12786"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,12786,a(flip),b,8201,a(flip))].">
      <j1 rule="hyper" parents="130 12786 8201"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,12786,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 12786 20"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = w
    ]]></literal>
    <justification jstring="[para(12786(a,1),724(a,1,1))].">
      <j1 rule="para" parents="12786 724"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(12786(a,1),8211(a,1,1))].">
      <j1 rule="para" parents="12786 8211"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,10096,a,b,12787,a)].">
      <j1 rule="hyper" parents="319 10096 12787"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12787,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12787 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12801">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4848,a,b,12787,a)].">
      <j1 rule="hyper" parents="64 4848 12787"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6454,a(flip),b,12787,a),flip(a)].">
      <j1 rule="hyper" parents="64 6454 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(106(a,1),12787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(303(a,1),12787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="303 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(669(a,1),12787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="669 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      K(x,K((1 / (y \ z)) / u,L(u / y,y,y \ z))) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[para(12787(a,1),7887(a,1,2))].">
      <j1 rule="para" parents="12787 7887"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(8210(a,1),12787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,L(u,w,v5))) = K(x,L(y,z,R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(12787(a,1),12558(a,1,2,3))].">
      <j1 rule="para" parents="12787 12558"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5461,a(flip),b,12790,a),flip(a)].">
      <j1 rule="hyper" parents="64 5461 12790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4726,a(flip),b,12790,a),flip(a)].">
      <j1 rule="hyper" parents="64 4726 12790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,12790,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 12790 20"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      L(K(x,y),z,u) \ ((K(x,y) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[para(12790(a,1),194(a,1,1))].">
      <j1 rule="para" parents="12790 194"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12790(a,1),6868(a,2,2))].">
      <j1 rule="para" parents="12790 6868"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12790(a,2),10130(a,1))].">
      <j1 rule="para" parents="12790 10130"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(12790(a,1),12499(a,1,1))].">
      <j1 rule="para" parents="12790 12499"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,10133,a,b,12791,a),flip(a)].">
      <j1 rule="hyper" parents="319 10133 12791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(12791(a,1),5235(a,1,2,1))].">
      <j1 rule="para" parents="12791 5235"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(x,L(w,y,z)))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12791(a,1),6363(a,1,1,2,2))].">
      <j1 rule="para" parents="12791 6363"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      (T(x,y) * z) * K(y,L(T(x,y) * z,x,z)) = ((x * y) * z) / R(y,x,z)
    ]]></literal>
    <justification jstring="[para(12791(a,1),11686(a,1,2))].">
      <j1 rule="para" parents="12791 11686"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      a(L(x,y,y),z,K(u,L(w,v5,v6))) = a(R(u,v5,v6),z,K(w,x))
    ]]></literal>
    <justification jstring="[para(12791(a,1),12567(a,1,3))].">
      <j1 rule="para" parents="12791 12567"/>
    </justification>
  </clause>

  <clause id="12821">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = L(K(y * z,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,526,a,b,12799,a)].">
      <j1 rule="hyper" parents="319 526 12799"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      L(K(x,y / (z / u)),u \ z,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(8210(a,1),12799(a,2,2))].">
      <j1 rule="para" parents="8210 12799"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12799(a,1),10130(a,1))].">
      <j1 rule="para" parents="12799 10130"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      K(L(x,y,z),u) \ u = T(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4030,a(flip),b,12800,a)].">
      <j1 rule="hyper" parents="319 4030 12800"/>
    </justification>
  </clause>

  <clause id="12826">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,z * z),L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9352,a,b,12800,a)].">
      <j1 rule="hyper" parents="64 9352 12800"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      T(x,L(y,z,u)) * R(T(y,x),z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(130,a,12800,a(flip),b,3286,a)].">
      <j1 rule="hyper" parents="130 12800 3286"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(106(a,1),12800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="106 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(303(a,1),12800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="303 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(z,u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(12800(a,1),6993(a,1,2))].">
      <j1 rule="para" parents="12800 6993"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w)) \ ((R(w,v5,v6) * T(u,w)) / T(u,w)) = (T(T(u,w),R(x,y,z)) * R(T(w,u),v5,v6)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(12800(a,2),6450(a,2,1,1))].">
      <j1 rule="para" parents="12800 6450"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(130,a,12816,a(flip),b,4849,a)].">
      <j1 rule="hyper" parents="130 12816 4849"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(106(a,1),12816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 12816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      a(L(x,y,y),z,K(L(u,w,v5),v6)) = a(R(u,w,v5),z,K(v6,x))
    ]]></literal>
    <justification jstring="[para(12816(a,1),12567(a,1,3))].">
      <j1 rule="para" parents="12816 12567"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      T(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12825(a,1),4050(a,1))].">
      <j1 rule="para" parents="12825 4050"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(5573(a,2),12814(a,1))].">
      <j1 rule="para" parents="5573 12814"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(106(a,1),12823(a,1,2))].">
      <j1 rule="para" parents="106 12823"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,(x * u) \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6280,a(flip),b,12794,a),flip(a)].">
      <j1 rule="hyper" parents="64 6280 12794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(903(a,1),12794(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="903 12794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(4826,a,12810,a),flip(a)].">
      <j1 rule="hyper" parents="4826 12810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      (x \ K(L(y,z,u) \ 1,w)) \ (x \ 1) = K(w,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(12842(a,1),12018(a,1,1,2))].">
      <j1 rule="para" parents="12842 12018"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(12349,a,12789,a)].">
      <j1 rule="hyper" parents="12349 12789"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12737,a,b,12789,a),flip(a)].">
      <j1 rule="hyper" parents="64 12737 12789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      a(x,y,K(z,y / (u / z))) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(127,a,12792,a(flip),b,12656,a)].">
      <j1 rule="hyper" parents="127 12792 12656"/>
    </justification>
  </clause>

  <clause id="12847">
    <literal><![CDATA[
      (K(x,y) * z) * (u * u) = K(x,y) * (z * (u * u))
    ]]></literal>
    <justification jstring="[para(478(a,1),12796(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="478 12796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12848">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,K(w,L(v5,z,u))) \ 1) = K(x,((K(w,v5) * z) * u) \ (K(w,L(v5,z,u)) * y))
    ]]></literal>
    <justification jstring="[para(12796(a,1),5085(a,2,2,1))].">
      <j1 rule="para" parents="12796 5085"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,L(y,z,u))) = (z * u) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12796(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="12796 5822"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      K(x,L(y,z,z \ (u \ z))) * (z * (z \ (z / u))) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[para(11278(a,1),12796(a,1,1,2))].">
      <j1 rule="para" parents="11278 12796"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      K(x * y,L(z / x,x,y)) = K(x * y,(x * y) \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4175,a(flip),b,12803,a),flip(a)].">
      <j1 rule="hyper" parents="319 4175 12803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) * (z * u) = (z * u) * K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(12803(a,2),6190(a,1,1))].">
      <j1 rule="para" parents="12803 6190"/>
    </justification>
  </clause>

  <clause id="12853">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),w / (u * w),T(z,u \ 1))) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(3430(a,1),12804(a,2,2,2))].">
      <j1 rule="para" parents="3430 12804"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(12804(a,1),10169(a,2,2))].">
      <j1 rule="para" parents="12804 10169"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,x \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      y \ (x * (K((x \ y) / (z / x),u) * (x \ y))) = w
    ]]></literal>
    <justification jstring="[para(12809(a,1),6128(a,1))].">
      <j1 rule="para" parents="12809 6128"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(4356(a,2),12811(a,2,1))].">
      <j1 rule="para" parents="4356 12811"/>
    </justification>
  </clause>

  <clause id="12858">
    <literal><![CDATA[
      L(K(x,y),y * x,z) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[para(3999(a,1),12812(a,1,2,1))].">
      <j1 rule="para" parents="3999 12812"/>
    </justification>
  </clause>

  <clause id="12859">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),z / ((u \ 1) \ 1),u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(9630(a,1),12828(a,2,2,2))].">
      <j1 rule="para" parents="9630 12828"/>
    </justification>
  </clause>

  <clause id="12861">
    <literal><![CDATA[
      T(x,L((y / K(z,L(u,w,v5))) / (v5 * w),v5 * w,K(z,L(u,w,v5)))) = T(x,y / (v5 * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[para(10115(a,1),12829(a,2,2,2))].">
      <j1 rule="para" parents="10115 12829"/>
    </justification>
  </clause>

  <clause id="12862">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(7164,a,12834,a)].">
      <j1 rule="hyper" parents="7164 12834"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      K(L(x,y,z),u) \ (y * z) = (K(x,u) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(10120,a,12856,a)].">
      <j1 rule="hyper" parents="10120 12856"/>
    </justification>
  </clause>

  <clause id="12865">
    <literal><![CDATA[
      L(K(x,y),z,z \ u) * u = (K(y,x) \ z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(331,a,12856,a)].">
      <j1 rule="hyper" parents="331 12856"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      L(K(x,y),z,(K(y,x) \ z) \ u) \ u = z * ((K(y,x) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,12856,a)].">
      <j1 rule="hyper" parents="127 10 12856"/>
    </justification>
  </clause>

  <clause id="12867">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (z * u) = (K(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,4838,a,b,12856,a)].">
      <j1 rule="hyper" parents="64 4838 12856"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / ((x * (y * z)) * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(12704,a,12487,a(flip))].">
      <j1 rule="hyper" parents="12704 12487"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,L((y * z) \ u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(10152,a,12749,a)].">
      <j1 rule="hyper" parents="10152 12749"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11806,a(flip),b,12749,a),flip(a)].">
      <j1 rule="hyper" parents="64 11806 12749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12871">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),12749(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 12749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(12752(a,1),11199(a,1))].">
      <j1 rule="para" parents="12752 11199"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(12872,a,8142,a)].">
      <j1 rule="hyper" parents="12872 8142"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8797,a,12873,a),flip(a)].">
      <j1 rule="hyper" parents="8797 12873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(12873(a,1),8159(a,1,2))].">
      <j1 rule="para" parents="12873 8159"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,12874,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12874 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12879">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(12876(a,1),7298(a,1,1))].">
      <j1 rule="para" parents="12876 7298"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(12876(a,1),7299(a,1,2))].">
      <j1 rule="para" parents="12876 7299"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      (x \ (1 / y)) * K(z,y) = x \ (1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5163(a,1),12769(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5163 12769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      (x \ (1 / T(y,z))) * K(T(u,z),T(y,z)) = x \ (1 / (K(y,u) * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6869(a,1),12881(a,2,2,2))].">
      <j1 rule="para" parents="6869 12881"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6703(a,1),12776(a,1,2))].">
      <j1 rule="para" parents="6703 12776"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6748(a,2),12776(a,1,2))].">
      <j1 rule="para" parents="6748 12776"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      K(x,y) * (z * (K(K(x,y) * z,u) * K(K(x,y) * z,u))) = T(K(x,y) * z,u) * K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(4425,a,12847,a),flip(a)].">
      <j1 rule="hyper" parents="4425 12847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,12520,a(flip),b,12883,a),flip(a)].">
      <j1 rule="hyper" parents="64 12520 12883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      (x \ y) \ K(z,T(T(y,u),x)) = (x \ T(y,T(z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(6153(a,1),12886(a,1,2))].">
      <j1 rule="para" parents="6153 12886"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(u,z,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(8624(a,1),12555(a,1))].">
      <j1 rule="para" parents="8624 12555"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = w
    ]]></literal>
    <justification jstring="[para(10307(a,1),12560(a,1,2))].">
      <j1 rule="para" parents="10307 12560"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(12674(a,2),12560(a,1))].">
      <j1 rule="para" parents="12674 12560"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(12652,a,12601,a)].">
      <j1 rule="hyper" parents="12652 12601"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,K(w,x))) = v5
    ]]></literal>
    <justification jstring="[para(12601(a,1),12652(a,1))].">
      <j1 rule="para" parents="12601 12652"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),12896(a,1,3))].">
      <j1 rule="para" parents="6758 12896"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(z,y)) = a(z,u,K(x,K(w,y)))
    ]]></literal>
    <justification jstring="[hyper(10243,a,12898,a)].">
      <j1 rule="hyper" parents="10243 12898"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      K(x * L(T(y,x),z,u),y * x) = a(T(y,x),z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(12654,a,12236,a),flip(a)].">
      <j1 rule="hyper" parents="12654 12236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12901">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(12729(a,1),12798(a,1,1))].">
      <j1 rule="para" parents="12729 12798"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(7330,a,12901,a)].">
      <j1 rule="hyper" parents="7330 12901"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(574,a,12901,a)].">
      <j1 rule="hyper" parents="574 12901"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      T(L(x,y,K(z,L(u,y * x,x))),x \ (K(z,L(u,y * x,x)) * y)) = (x \ (K(z,L(u,y * x,x)) * y)) \ (K(z,u) * ((y * x) / x))
    ]]></literal>
    <justification jstring="[hyper(417,a,12903,a(flip),b,12256,a)].">
      <j1 rule="hyper" parents="417 12903 12256"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      (K(x * y,z) * y) / x = K(x * y,z) * (y / x)
    ]]></literal>
    <justification jstring="[para(12593(a,1),12903(a,1,1,1))].">
      <j1 rule="para" parents="12593 12903"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      (x * K(x * y,z)) / y = K(y * x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(9294(a,1),12905(a,1,1))].">
      <j1 rule="para" parents="9294 12905"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12801(a,1),321(a,1,1))].">
      <j1 rule="para" parents="12801 321"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(5416,a,12805,a),flip(a)].">
      <j1 rule="hyper" parents="5416 12805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(511(a,1),12805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="511 12805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(12893,a,12807,a)].">
      <j1 rule="hyper" parents="12893 12807"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      T(x,L(y / (z / u),z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12910,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 12910 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      T(x,L(y / K(z * u,w),z \ T(u * z,w),T(u,z))) = T(x,(y * T(u,z)) / (z \ T(u * z,w)))
    ]]></literal>
    <justification jstring="[para(12421(a,1),12911(a,1,2,1,2))].">
      <j1 rule="para" parents="12421 12911"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      L(K(x,((y / z) / u) \ x),z \ y,z) = K(x,((x * u) * z) / y)
    ]]></literal>
    <justification jstring="[para(5589(a,1),12822(a,1,1))].">
      <j1 rule="para" parents="5589 12822"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      T(T(x,y),L(y,z,u)) * R(T(y,x),z,u) = T(x,y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(3252(a,1),12827(a,1,2,1))].">
      <j1 rule="para" parents="3252 12827"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),1 / z)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(4435(a,1),12844(a,2,2,1))].">
      <j1 rule="para" parents="4435 12844"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12844(a,1),12559(a,1,2))].">
      <j1 rule="para" parents="12844 12559"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      L(K(x,y),y * x,L(z,y,x)) \ (x * (y * z)) = (y * x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),12858(a,1,2))].">
      <j1 rule="para" parents="94 12858"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,u \ x) = (K(z,y) \ u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6126,a,b,12865,a)].">
      <j1 rule="hyper" parents="64 6126 12865"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,z,K(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(12524(a,1),12891(a,1,2))].">
      <j1 rule="para" parents="12524 12891"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      T(x,a(y,z,a(u,w,v5))) != x * v6
    ]]></literal>
    <literal><![CDATA[
      a(x,z,a(u,w,K(v5,y))) = v6
    ]]></literal>
    <justification jstring="[para(12617(a,1),44(a,1))].">
      <j1 rule="para" parents="12617 44"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = T(x,a(y,w,a(v5,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12617,a(flip),b,12618,a),flip(a)].">
      <j1 rule="hyper" parents="64 12617 12618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = T(x,L(a(y,x,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12642,a(flip),b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="64 12642 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,x))
    ]]></literal>
    <justification jstring="[para(5644(a,1),12634(a,2,3))].">
      <j1 rule="para" parents="5644 12634"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(u,L(x,y,z)) * w) = K(u,x) * w
    ]]></literal>
    <justification jstring="[para(10140(a,1),12657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10140 12657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(768(a,1),12764(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="768 12764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11493,a(flip),b,12783,a),flip(a)].">
      <j1 rule="hyper" parents="64 11493 12783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = (((w \ v5) \ v5) * K(u,((x \ z) * x) / (y * x))) \ T(w,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,5177,a,b,12862,a),flip(a)].">
      <j1 rule="hyper" parents="319 5177 12862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = 1 / K(((z \ u) * z) / (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(206,a,12862,a(flip),b,4213,a),flip(a)].">
      <j1 rule="hyper" parents="206 12862 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(8628,a,12526,a)].">
      <j1 rule="hyper" parents="8628 12526"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(12582,a,12640,a),flip(a)].">
      <j1 rule="hyper" parents="12582 12640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,3795,a(flip),b,12934,a(flip))].">
      <j1 rule="hyper" parents="35 3795 12934"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(361(a,1),12677(a,2,2))].">
      <j1 rule="para" parents="361 12677"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(12936(a,2),138(a,1)),flip(b)].">
      <j1 rule="para" parents="12936 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      K(x,L(y,z,u * L(u \ 1,u,w))) = 1 * K(x,y)
    ]]></literal>
    <justification jstring="[para(361(a,1),12694(a,2,1))].">
      <j1 rule="para" parents="361 12694"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      K(x,L(y,z,u * L(u \ 1,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(12939(a,2),132(a,1)),flip(b)].">
      <j1 rule="para" parents="12939 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(12707,a,12586,a)].">
      <j1 rule="hyper" parents="12707 12586"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12636,a(flip),b,12942,a),flip(a)].">
      <j1 rule="hyper" parents="319 12636 12942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(12760(a,1),10267(a,1,2))].">
      <j1 rule="para" parents="12760 10267"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(244,a,12813,a,b,9218,a(flip))].">
      <j1 rule="hyper" parents="244 12813 9218"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      K((T(x,y) * K(z,u)) \ 1,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(z,T(u,x * y)) * x) \ 1,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(12945(a,1),6430(a,1,1,1))].">
      <j1 rule="para" parents="12945 6430"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(6845(a,1),12945(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6845 12945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,w)) = K(x,y * T(u,w))
    ]]></literal>
    <justification jstring="[para(12947(a,1),6034(a,1,2,2))].">
      <j1 rule="para" parents="12947 6034"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      a(R(x,y,z),u,K(w,v5)) = a(x,u,K(w,L(v5,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12646,a(flip),b,12820,a),flip(a)].">
      <j1 rule="hyper" parents="64 12646 12820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,L(y,z,z)),z * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,23,a,b,12826,a),flip(a)].">
      <j1 rule="hyper" parents="319 23 12826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(x,(z * z) * L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,1047,a(flip),b,12826,a),flip(a)].">
      <j1 rule="hyper" parents="319 1047 12826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      a(R(x,y,z),u,K(w,v5)) = a(L(x,y,z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,12567,a(flip),b,12836,a),flip(a)].">
      <j1 rule="hyper" parents="64 12567 12836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(x,u,K(w,L(v5,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12949,a(flip),b,12952,a),flip(a)].">
      <j1 rule="hyper" parents="64 12949 12952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10910,a(flip),b,12953,a),flip(a)].">
      <j1 rule="hyper" parents="64 10910 12953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = T(L(u,w,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(12954(a,1),12562(a,1,1))].">
      <j1 rule="para" parents="12954 12562"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = L(T(u,a(z,y,x)),w,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,12955,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      K(x * (y \ z),L(y / x,x,y \ z)) = K(x * (y \ z),(x * (y \ z)) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12851(a,2,2,2))].">
      <j1 rule="para" parents="10 12851"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(12252(a,1),12868(a,2,2))].">
      <j1 rule="para" parents="12252 12868"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(L(w,u,v5) \ w) \ y)) = v6
    ]]></literal>
    <justification jstring="[para(12535(a,1),12892(a,1,2,3))].">
      <j1 rule="para" parents="12535 12892"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      K(x,L(K(y,T(z,x)),u,u \ x)) \ ((K(z,y) \ u) * (u \ x)) = L(K(y,T(z,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[hyper(127,a,12918,a(flip),b,3999,a)].">
      <j1 rule="hyper" parents="127 12918 3999"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      x * K(y,L(T(z,K(z,y) / u),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(11991(a,1),12944(a,2,2))].">
      <j1 rule="para" parents="11991 12944"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,y),z * z)
    ]]></literal>
    <justification jstring="[para(11953(a,1),12950(a,2,1))].">
      <j1 rule="para" parents="11953 12950"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(x,(z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,1048,a(flip),b,12963,a),flip(a)].">
      <j1 rule="hyper" parents="319 1048 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(94(a,1),12951(a,2,2))].">
      <j1 rule="para" parents="94 12951"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12964,a(flip),b,12966,a)].">
      <j1 rule="hyper" parents="64 12964 12966"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12963,a(flip),b,12966,a)].">
      <j1 rule="hyper" parents="64 12963 12966"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1047,a,b,12967,a)].">
      <j1 rule="hyper" parents="64 1047 12967"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      x \ T(x,y * (y * z)) = K(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,12967,a(flip),b,4019,a(flip))].">
      <j1 rule="hyper" parents="127 12967 4019"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      T(x,((y * y) * z) / T(u,y * (y * z))) = T(x,((y * y) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(12967(a,1),11066(a,1,2,2))].">
      <j1 rule="para" parents="12967 11066"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      (x * x) * T(y,x * (x * z)) = T(y,z) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,12968,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 12968 22"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      L(T(x,y * (y * z)),u * u,w) = T(T(x,y * y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,477,a,b,12969,a)].">
      <j1 rule="hyper" parents="319 477 12969"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      T(T(x,y * (y * z)),u) = T(T(x,z),y * (y * u))
    ]]></literal>
    <justification jstring="[para(12968(a,1),12969(a,1,1))].">
      <j1 rule="para" parents="12968 12969"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      K(x,(y * y) * z) = K(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(4106,a,12970,a),flip(a)].">
      <j1 rule="hyper" parents="4106 12970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      T(x,y \ 1) * (y * y) = (y * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),12972(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 12972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      T(T(x,y),z * (z * x)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(394,a,12974,a),flip(a)].">
      <j1 rule="hyper" parents="394 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      T(T(x,y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(12973(a,1),495(a,1))].">
      <j1 rule="para" parents="12973 495"/>
    </justification>
  </clause>

  <clause id="12979">
    <literal><![CDATA[
      T(T(x,y),z * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),12978(a,1))].">
      <j1 rule="para" parents="23 12978"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(1047(a,1),12978(a,1))].">
      <j1 rule="para" parents="1047 12978"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(12560,a,12671,a),flip(a)].">
      <j1 rule="hyper" parents="12560 12671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(12672(a,1),12560(a,1))].">
      <j1 rule="para" parents="12672 12560"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = a(w,u \ z,K(u,K(x,y))) * K(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(95(a,2),12697(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="95 12697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(12560,a,12728,a),flip(a)].">
      <j1 rule="hyper" parents="12560 12728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(12728(a,1),12560(a,1))].">
      <j1 rule="para" parents="12728 12560"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12727,a,b,12984,a)].">
      <j1 rule="hyper" parents="64 12727 12984"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),12986(a,1,2,3,1)),flip(a)].">
      <j1 rule="para" parents="9 12986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      K(x,L(y,z * u,(z * u) \ z)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12737,a(flip),b,12987,a)].">
      <j1 rule="hyper" parents="64 12737 12987"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      K(x,L(y,z,L(u \ 1,u,w))) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(224(a,2),12987(a,1,2,3))].">
      <j1 rule="para" parents="224 12987"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12987,a(flip),b,12988,a)].">
      <j1 rule="hyper" parents="64 12987 12988"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12789,a(flip),b,12990,a),flip(a)].">
      <j1 rule="hyper" parents="64 12789 12990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(12727(a,2),12985(a,1))].">
      <j1 rule="para" parents="12727 12985"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12675,a,12735,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12675 12735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      K(x,L(y \ a(z,u,u \ 1),y,z)) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(10218,a,12995,a)].">
      <j1 rule="hyper" parents="10218 12995"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(10231(a,1),12744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10231 12744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12754(a,1),4250(a,1))].">
      <j1 rule="para" parents="12754 4250"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(12998,a,7153,a)].">
      <j1 rule="hyper" parents="12998 7153"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * (y / x),x) = u
    ]]></literal>
    <justification jstring="[para(8260(a,1),12762(a,1))].">
      <j1 rule="para" parents="8260 12762"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      L(x,x \ (y \ z),K(y,z)) \ ((y \ z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * ((y \ z) / x),x) = u
    ]]></literal>
    <justification jstring="[para(5624(a,1),13000(a,1,2))].">
      <j1 rule="para" parents="5624 13000"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      K(x,L(y,z,R(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(12808(a,1),12561(a,1))].">
      <j1 rule="para" parents="12808 12561"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,L(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(13002,a,10269,a)].">
      <j1 rule="hyper" parents="13002 10269"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,12568,a(flip),b,12821,a)].">
      <j1 rule="hyper" parents="131 12568 12821"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9351,a(flip),b,13004,a)].">
      <j1 rule="hyper" parents="64 9351 13004"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,13004,a(flip),b,9351,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 13004 9351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      R(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(12581,a,13005,a),flip(a)].">
      <j1 rule="hyper" parents="12581 13005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      (x * ((y * z) * u)) \ (x * ((y * z) * R(u,y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(u,y,z),(y * z) * u,x) = w
    ]]></literal>
    <justification jstring="[para(13005(a,1),489(a,1,2,2))].">
      <j1 rule="para" parents="13005 489"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(u,z,K(x,T(y,z))) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(6113(a,1),13005(a,1,1,1))].">
      <j1 rule="para" parents="6113 13005"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,96,a,b,13006,a),flip(a)].">
      <j1 rule="hyper" parents="319 96 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5671(a,1),13006(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5671 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) = a(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13010(a,2),11420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13010 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(13012(a,2),11563(a,1))].">
      <j1 rule="para" parents="13012 11563"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4751,a,12843,a),flip(a)].">
      <j1 rule="hyper" parents="4751 12843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T((u * z) / y,y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(761(a,1),13015(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="761 13015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(y,z)) = a(z,u,K(x,K(w,y)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),12899(a,1,2))].">
      <j1 rule="para" parents="6758 12899"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(242(a,1),12900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="242 12900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4214,a(flip),b,12932,a),flip(a)].">
      <j1 rule="hyper" parents="319 4214 12932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(6244,a,13019,a)].">
      <j1 rule="hyper" parents="6244 13019"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,11210,a(flip),b,13020,a),flip(a)].">
      <j1 rule="hyper" parents="319 11210 13020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,T(u * z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(5140(a,1),13021(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5140 13021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((((z \ 1) / u) * u) \ y,u))
    ]]></literal>
    <justification jstring="[para(8155(a,2),13021(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8155 13021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * K(y,x),w) = a(y,z,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9811,a(flip),b,13017,a)].">
      <j1 rule="hyper" parents="64 9811 13017"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(8620(a,1),13024(a,1,1))].">
      <j1 rule="para" parents="8620 13024"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),13025(a,2,3))].">
      <j1 rule="para" parents="6758 13025"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(646(a,1),12703(a,1,2))].">
      <j1 rule="para" parents="646 12703"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12959,a,b,13027,a),flip(a)].">
      <j1 rule="hyper" parents="64 12959 13027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      (x * y) / a(y / z,z,x) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(13028(a,1),9725(a,1,2))].">
      <j1 rule="para" parents="13028 9725"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,12226,a,b,13029,a)].">
      <j1 rule="hyper" parents="64 12226 13029"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      a(x * (y / x),x,z) * (y * (T(x,y) * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,230,a(flip),b,12706,a),flip(a)].">
      <j1 rule="hyper" parents="319 230 12706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(4841,a,12815,a)].">
      <j1 rule="hyper" parents="4841 12815"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),12845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,T(y,z \ 1) \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[para(3361(a,2),13033(a,2,2,2,2))].">
      <j1 rule="para" parents="3361 13033"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,y / ((1 / u) * z)))
    ]]></literal>
    <justification jstring="[para(12164(a,1),12854(a,1,2))].">
      <j1 rule="para" parents="12164 12854"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(772(a,1),12996(a,1,2))].">
      <j1 rule="para" parents="772 12996"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(y,L(z,u,x))) = u * T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10258,a,b,13032,a)].">
      <j1 rule="hyper" parents="64 10258 13032"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      a((x \ y) * (K(y,z) * x),u,w) = a(T(T(y,x),z),u,w)
    ]]></literal>
    <justification jstring="[para(5808(a,1),12070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5808 12070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      a(T((x \ y) * x,z),u,w) = a(T(T(y,x),z),u,w)
    ]]></literal>
    <justification jstring="[para(12068(a,1),13039(a,1,1))].">
      <j1 rule="para" parents="12068 13039"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      a(x,y,(z \ u) * (K(u,w) * z)) = a(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(5808(a,1),12071(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5808 12071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      a(x,y,T((z \ u) * z,w)) = a(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(12068(a,1),13042(a,1,3))].">
      <j1 rule="para" parents="12068 13042"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      T(x,y \ (((1 / z) * K(u,w)) \ v5)) = T(x,y \ ((z \ K(u,w)) \ v5))
    ]]></literal>
    <justification jstring="[para(12356(a,1),12084(a,1,2,2,1))].">
      <j1 rule="para" parents="12356 12084"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,6241,a,b,12171,a),flip(a)].">
      <j1 rule="hyper" parents="35 6241 12171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13046(a,2),7180(a,1))].">
      <j1 rule="para" parents="13046 7180"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(109(a,1),12316(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="109 12316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3252(a,1),13048(a,2,2))].">
      <j1 rule="para" parents="3252 13048"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      ((x \ T(y,z)) * K(z,T(y,u))) * K(z,y) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[para(6099(a,2),12369(a,1,1,2))].">
      <j1 rule="para" parents="6099 12369"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K(x,x \ y) * K(x * (y / x),z) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[para(4242(a,1),12385(a,1,1))].">
      <j1 rule="para" parents="4242 12385"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      K(x,x \ y) * K(y,T(z,x)) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[para(9298(a,1),13051(a,1,2))].">
      <j1 rule="para" parents="9298 13051"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      K(x \ y,x) \ K(y,T(z,x)) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[hyper(4393,a,13052,a)].">
      <j1 rule="hyper" parents="4393 13052"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(11997(a,1),12412(a,1,2,1))].">
      <j1 rule="para" parents="11997 12412"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (1 \ T(1 / (y / z),y))) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(8481(a,1),12430(a,1,2,1,1))].">
      <j1 rule="para" parents="8481 12430"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ y,u,w) * (a(y,z,y) \ z)) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(8537(a,2),12430(a,1,2,2))].">
      <j1 rule="para" parents="8537 12430"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(z \ 1,x)) = L(T(x,a(z \ 1,w,u)),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,12622,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 12622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(10289(a,1),12668(a,1,2))].">
      <j1 rule="para" parents="10289 12668"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      K(x * (y \ 1),y * (x \ z)) = K(x / y,(x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(12190,a,12721,a)].">
      <j1 rule="hyper" parents="12190 12721"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) = K(x / y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(12211,a,13059,a),flip(a)].">
      <j1 rule="hyper" parents="12211 13059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(x \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(13060(a,2),9283(a,1))].">
      <j1 rule="para" parents="13060 9283"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(13061,a,11617,a),flip(a)].">
      <j1 rule="hyper" parents="13061 11617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(x \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(11617(a,1),13061(a,1))].">
      <j1 rule="para" parents="11617 13061"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,R(y / x,u,w) \ z)) = K(x \ y,R(y / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(13062(a,1),11620(a,1,1))].">
      <j1 rule="para" parents="13062 11620"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12665,a(flip),b,12722,a),flip(a)].">
      <j1 rule="hyper" parents="64 12665 12722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(30(a,1),13066(a,1,2))].">
      <j1 rule="para" parents="30 13066"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(302(a,1),13066(a,1,2,1))].">
      <j1 rule="para" parents="302 13066"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1584(a,1),13066(a,1,2))].">
      <j1 rule="para" parents="1584 13066"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      T(x,L(L(y,z,u),z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,13069,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13069 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      T(x,L((y * z) \ u,z,y)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(302(a,1),13070(a,1,2,1))].">
      <j1 rule="para" parents="302 13070"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      T(x,L((y * z) \ (z * u),y,z)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(9221(a,1),13070(a,1,2,1))].">
      <j1 rule="para" parents="9221 13070"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(13067(a,1),10115(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13067 10115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(13067(a,1),12766(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13067 12766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(13067(a,1),12796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13067 12796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(13067(a,1),12903(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13067 12903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z \ 1)) = K(x,u \ (z \ (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(22(a,2),13068(a,1,2,1))].">
      <j1 rule="para" parents="22 13068"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      K(x,L(a(y,y \ z,u),(y \ z) * u,y \ 1)) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(86(a,1),13068(a,1,2,1))].">
      <j1 rule="para" parents="86 13068"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      x * K(y,L(T(z,u * x),x,u \ 1)) = u \ (K(y,z) * (u * x))
    ]]></literal>
    <justification jstring="[hyper(127,a,6113,a(flip),b,13073,a),flip(a)].">
      <j1 rule="hyper" parents="127 6113 13073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(12727(a,1),13073(a,1,2,2))].">
      <j1 rule="para" parents="12727 13073"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,10203,a(flip),b,13074,a),flip(a)].">
      <j1 rule="hyper" parents="35 10203 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      (K(x,L(y,z * u,(z \ K(u,z)) \ 1)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(8494(a,1),13075(a,2,2))].">
      <j1 rule="para" parents="8494 13075"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(K(x,y) / x) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(12320(a,1),13080(a,2,1))].">
      <j1 rule="para" parents="12320 13080"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(13077(a,1),13079(a,1,2))].">
      <j1 rule="para" parents="13077 13079"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      x \ (K(y,R(z,x,u)) * (x * u)) = u * K(y,u \ (x \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[para(105(a,1),13084(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="105 13084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5) \ 1)) = K(x,L(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12684,a(flip),b,12723,a),flip(a)].">
      <j1 rule="hyper" parents="64 12684 12723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      K(x,L(y,z,a(u \ 1,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12937,a,13086,a),flip(a)].">
      <j1 rule="hyper" parents="12937 13086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      K(x,(a(y \ 1,y,z) \ u) \ w) = K(x,u \ (a(y \ 1,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12734,a(flip),b,13087,a),flip(a)].">
      <j1 rule="hyper" parents="64 12734 13087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      K(x,T(y,y \ (z * (y \ u))) * w) = K(x,T(y,y \ (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(12753(a,1),12755(a,1,2,1))].">
      <j1 rule="para" parents="12753 12755"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13068,a(flip),b,12869,a),flip(a)].">
      <j1 rule="hyper" parents="319 13068 12869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) / z) \ w)) = T(x,y \ ((z \ K(z,u)) \ w))
    ]]></literal>
    <justification jstring="[para(4916(a,1),13045(a,1,2,2,1))].">
      <j1 rule="para" parents="4916 13045"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      (x \ T(y,K(z,u))) * K(z,y) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[para(12454(a,1),13050(a,1,1))].">
      <j1 rule="para" parents="12454 13050"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      L(T(x,a(y \ 1,z,u)),w,y) = L(x,w,y) * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10306(a,1),13057(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10306 13057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      L(x,y,z) != L(u,y,z) * a(w,v5,K(u,z))
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z \ 1,v5,w)) = x
    ]]></literal>
    <justification jstring="[para(13093(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="13093 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      K(x,T(y,y \ (z * u)) * w) = K(x,T(y,z * (y \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(11299,a,13089,a),flip(a)].">
      <j1 rule="hyper" parents="11299 13089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(13095(a,1),11299(a,1))].">
      <j1 rule="para" parents="13095 11299"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = L(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8248,a(flip),b,12255,a),flip(a)].">
      <j1 rule="hyper" parents="319 8248 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(10096(a,1),12259(a,1,1))].">
      <j1 rule="para" parents="10096 12259"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,K(w,L(x,y,u))) = v5
    ]]></literal>
    <justification jstring="[para(6742(a,1),12699(a,1,1,3))].">
      <j1 rule="para" parents="6742 12699"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4996,a(flip),b,12841,a),flip(a)].">
      <j1 rule="hyper" parents="319 4996 12841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(6430,a,13100,a)].">
      <j1 rule="hyper" parents="6430 13100"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      K((x / y) \ 1,L(T(z,u),y,y \ u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),13101(a,1,2))].">
      <j1 rule="para" parents="25 13101"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(7216(a,1),12846(a,1,1,3))].">
      <j1 rule="para" parents="7216 12846"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (K(z,u / x) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,12796,a(flip),b,12852,a),flip(a)].">
      <j1 rule="hyper" parents="64 12796 12852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (x * K(z,x \ u)) * y
    ]]></literal>
    <justification jstring="[para(6190(a,1),13104(a,2,1))].">
      <j1 rule="para" parents="6190 13104"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,y \ (y * x))) * u
    ]]></literal>
    <justification jstring="[hyper(8942,a,13105,a)].">
      <j1 rule="hyper" parents="8942 13105"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      L(K(x,K(y,z)),z * K(x,y),L(u,z,K(x,y))) \ (K(x,y) * (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6705(a,1),12917(a,1,1,1))].">
      <j1 rule="para" parents="6705 12917"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(11661(a,1),13085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11661 13085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = T(K(y,x \ (z \ ((u * z) * x))),x)
    ]]></literal>
    <justification jstring="[hyper(127,a,13109,a(flip),b,3268,a)].">
      <j1 rule="hyper" parents="127 13109 3268"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(10108(a,1),13098(a,1,1))].">
      <j1 rule="para" parents="10108 13098"/>
    </justification>
  </clause>

  <clause id="13112">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(12545(a,1),13103(a,1,1))].">
      <j1 rule="para" parents="12545 13103"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12077,a(flip),b,12030,a)].">
      <j1 rule="hyper" parents="64 12077 12030"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,v5),w)) = R(x,y,z \ ((u \ w) \ T(w,v5)))
    ]]></literal>
    <justification jstring="[para(6389(a,1),12063(a,1,3,2))].">
      <j1 rule="para" parents="6389 12063"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ K(y,T(z,x))) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(6099(a,2),12315(a,1,2,1,2))].">
      <j1 rule="para" parents="6099 12315"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(12324(a,2),12344(a,1))].">
      <j1 rule="para" parents="12324 12344"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(u \ v5,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12547(a,1),12678(a,2,2))].">
      <j1 rule="para" parents="12547 12678"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(13118(a,2),10155(a,1))].">
      <j1 rule="para" parents="13118 10155"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(108(a,1),13119(a,1,2,3,1,2))].">
      <j1 rule="para" parents="108 13119"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(13120,a,xx),flip(a)].">
      <j1 rule="hyper" parents="13120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(171(a,1),13121(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="171 13121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12819(a,1),6576(a,1,2,1))].">
      <j1 rule="para" parents="12819 6576"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13123(a,2),6676(a,1))].">
      <j1 rule="para" parents="13123 6676"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12510(a,1),13124(a,1))].">
      <j1 rule="para" parents="12510 13124"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      x \ (1 / (K(y,z) * T(y,u))) = (x \ (1 / T(y,u))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(6851(a,1),12882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6851 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      (x \ (1 / T(y,z))) * K(u,y) = x \ (K(u,y) / T(y,z))
    ]]></literal>
    <justification jstring="[para(7443(a,1),13127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7443 13127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      T(T(x,x * y) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(3327(a,1),12303(a,1,1,1))].">
      <j1 rule="para" parents="3327 12303"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,12591,a(flip),b,12736,a),flip(a)].">
      <j1 rule="hyper" parents="319 12591 12736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(12736(a,2),12627(a,1))].">
      <j1 rule="para" parents="12736 12627"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      K(x,y \ (L(y,z,z \ 1) * u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5291,a(flip),b,13131,a)].">
      <j1 rule="hyper" parents="64 5291 13131"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(1165(a,1),13134(a,1,2))].">
      <j1 rule="para" parents="1165 13134"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      K(x * (y \ z),(x * (y \ z)) \ z) = K(x * (y \ z),y / x)
    ]]></literal>
    <justification jstring="[hyper(12758,a,12957,a),flip(a)].">
      <j1 rule="hyper" parents="12758 12957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,R(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(266(a,1),12992(a,2,2,1))].">
      <j1 rule="para" parents="266 12992"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12989,a(flip),b,13003,a)].">
      <j1 rule="hyper" parents="64 12989 13003"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13090,a(flip),b,13139,a),flip(a)].">
      <j1 rule="hyper" parents="64 13090 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(383(a,1),13141(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="383 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(12308,a,13142,a),flip(a)].">
      <j1 rule="hyper" parents="12308 13142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),w)) = v5
    ]]></literal>
    <justification jstring="[para(13143(a,1),12308(a,1))].">
      <j1 rule="para" parents="13143 12308"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(((u * z) / y) \ 1,y / z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6107,a,b,13016,a),flip(a)].">
      <j1 rule="hyper" parents="319 6107 13016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(9(a,1),13106(a,2,1,2,2))].">
      <j1 rule="para" parents="9 13106"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * u) * z)) = (y * z) \ ((y * K(x,u)) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,13146,a(flip),b,8941,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 13146 8941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * (u / y)) * z)) = R(T(K(x,y \ u),y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,7097,a(flip),b,13147,a),flip(a)].">
      <j1 rule="hyper" parents="319 7097 13147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(11096(a,1),13130(a,1,1,2))].">
      <j1 rule="para" parents="11096 13130"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(6055(a,2),13150(a,1,1))].">
      <j1 rule="para" parents="6055 13150"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(410,a,13151,a)].">
      <j1 rule="hyper" parents="410 13151"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(3327(a,1),13153(a,2,2,1,1))].">
      <j1 rule="para" parents="3327 13153"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7701,a(flip),b,13145,a),flip(a)].">
      <j1 rule="hyper" parents="319 7701 13145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(5255,a,13155,a),flip(a)].">
      <j1 rule="hyper" parents="5255 13155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      K(x,T(y / (z * (z \ u)),y / (z \ u))) = K(x,T(u,z) \ ((z \ u) * (y / (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(319,a,11172,a(flip),b,13156,a),flip(a)].">
      <j1 rule="hyper" parents="319 11172 13156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      K(x,T(y / ((z / (z * u)) * (z * u)),y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u))))
    ]]></literal>
    <justification jstring="[para(4805(a,1),13156(a,2,2,1))].">
      <j1 rule="para" parents="4805 13156"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12449(a,1),11998(a,2,2))].">
      <j1 rule="para" parents="12449 11998"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,3507,a(flip),b,13159,a),flip(a)].">
      <j1 rule="hyper" parents="319 3507 13159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5120,a,13160,a)].">
      <j1 rule="hyper" parents="5120 13160"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[para(12592(a,1),12021(a,1,2))].">
      <j1 rule="para" parents="12592 12021"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(13163(a,1),12267(a,1,2))].">
      <j1 rule="para" parents="13163 12267"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(4463(a,1),12314(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4463 12314"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(4095(a,1),13166(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4095 13166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,T((y / z) \ 1,y),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),12323(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 12323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(8244(a,1),13168(a,2,2))].">
      <j1 rule="para" parents="8244 13168"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(11794(a,1),13169(a,2,2))].">
      <j1 rule="para" parents="11794 13169"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(12325,a,13170,a)].">
      <j1 rule="hyper" parents="12325 13170"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),13171(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 13171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      K(x,(T(y * z,z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12312,a(flip),b,12447,a)].">
      <j1 rule="hyper" parents="64 12312 12447"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(12787(a,1),12817(a,1,2,2))].">
      <j1 rule="para" parents="12787 12817"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(T(x,w),y,z) = (L(x,y,z) * u) / L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10281,a(flip),b,13174,a),flip(a)].">
      <j1 rule="hyper" parents="64 10281 13174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13176">
    <literal><![CDATA[
      K(x,L(y,z,(L(u,w,v5) \ u) \ y)) = K(x,L(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(12960,a,12684,a)].">
      <j1 rule="hyper" parents="12960 12684"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,L(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(12985,a,13176,a)].">
      <j1 rule="hyper" parents="12985 13176"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,z,z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12737,a(flip),b,13177,a),flip(a)].">
      <j1 rule="hyper" parents="64 12737 13177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,z,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13177,a(flip),b,13178,a),flip(a)].">
      <j1 rule="hyper" parents="319 13177 13178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = a(w,z,K(u,K(x,y))) * K(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(12615(a,1),12983(a,2,1))].">
      <j1 rule="para" parents="12615 12983"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12697,a(flip),b,13180,a),flip(a)].">
      <j1 rule="hyper" parents="319 12697 13180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ w,u))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(95(a,1),13181(a,1,2,2))].">
      <j1 rule="para" parents="95 13181"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(9222(a,2),13182(a,1,2,2))].">
      <j1 rule="para" parents="9222 13182"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K(((y \ z) \ 1) / x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6742,a,b,12185,a),flip(a)].">
      <j1 rule="hyper" parents="319 6742 12185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,(x / z) \ (T(x,y) / z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(12057(a,1),12212(a,2,1))].">
      <j1 rule="para" parents="12057 12212"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,K(x,T(y,z))) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(12118(a,1),13185(a,1,2,2))].">
      <j1 rule="para" parents="12118 13185"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(x / z,T(y,z))) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(6742(a,1),13186(a,1,2))].">
      <j1 rule="para" parents="6742 13186"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z \ x,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(6156(a,1),13187(a,1,2,2))].">
      <j1 rule="para" parents="6156 13187"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7010(a,1),13188(a,1,2))].">
      <j1 rule="para" parents="7010 13188"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(6758(a,1),13189(a,1,2))].">
      <j1 rule="para" parents="6758 13189"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ ((T(y,z) \ z) / u)) = T(x,(((y \ T(z,y)) \ z) \ z) / u)
    ]]></literal>
    <justification jstring="[para(5849(a,1),12309(a,1,2,1))].">
      <j1 rule="para" parents="5849 12309"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(12422,a,11990,a),flip(a)].">
      <j1 rule="hyper" parents="12422 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(12422,a,11982,a)].">
      <j1 rule="hyper" parents="12422 11982"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13193(a,1),5384(a,1))].">
      <j1 rule="para" parents="13193 5384"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      T(x,(T(y,z / y) / (1 / (1 / (z / y)))) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(2755(a,1),12462(a,1,2,1,1))].">
      <j1 rule="para" parents="2755 12462"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / (1 / (1 / (z / y)))) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(3274(a,1),13196(a,1,2,1,1))].">
      <j1 rule="para" parents="3274 13196"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x / y) * R((x / y) \ 1,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,1050,a(flip),b,12515,a),flip(a)].">
      <j1 rule="hyper" parents="319 1050 12515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,1438,a(flip),b,13198,a),flip(a)].">
      <j1 rule="hyper" parents="319 1438 13198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(7802(a,1),13199(a,2,1,2))].">
      <j1 rule="para" parents="7802 13199"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,8694,a(flip),b,13200,a),flip(a)].">
      <j1 rule="hyper" parents="319 8694 13200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(9068(a,1),13201(a,1,1))].">
      <j1 rule="para" parents="9068 13201"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(11649,a,13202,a)].">
      <j1 rule="hyper" parents="11649 13202"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9748,a,b,13203,a)].">
      <j1 rule="hyper" parents="64 9748 13203"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(11338,a,12870,a)].">
      <j1 rule="hyper" parents="11338 12870"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,R(z,y,y \ 1) \ ((y \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(11543,a,13205,a)].">
      <j1 rule="hyper" parents="11543 13205"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13068,a(flip),b,13206,a),flip(a)].">
      <j1 rule="hyper" parents="64 13068 13206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(538(a,1),13207(a,1,2,1))].">
      <j1 rule="para" parents="538 13207"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13208(a,2,2,2))].">
      <j1 rule="para" parents="9 13208"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4761,a(flip),b,13209,a)].">
      <j1 rule="hyper" parents="64 4761 13209"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,L(u,y,x))) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(8412(a,1),13038(a,1,1))].">
      <j1 rule="para" parents="8412 13038"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,L(z,y,x))) = y * T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6791(a,1),13211(a,1,1,2))].">
      <j1 rule="para" parents="6791 13211"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      x \ ((y * T(x,K(z,u))) * K(z,K(u,y * x))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(10666,a,13212,a)].">
      <j1 rule="hyper" parents="10666 13212"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      x \ ((y * T(x,K(z,u))) * (K(u,T(z,y * x)) * K(z,u))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(7060(a,2),13213(a,1,2,2))].">
      <j1 rule="para" parents="7060 13213"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * x))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(8286(a,2),13214(a,1,2))].">
      <j1 rule="para" parents="8286 13214"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * T(x,K(z,w))))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(6825(a,2),13215(a,1,2,2,2))].">
      <j1 rule="para" parents="6825 13215"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,y \ 1))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12720,a,b,13078,a)].">
      <j1 rule="hyper" parents="64 12720 13078"/>
    </justification>
  </clause>

  <clause id="13218">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(z,u) \ ((u \ z) * (y / (u \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),13157(a,1,2,1,2))].">
      <j1 rule="para" parents="10 13157"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K((y \ z) \ (x \ 1),y))
    ]]></literal>
    <justification jstring="[para(12170(a,1),13184(a,2,2))].">
      <j1 rule="para" parents="12170 13184"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,1))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(12726(a,1),13217(a,1,3))].">
      <j1 rule="para" parents="12726 13217"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(498(a,1),13220(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="498 13220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,10197,a(flip),b,13221,a),flip(a)].">
      <j1 rule="hyper" parents="319 10197 13221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((((z \ u) * y) \ y) * ((z \ u) * y))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(8238(a,1),13222(a,1,2,1))].">
      <j1 rule="para" parents="8238 13222"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K(z \ (y * (x \ 1)),y))
    ]]></literal>
    <justification jstring="[para(5687(a,1),13219(a,2,2))].">
      <j1 rule="para" parents="5687 13219"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z \ (y * (x \ 1))))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a(flip),b,13224,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 13224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z \ (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,8049,a(flip),b,13225,a),flip(a)].">
      <j1 rule="hyper" parents="319 8049 13225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,L(x,y,y \ 1)) = K((1 / y) \ ((y * x) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(12281,a,12228,a),flip(a)].">
      <j1 rule="hyper" parents="12281 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,L(x,y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * ((y * x) \ z),x) = u
    ]]></literal>
    <justification jstring="[para(13227(a,2),12210(a,1))].">
      <j1 rule="para" parents="13227 12210"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ z,R(x,y,y \ 1)) = K((y \ 1) \ ((x * y) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(12276,a,12230,a),flip(a)].">
      <j1 rule="hyper" parents="12276 12230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ z,R(x,y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * ((x * y) \ z),x) = u
    ]]></literal>
    <justification jstring="[para(13230(a,2),12261(a,1))].">
      <j1 rule="para" parents="13230 12261"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(9076(a,1),12299(a,1,2))].">
      <j1 rule="para" parents="9076 12299"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13175,a(flip),b,12818,a)].">
      <j1 rule="hyper" parents="64 13175 12818"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),z \ 1)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(1587(a,1),12915(a,1,2))].">
      <j1 rule="para" parents="1587 12915"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(x,y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10147,a(flip),b,13234,a),flip(a)].">
      <j1 rule="hyper" parents="64 10147 13234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[para(11790(a,1),13235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11790 13235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (z \ 1))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,4687,a(flip),b,13237,a)].">
      <j1 rule="hyper" parents="64 4687 13237"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(12395(a,1),12147(a,1,1,1,2))].">
      <j1 rule="para" parents="12395 12147"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(4505(a,1),13239(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4505 13239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2782(a,2),13240(a,1,2,2,1))].">
      <j1 rule="para" parents="2782 13240"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(81(a,1),13241(a,1,2,2))].">
      <j1 rule="para" parents="81 13241"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(8543(a,1),13242(a,1,2))].">
      <j1 rule="para" parents="8543 13242"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(206,a,13244,a,b,xx)].">
      <j1 rule="hyper" parents="206 13244"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10859(a,1),12785(a,2,2))].">
      <j1 rule="para" parents="10859 12785"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w * K(z,z \ u))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(12781(a,1),13246(a,1,2,3))].">
      <j1 rule="para" parents="12781 13246"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = (((w \ v5) \ v5) * K(u,T(z,x) / (y * x))) \ T(w,w \ v5)
    ]]></literal>
    <justification jstring="[para(11210(a,1),12931(a,2,1,2))].">
      <j1 rule="para" parents="11210 12931"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5177,a(flip),b,13248,a),flip(a)].">
      <j1 rule="hyper" parents="319 5177 13248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      K((x * ((y \ 1) / z)) \ u,T(w,z * y)) = K(T(u,x) / (((y \ 1) / z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12160,a(flip),b,13249,a)].">
      <j1 rule="hyper" parents="64 12160 13249"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      L(x,x \ (y \ z),K(y,z)) \ ((y \ z) * K(y,z)) = T(K(y,z) * ((y \ z) / x),x)
    ]]></literal>
    <justification jstring="[hyper(13001,a,xx),flip(a)].">
      <j1 rule="hyper" parents="13001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(12534(a,1),13009(a,1,2))].">
      <j1 rule="para" parents="12534 13009"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      (x * K(y,T(z,x))) * R(u,x,K(y,T(z,x))) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12933,a(flip),b,13252,a),flip(a)].">
      <j1 rule="hyper" parents="64 12933 13252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(6113(a,1),13253(a,1,1))].">
      <j1 rule="para" parents="6113 13253"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(8206(a,1),13254(a,1,2))].">
      <j1 rule="para" parents="8206 13254"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(488,a,13255,a),flip(a)].">
      <j1 rule="hyper" parents="488 13255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(840,a,13256,a),flip(a)].">
      <j1 rule="hyper" parents="840 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      L(x / y,y,K(z,u)) = (x * K(z,u)) / (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(805,a,13256,a),flip(a)].">
      <j1 rule="hyper" parents="805 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) / (y * T(z,u)) = L(x,y * z,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4949,a,b,13256,a)].">
      <j1 rule="hyper" parents="64 4949 13256"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13007,a(flip),b,13256,a),flip(a)].">
      <j1 rule="hyper" parents="64 13007 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5188,a(flip),b,13256,a),flip(a)].">
      <j1 rule="hyper" parents="64 5188 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(130,a,13256,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 13256 20"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(13256(a,1),519(a,1,1))].">
      <j1 rule="para" parents="13256 519"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13256(a,1),5538(a,1))].">
      <j1 rule="para" parents="13256 5538"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(11589(a,2),13256(a,1,3))].">
      <j1 rule="para" parents="11589 13256"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(4221,a,13261,a)].">
      <j1 rule="hyper" parents="4221 13261"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12716,a,b,13261,a)].">
      <j1 rule="hyper" parents="319 12716 13261"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12614,a,b,13261,a)].">
      <j1 rule="hyper" parents="319 12614 13261"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12563,a,b,13261,a)].">
      <j1 rule="hyper" parents="319 12563 13261"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12551,a,b,13261,a)].">
      <j1 rule="hyper" parents="319 12551 13261"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12543,a,b,13261,a)].">
      <j1 rule="hyper" parents="319 12543 13261"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11476,a,b,13261,a)].">
      <j1 rule="hyper" parents="319 11476 13261"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      L(x * y,z,K(u,y)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12943,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 12943 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(319,a,12719,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 12719 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12716,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 12716 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(T(x,a(w,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,12714,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 12714 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12635,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 12635 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      L(a(x,y,y \ 1),z,K(u,w)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,11584,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 11584 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(319,a,111,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="319 111 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * K(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,13261,a,b,4930,a)].">
      <j1 rule="hyper" parents="131 13261 4930"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,13261,a,b,12614,a)].">
      <j1 rule="hyper" parents="127 13261 12614"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,13261,a,b,11573,a)].">
      <j1 rule="hyper" parents="127 13261 11573"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,12624,a(flip),b,13261,a),flip(a)].">
      <j1 rule="hyper" parents="42 12624 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      L(x,y,K(L(z,u,x),w)) = T(x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(11603,a,13261,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11603 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(13261(a,2),393(a,1))].">
      <j1 rule="para" parents="13261 393"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(13261(a,2),11572(a,2,2))].">
      <j1 rule="para" parents="13261 11572"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(13261(a,2),12623(a,1,1))].">
      <j1 rule="para" parents="13261 12623"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x * w) = L(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[para(13261(a,2),12578(a,2,1))].">
      <j1 rule="para" parents="13261 12578"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(13261(a,2),12585(a,2,2))].">
      <j1 rule="para" parents="13261 12585"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(13261(a,2),12935(a,1,1))].">
      <j1 rule="para" parents="13261 12935"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12635,a(flip),b,13268,a),flip(a)].">
      <j1 rule="hyper" parents="319 12635 13268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13268(a,1),4221(a,1))].">
      <j1 rule="para" parents="13268 4221"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13268,a,b,13286,a)].">
      <j1 rule="hyper" parents="64 13268 13286"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),z,K(y,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,12635,a,b,13286,a),flip(a)].">
      <j1 rule="hyper" parents="41 12635 13286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,13286,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 13286 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(42,a,4774,a,b,13296,a),flip(a)].">
      <j1 rule="hyper" parents="42 4774 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13270(a,2),4221(a,1))].">
      <j1 rule="para" parents="13270 4221"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      a(x,y,z) \ L(u,y,K(x,z)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,13271,a(flip),b,12718,a(flip))].">
      <j1 rule="hyper" parents="127 13271 12718"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      T(x,K(y,z) \ u) \ (u \ (K(y,z) * (x * (K(y,z) \ u)))) = a(y,K(y,z) \ u,K(z,T(x,K(y,z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(127,a,716,a(flip),b,13272,a)].">
      <j1 rule="hyper" parents="127 716 13272"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(13272(a,1),12564(a,1))].">
      <j1 rule="para" parents="13272 12564"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),z,K(x \ y,u)) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(12354,a,13275,a),flip(a)].">
      <j1 rule="hyper" parents="12354 13275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      L(T(T(x,L(y,z,u)),y),z,K(y,u)) \ w = K(L(y,z,u),x) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(13294(a,2),4447(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13294 4447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(8855(a,1),13287(a,1,3))].">
      <j1 rule="para" parents="8855 13287"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(12687(a,2),13295(a,1))].">
      <j1 rule="para" parents="12687 13295"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13007(a,2),13295(a,1))].">
      <j1 rule="para" parents="13007 13295"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13269(a,1),13295(a,1))].">
      <j1 rule="para" parents="13269 13295"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13278(a,2),13295(a,1))].">
      <j1 rule="para" parents="13278 13295"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a,b,13306,a),flip(a)].">
      <j1 rule="hyper" parents="319 13261 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a,b,13293,a)].">
      <j1 rule="hyper" parents="319 13261 13293"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(38,a,820,a(flip),b,13312,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 820 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      K(x,y) \ L((z * K(x,L(y,z,a(u,w,v5)))) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(417,a,13282,a,b,12766,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="417 13282 12766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[para(5786(a,1),13301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5786 13301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(11589(a,2),13267(a,2,3))].">
      <j1 rule="para" parents="11589 13267"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(13261(a,2),13279(a,2,1))].">
      <j1 rule="para" parents="13261 13279"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(12525(a,2),13283(a,2,2))].">
      <j1 rule="para" parents="12525 13283"/>
    </justification>
  </clause>

  <clause id="13320">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a(flip),b,13318,a(flip))].">
      <j1 rule="hyper" parents="41 25 13318"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13318(a,2),9603(a,1))].">
      <j1 rule="para" parents="13318 9603"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(11589(a,2),13320(a,1,3))].">
      <j1 rule="para" parents="11589 13320"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = L(z,x \ y,K(x,y)) \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(13320(a,1),13251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13320 13251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      a(x,(y * K(z,u)) * L(w / y,y,K(z,u)),x) = a(x,w * K(z,u),x)
    ]]></literal>
    <justification jstring="[para(13259(a,2),11498(a,1,2,2))].">
      <j1 rule="para" parents="13259 11498"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) * (K(z,u) * y) = (x * y) * K(z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6125,a(flip),b,13263,a)].">
      <j1 rule="hyper" parents="64 6125 13263"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      L(x,1 / T(y,z),K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(5496(a,1),13263(a,1,2))].">
      <j1 rule="para" parents="5496 13263"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[para(11950(a,1),13263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11950 13263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = L(a(K(z,y) * x,u,u \ 1),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(768(a,1),13299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="768 13299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(11589(a,2),13322(a,2,3))].">
      <j1 rule="para" parents="11589 13322"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13320,a(flip),b,13258,a),flip(a)].">
      <j1 rule="hyper" parents="64 13320 13258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      (x * K(y,z)) / (L(x,u,u \ 1) * K(y,z)) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3954(a,1),13332(a,1,2,1))].">
      <j1 rule="para" parents="3954 13332"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = (z \ (x \ y)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13001,a,13264,a)].">
      <j1 rule="hyper" parents="13001 13264"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4244(a,1),13264(a,1,2))].">
      <j1 rule="para" parents="4244 13264"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      x \ (T(y,z) * K(u,y)) = (x \ T(y,z)) * K(u,y)
    ]]></literal>
    <justification jstring="[para(11969(a,1),13264(a,1,1))].">
      <j1 rule="para" parents="11969 13264"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      (x \ T(y,K(z,u))) * K(z,y) = x \ (y * K(z,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7062(a,1),13337(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7062 13337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13092,a(flip),b,13338,a),flip(a)].">
      <j1 rule="hyper" parents="64 13092 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6112,a,b,13339,a),flip(a)].">
      <j1 rule="hyper" parents="319 6112 13339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = (y \ x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12518,a,b,13340,a)].">
      <j1 rule="hyper" parents="64 12518 13340"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = K(z,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(7154,a,13341,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7154 13341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = K(y,z) * ((x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(78(a,1),13342(a,1,1,1))].">
      <j1 rule="para" parents="78 13342"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      ((x * (T(y * z,x) / x)) * K(z,u)) / (y * T(z,u)) = L(a(x,x \ (y * z),x),y * z,K(z,u))
    ]]></literal>
    <justification jstring="[para(8711(a,1),13260(a,1,1,1))].">
      <j1 rule="para" parents="8711 13260"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      (L(K(x,T(y,z)) \ z,K(x,T(y,z)),K(x,T(y,z))) \ L(K(x,T(y,z)) \ (z * u),K(x,T(y,z)),K(x,T(y,z)))) * (K(x,y) * z) = (u * z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1744(a,2),13325(a,1,1))].">
      <j1 rule="para" parents="1744 13325"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(10780(a,1),13335(a,1,1))].">
      <j1 rule="para" parents="10780 13335"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(11968(a,1),13346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11968 13346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * (z / y)) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,11364,a(flip),b,13347,a),flip(a)].">
      <j1 rule="hyper" parents="64 11364 13347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      (K(x,x \ y) * z) / y = K(x,x \ y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9186,a(flip),b,13348,a),flip(a)].">
      <j1 rule="hyper" parents="64 9186 13348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(10802(a,1),13323(a,2,1))].">
      <j1 rule="para" parents="10802 13323"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(5624(a,2),13350(a,2,2))].">
      <j1 rule="para" parents="5624 13350"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13334,a(flip),b,13351,a),flip(a)].">
      <j1 rule="hyper" parents="64 13334 13351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4507,a,b,13352,a)].">
      <j1 rule="hyper" parents="64 4507 13352"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(12456(a,1),13353(a,2,1))].">
      <j1 rule="para" parents="12456 13353"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12237,a(flip),b,13354,a),flip(a)].">
      <j1 rule="hyper" parents="64 12237 13354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5185,a,13355,a)].">
      <j1 rule="hyper" parents="5185 13355"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(8824(a,1),13327(a,1,1))].">
      <j1 rule="para" parents="8824 13327"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(9572(a,1),13357(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9572 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8455,a,b,13358,a)].">
      <j1 rule="hyper" parents="64 8455 13358"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(4056(a,1),13359(a,2,2))].">
      <j1 rule="para" parents="4056 13359"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2733,a,13360,a),flip(a)].">
      <j1 rule="hyper" parents="2733 13360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(8456,a,13361,a)].">
      <j1 rule="hyper" parents="8456 13361"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[para(13363(a,1),9850(a,2,2))].">
      <j1 rule="para" parents="13363 9850"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(13364(a,1),7235(a,1,2))].">
      <j1 rule="para" parents="13364 7235"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9768,a(flip),b,13365,a),flip(a)].">
      <j1 rule="hyper" parents="64 9768 13365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(208(a,1),13367(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="208 13367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      L(T(T(x,L(y,z,u)),y),z,K(y,u)) \ w = K(y,L(x,z,u)) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(10133(a,1),13305(a,2,1))].">
      <j1 rule="para" parents="10133 13305"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      L(T(T(x,y),L(y,z,u)),z,K(y,u)) \ w = K(y,L(x,z,u)) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(23(a,1),13369(a,1,1,1))].">
      <j1 rule="para" parents="23 13369"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (T(y,L(x,z,u)) \ w) = T(T(y,x),x) \ w
    ]]></literal>
    <justification jstring="[para(13297(a,1),13370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13297 13370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,13281,a(flip),b,13329,a),flip(a)].">
      <j1 rule="hyper" parents="319 13281 13329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((z \ 1) \ y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),13023(a,2,2,1,1))].">
      <j1 rule="para" parents="12 13023"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11979,a(flip),b,13375,a),flip(a)].">
      <j1 rule="hyper" parents="319 11979 13375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(12131(a,1),13376(a,1,2,1))].">
      <j1 rule="para" parents="12131 13376"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(8155(a,1),13378(a,1,2,2))].">
      <j1 rule="para" parents="8155 13378"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * ((K(z,u) * (y * T(x,K(z,w)))) \ (y * T(x,K(z,w))))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5934(a,2),13216(a,1,2,2))].">
      <j1 rule="para" parents="5934 13216"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(12924(a,1),12658(a,2,2))].">
      <j1 rule="para" parents="12924 12658"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),z / u,u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(8825(a,1),12859(a,1,2))].">
      <j1 rule="para" parents="8825 12859"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(9222(a,1),13383(a,1,2))].">
      <j1 rule="para" parents="9222 13383"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * T(u,u \ 1)) / z)
    ]]></literal>
    <justification jstring="[para(9643(a,1),13384(a,2,2))].">
      <j1 rule="para" parents="9643 13384"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9662,a(flip),b,13385,a),flip(a)].">
      <j1 rule="hyper" parents="319 9662 13385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      L(K(x,K(y,T(z,x))),u,u \ x) \ ((K(z,y) \ u) * (u \ x)) = L(K(y,T(z,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(10096(a,2),12961(a,1,1))].">
      <j1 rule="para" parents="10096 12961"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11693(a,1),13011(a,1,2,2))].">
      <j1 rule="para" parents="11693 13011"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ (K(x,y) * ((y * z) * R(x,y,z))) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7357(a,1),13388(a,1,2))].">
      <j1 rule="para" parents="7357 13388"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      L(a(x,y,z),(y * z) * x,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13008,a,13389,a)].">
      <j1 rule="hyper" parents="13008 13389"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,R(x \ y,u,w) \ z)) = K(x \ y,R(y / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(5864(a,1),13065(a,1,2,2))].">
      <j1 rule="para" parents="5864 13065"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,z \ 1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(4205(a,2),13082(a,1,1,1,2,3))].">
      <j1 rule="para" parents="4205 13082"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      ((x * (T(y * z,x) / x)) * K(z,u)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10981,a(flip),b,13344,a),flip(a)].">
      <j1 rule="hyper" parents="319 10981 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,u \ x) \ ((K(y,z) \ u) * (u \ x)) = L(K(z,T(y,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(6790(a,1),13387(a,1,1,1))].">
      <j1 rule="para" parents="6790 13387"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((K(y,z) \ u) * (u \ x)) = L(K(z,T(y,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(12745(a,1),13395(a,1,1))].">
      <j1 rule="para" parents="12745 13395"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      K(x \ y,R(y / x,z,u) \ w) = K(x \ y,(y \ w) * x) * K(y,K(x,w))
    ]]></literal>
    <justification jstring="[para(11647(a,1),13391(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11647 13391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z)) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(517(a,1),13398(a,1,2)),flip(a)].">
      <j1 rule="para" parents="517 13398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(10853(a,1),13392(a,1,1,1,2))].">
      <j1 rule="para" parents="10853 13392"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(z,u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(208(a,1),13401(a,1,1,1,2,3,1))].">
      <j1 rule="para" parents="208 13401"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      T(x,L((y * K(L(z,u,w),v5)) / (w * u),w * u,K(v5,L(z,u,w)))) = T(x,y / (w * (u * K(v5,z))))
    ]]></literal>
    <justification jstring="[para(5174(a,1),12861(a,1,2,1,1))].">
      <j1 rule="para" parents="5174 12861"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      T(x,L(y * K(z,u * w),u \ T(w * u,z),T(w,u))) = T(x,(y * T(w,u)) / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[para(5174(a,1),12912(a,1,2,1))].">
      <j1 rule="para" parents="5174 12912"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      K(x,y) \ L(K(x,T(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12902(a,1),13314(a,1,2,1))].">
      <j1 rule="para" parents="12902 13314"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      K(x,y) * L(K(y,T(x,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(4384,a,13405,a)].">
      <j1 rule="hyper" parents="4384 13405"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      T(x,L((y * K(z,L(u,w,v5))) / (v5 * w),v5 * w,K(u,L(z,w,v5)))) = T(x,y / (v5 * (w * K(u,z))))
    ]]></literal>
    <justification jstring="[para(10133(a,1),13403(a,1,2,1,1,2))].">
      <j1 rule="para" parents="10133 13403"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      K(x,y) * (z * (K(K(x,y) * z,u) * K(K(x,y) * z,u))) = T(T(K(x,y) * z,u),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4164,a(flip),b,12885,a),flip(a)].">
      <j1 rule="hyper" parents="319 4164 12885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),(w * u) \ w,T(z,u \ 1))) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(11783(a,1),12853(a,1,2))].">
      <j1 rule="para" parents="11783 12853"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      T(x,K(y,z) * u) \ (u \ (K(z,y) * (x * (K(z,y) \ u)))) = a(z,K(z,y) \ u,K(y,T(x,K(z,y) \ u)))
    ]]></literal>
    <justification jstring="[para(4356(a,1),13302(a,1,1,2))].">
      <j1 rule="para" parents="4356 13302"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,z * u))
    ]]></literal>
    <justification jstring="[para(9252(a,1),13022(a,2,2))].">
      <j1 rule="para" parents="9252 13022"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (T(z * u,u \ 1) * ((u * z) \ z))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(6330(a,1),13411(a,1,2,1))].">
      <j1 rule="para" parents="6330 13411"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (K(z * u,u \ 1) * T(z,u))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(5139(a,1),13412(a,1,2,2))].">
      <j1 rule="para" parents="5139 13412"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(K(z * u,u \ 1) * z,u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(7387(a,2),13413(a,1,2,2))].">
      <j1 rule="para" parents="7387 13413"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(z * K(u * z,u \ 1),u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(9295(a,1),13414(a,1,2,2,1))].">
      <j1 rule="para" parents="9295 13414"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (u \ T(z * u,u \ 1))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(12045(a,1),13415(a,1,2,2))].">
      <j1 rule="para" parents="12045 13415"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(5174(a,1),12409(a,1,1,2))].">
      <j1 rule="para" parents="5174 12409"/>
    </justification>
  </clause>

  <clause id="13418">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),(x \ y) * T(x,L(x \ y,z,u))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(22(a,2),12427(a,1,2,2))].">
      <j1 rule="para" parents="22 12427"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),L(x * (x \ y),z,K(u,x \ y))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(13276(a,2),13418(a,1,2))].">
      <j1 rule="para" parents="13276 13418"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),L(y,z,K(u,x \ y))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),13419(a,1,2,1))].">
      <j1 rule="para" parents="10 13419"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      K(L(x,y,z),T(T(u,w),v5)) \ ((R(w,v6,v7) * T(u,w)) / T(u,w)) = (T(T(u,w),R(T(x,v5),y,z)) * R(T(w,u),v6,v7)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(6154(a,1),12831(a,1,1))].">
      <j1 rule="para" parents="6154 12831"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u))))
    ]]></literal>
    <justification jstring="[para(12(a,1),13158(a,1,2,1,2))].">
      <j1 rule="para" parents="12 13158"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5137(a,2),13380(a,1,2))].">
      <j1 rule="para" parents="5137 13380"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z \ u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11221,a,b,13423,a),flip(a)].">
      <j1 rule="hyper" parents="319 11221 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,K(z,y) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(39,a,4057,a(flip),b,13423,a),flip(a)].">
      <j1 rule="hyper" parents="39 4057 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(u,z) * y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),13423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(u * T((K(x,y) * z) / K(x,y),K(y,x)),K(y,x)) = T(u,T(K(x,y),z) * z)
    ]]></literal>
    <justification jstring="[para(3103(a,2),13423(a,2,2))].">
      <j1 rule="para" parents="3103 13423"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(6791(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="6791 13423"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u \ 1)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(7033(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="7033 13423"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      (x * K(y,z)) \ T(u * T(x * K(y,z),K(y,z)),K(y,z)) = T(u,T(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6801(a,1),13423(a,2,2))].">
      <j1 rule="para" parents="6801 13423"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      K(x \ T(T(y * T(z,K(u,w)),K(u,w)) / z,T(y * T(z,K(u,w)),K(u,w))),v5) = K(x \ T(y,K(w,u) * z),v5)
    ]]></literal>
    <justification jstring="[para(13423(a,1),11123(a,2,1,2))].">
      <j1 rule="para" parents="13423 11123"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11397,a,b,13427,a)].">
      <j1 rule="hyper" parents="64 11397 13427"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(6791(a,1),13430(a,1,2))].">
      <j1 rule="para" parents="6791 13430"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      T(R(x * K(K(y,z),u),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8448(a,2),13434(a,1,1))].">
      <j1 rule="para" parents="8448 13434"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13423,a(flip),b,13435,a)].">
      <j1 rule="hyper" parents="64 13423 13435"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11238,a(flip),b,13437,a),flip(a)].">
      <j1 rule="hyper" parents="319 11238 13437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11221,a(flip),b,13437,a),flip(a)].">
      <j1 rule="hyper" parents="319 11221 13437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(127,a,13437,a,b,4019,a(flip))].">
      <j1 rule="hyper" parents="127 13437 4019"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),13437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 13437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4314(a,1),13437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4314 13437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      T(x,K(T(y,z),z / u) * w) = T(x,K(u \ z,y) * w)
    ]]></literal>
    <justification jstring="[para(6109(a,1),13437(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6109 13437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * y) \ u)) = T(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(9187(a,1),13437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9187 13437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,z) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(13437(a,1),11225(a,1,2,1))].">
      <j1 rule="para" parents="13437 11225"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,12969,a(flip),b,13442,a),flip(a)].">
      <j1 rule="hyper" parents="41 12969 13442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(13447(a,1),50(a,2))].">
      <j1 rule="para" parents="13447 50"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * (z * x) = z * (K(x,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(13447(a,1),4926(a,1,2,1))].">
      <j1 rule="para" parents="13447 4926"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(12968(a,1),13448(a,1))].">
      <j1 rule="para" parents="12968 13448"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      T(T(x,K(y,K(z,u))),K(u,z) * y) = T(x,y * K(z,z * u))
    ]]></literal>
    <justification jstring="[hyper(9340,a,13438,a),flip(a)].">
      <j1 rule="hyper" parents="9340 13438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13437,a,b,13439,a),flip(a)].">
      <j1 rule="hyper" parents="319 13437 13439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(4106,a,13441,a)].">
      <j1 rule="hyper" parents="4106 13441"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13441(a,1),4106(a,1))].">
      <j1 rule="para" parents="13441 4106"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(11269,a,13453,a),flip(a)].">
      <j1 rule="hyper" parents="11269 13453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4081(a,1),13453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4081 13453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4356(a,2),13453(a,1,2))].">
      <j1 rule="para" parents="4356 13453"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4314(a,1),13453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4314 13453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      K(x,K(y,z) \ T(K(y,z) * u,w)) = K(x,K(y,z) * T(K(z,y) \ u,w))
    ]]></literal>
    <justification jstring="[para(4878(a,2),13453(a,1,2))].">
      <j1 rule="para" parents="4878 13453"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(6213(a,1),13453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6213 13453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      K(x,K(y,z) \ (y * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4081(a,1),13457(a,2,2))].">
      <j1 rule="para" parents="4081 13457"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      K(x,K(y,z) \ (z \ u)) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4314(a,1),13457(a,2,2))].">
      <j1 rule="para" parents="4314 13457"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4293(a,2),13443(a,1,2))].">
      <j1 rule="para" parents="4293 13443"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(4651(a,1),13443(a,1,2,1))].">
      <j1 rule="para" parents="4651 13443"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4510(a,1),13443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4510 13443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      T(x,T(y,y \ z) \ u) = T(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4512(a,2),13443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4512 13443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      K(K(x,x \ y) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(206,a,13452,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 13452 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / y) \ u)) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(4670(a,1),13452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4670 13452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z,z \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,z \ u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(13452(a,1),11225(a,1,2,1))].">
      <j1 rule="para" parents="13452 11225"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13453,a,b,13455,a),flip(a)].">
      <j1 rule="hyper" parents="319 13453 13455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4437(a,1),13456(a,1,2))].">
      <j1 rule="para" parents="4437 13456"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4348(a,1),13456(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4348 13456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4293(a,2),13458(a,1,2))].">
      <j1 rule="para" parents="4293 13458"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4510(a,1),13458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4510 13458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4512(a,2),13458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4512 13458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      T(x,T(T(y,z),z) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(232(a,1),13463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="232 13463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) / K(y \ z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(12153(a,1),13463(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12153 13463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      T(x,((y \ z) \ K(u,z \ y)) \ w) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(5097(a,1),13476(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5097 13476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(8468(a,1),13465(a,1,2,1,1))].">
      <j1 rule="para" parents="8468 13465"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y)) * w) = K(x,K(y,z \ u) * w)
    ]]></literal>
    <justification jstring="[para(8153(a,1),13470(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8153 13470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(12288,a,13471,a)].">
      <j1 rule="hyper" parents="12288 13471"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * (z * K(y,z))) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[para(8898(a,1),13472(a,2,2))].">
      <j1 rule="para" parents="8898 13472"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      K(x,((K(y,y \ z) * u) / z) * w) = K(x,T(((y \ z) * y) \ u,z) * w)
    ]]></literal>
    <justification jstring="[para(9227(a,1),13472(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9227 13472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,T(z,y)) * w) = K(x,(u / ((y \ z) * y)) * w)
    ]]></literal>
    <justification jstring="[para(9266(a,1),13472(a,1,2,1))].">
      <j1 rule="para" parents="9266 13472"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,(z * y) / z)) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(11229,a,13473,a),flip(a)].">
      <j1 rule="hyper" parents="11229 13473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),y) \ w) = K(x,T(z / y,u) \ w)
    ]]></literal>
    <justification jstring="[para(447(a,1),13473(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="447 13473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(3298(a,1),13473(a,1,2,1))].">
      <j1 rule="para" parents="3298 13473"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(3624(a,1),13473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3624 13473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(4363(a,1),13450(a,1,2,2))].">
      <j1 rule="para" parents="4363 13450"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(4292(a,1),13450(a,1,2,2))].">
      <j1 rule="para" parents="4292 13450"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(4356(a,2),13454(a,1,2))].">
      <j1 rule="para" parents="4356 13454"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13455(a,2),13454(a,1))].">
      <j1 rule="para" parents="13455 13454"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(u,z) * x) = w
    ]]></literal>
    <justification jstring="[para(13435(a,2),13489(a,1))].">
      <j1 rule="para" parents="13435 13489"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13439(a,2),13489(a,1))].">
      <j1 rule="para" parents="13439 13489"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      T(x,(T(y,z) * z) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(9637(a,1),13445(a,1,2))].">
      <j1 rule="para" parents="9637 13445"/>
    </justification>
  </clause>

  <clause id="13496">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(111(a,1),13495(a,1,2,1,1))].">
      <j1 rule="para" parents="111 13495"/>
    </justification>
  </clause>

  <clause id="13497">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11197,a(flip),b,13466,a),flip(a)].">
      <j1 rule="hyper" parents="64 11197 13466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = u / T(u,T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(206,a,13497,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 13497 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      T(x,(y / ((y / z) * (u * u))) \ w) = T(x,T((u * u) \ z,y) \ w)
    ]]></literal>
    <justification jstring="[para(688(a,1),13497(a,1,2,1,2))].">
      <j1 rule="para" parents="688 13497"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      T(x,(y * y) * ((z / (z / u)) \ w)) = T(T(x,T(u,z) \ w),y * y)
    ]]></literal>
    <justification jstring="[para(13497(a,1),1048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13497 1048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w) * ((u / (u / z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u / (u / z)) \ w) * y) = v5
    ]]></literal>
    <justification jstring="[para(13497(a,1),9330(a,1,2,1))].">
      <j1 rule="para" parents="13497 9330"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      K(K(x,x \ y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(13467(a,2),4117(a,1))].">
      <j1 rule="para" parents="13467 4117"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11314,a,13475,a),flip(a)].">
      <j1 rule="hyper" parents="11314 13475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(13475(a,1),11314(a,1))].">
      <j1 rule="para" parents="13475 11314"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(78(a,1),13505(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 13505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(11231,a,13507,a),flip(a)].">
      <j1 rule="hyper" parents="11231 13507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11983,a(flip),b,13481,a),flip(a)].">
      <j1 rule="hyper" parents="319 11983 13481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(4016(a,2),13509(a,1,2,1))].">
      <j1 rule="para" parents="4016 13509"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(4055(a,1),13509(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4055 13509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(4097(a,1),13509(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4097 13509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(u,y),y) / w)
    ]]></literal>
    <justification jstring="[para(5883(a,1),13511(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5883 13511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      K(x,T(T(y,T(z,u)),u) / w) = K(x,(T(y,z) * K(u,y)) / w)
    ]]></literal>
    <justification jstring="[para(6320(a,1),13511(a,1,2,1,1))].">
      <j1 rule="para" parents="6320 13511"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      K(x,(((y * z) / y) * K(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[para(5633(a,1),13510(a,1,2,1))].">
      <j1 rule="para" parents="5633 13510"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z / y) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[para(12378(a,1),13510(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12378 13510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13512,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13512 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,((K(y,z) * u) / (y \ z)) / w)
    ]]></literal>
    <justification jstring="[para(10851(a,1),13512(a,1,2,1,1))].">
      <j1 rule="para" parents="10851 13512"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,z / y) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(11182(a,1),13512(a,1,2,1))].">
      <j1 rule="para" parents="11182 13512"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      T(x,(y * (z / y)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11171,a(flip),b,13496,a),flip(a)].">
      <j1 rule="hyper" parents="64 11171 13496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,z * (y / z))) = T(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11178,a(flip),b,13520,a),flip(a)].">
      <j1 rule="hyper" parents="64 11178 13520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13522">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,13499,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 13499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11145,a(flip),b,13487,a),flip(a)].">
      <j1 rule="hyper" parents="64 11145 13487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      K(x,T(y,z * u) / (z * u)) = K(x,T(u * z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,11070,a,b,13523,a)].">
      <j1 rule="hyper" parents="319 11070 13523"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),13523(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 13523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      K(x,T((y * z) * (K(z,y) / z),K(z,y) / z) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(12320(a,1),13523(a,2,2,1))].">
      <j1 rule="para" parents="12320 13523"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10156,a,13526,a)].">
      <j1 rule="hyper" parents="10156 13526"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * x)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7253,a,13526,a),flip(a)].">
      <j1 rule="hyper" parents="7253 13526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11172,a,b,13526,a)].">
      <j1 rule="hyper" parents="319 11172 13526"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11081,a(flip),b,13526,a),flip(a)].">
      <j1 rule="hyper" parents="319 11081 13526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3041(a,2),13526(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3041 13526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),((u * (z / u)) \ w) * y) = T(x,y * ((u * (z / u)) \ w))
    ]]></literal>
    <justification jstring="[para(13526(a,1),9260(a,1,1,2))].">
      <j1 rule="para" parents="13526 9260"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * x)) = K(x,T(z,y) / (x \ y))
    ]]></literal>
    <justification jstring="[para(3252(a,1),13529(a,1,2,1))].">
      <j1 rule="para" parents="3252 13529"/>
    </justification>
  </clause>

  <clause id="13535">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(13530(a,1),4213(a,1,1))].">
      <j1 rule="para" parents="13530 4213"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      K(x,(T(y,z) * z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(232(a,1),13531(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 13531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13537">
    <literal><![CDATA[
      K(x,((y \ z) * (K(y,u) \ y)) \ w) = K(x,(y * (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[para(7634(a,1),13536(a,1,2,1))].">
      <j1 rule="para" parents="7634 13536"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (z * x)) = z * (K(x,y) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9738,a(flip),b,13449,a)].">
      <j1 rule="hyper" parents="64 9738 13449"/>
    </justification>
  </clause>

  <clause id="13541">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(11229,a,13508,a),flip(a)].">
      <j1 rule="hyper" parents="11229 13508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(13508(a,1),11229(a,1))].">
      <j1 rule="para" parents="13508 11229"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      K(x,y / (z / (z / u))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(81(a,1),13541(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="81 13541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13544">
    <literal><![CDATA[
      T(x,y / (z / (z / u))) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,13543,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13543 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      T(x,T(y,z / T(u,w)) * (z / (w / (w / u)))) = T(x,(z / (w / (w / u))) * y)
    ]]></literal>
    <justification jstring="[para(13544(a,1),9307(a,1,2,1))].">
      <j1 rule="para" parents="13544 9307"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(13525(a,1),11127(a,1))].">
      <j1 rule="para" parents="13525 11127"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z / y) \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(11203(a,1),13547(a,1))].">
      <j1 rule="para" parents="11203 13547"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13507,a(flip),b,13532,a),flip(a)].">
      <j1 rule="hyper" parents="64 13507 13532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      K(x,T(y,z) / (x \ z)) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13488,a(flip),b,13534,a),flip(a)].">
      <j1 rule="hyper" parents="64 13488 13534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(4229,a,13535,a),flip(a)].">
      <j1 rule="hyper" parents="4229 13535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11175,a(flip),b,13551,a),flip(a)].">
      <j1 rule="hyper" parents="64 11175 13551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,T(u,y * x)) = K(T(z,y) / (((x \ 1) / y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13250,a(flip),b,13552,a),flip(a)].">
      <j1 rule="hyper" parents="64 13250 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      K(T(x * y,y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),13552(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (z * x)) = z * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4165(a,1),13539(a,2,2))].">
      <j1 rule="para" parents="4165 13539"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(13555(a,1),13442(a,1,2))].">
      <j1 rule="para" parents="13555 13442"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(231(a,1),13556(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 13556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4130(a,1),13556(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 13556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * T(T(u,w),w))) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[para(13556(a,1),9306(a,1,2,1))].">
      <j1 rule="para" parents="13556 9306"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = x * K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4019,a(flip),b,13558,a),flip(a)].">
      <j1 rule="hyper" parents="319 4019 13558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(206,a,13558,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 13558 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(4105,a,13561,a)].">
      <j1 rule="hyper" parents="4105 13561"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13563(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(232(a,1),13563(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="232 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4016(a,1),13563(a,1,2,2))].">
      <j1 rule="para" parents="4016 13563"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) / K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(12153(a,1),13563(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12153 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      K(x,(y * z) * T(T(L(u,z,y),w),w)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(94(a,1),13565(a,2,2))].">
      <j1 rule="para" parents="94 13565"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      K(x,y * (z / (z / u))) = K(x,y * ((u \ z) \ z))
    ]]></literal>
    <justification jstring="[para(3360(a,1),13564(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3360 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(3361(a,1),13564(a,1,2,2))].">
      <j1 rule="para" parents="3361 13564"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      K(x,T((L(y,z,u) \ w) * y,a(y,z,u))) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(12943(a,2),13564(a,1,2))].">
      <j1 rule="para" parents="12943 13564"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,(1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(3234(a,1),13566(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3234 13566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,13562,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 13562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      K(x * T(T(y,z),z),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(232(a,1),13573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="232 13573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4016(a,1),13573(a,1,1,2))].">
      <j1 rule="para" parents="4016 13573"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      K(x,y * (z / (z / u))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,11112,a(flip),b,13569,a),flip(a)].">
      <j1 rule="hyper" parents="319 11112 13569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(78(a,1),13577(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="78 13577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(10156,a,13578,a)].">
      <j1 rule="hyper" parents="10156 13578"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      K(x,y * (z \ T((u \ (K(w,v5) * z)) * T(z,K(w,v5)),K(v5,w)))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[para(13430(a,2),13578(a,1,2,2))].">
      <j1 rule="para" parents="13430 13578"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      K(x,(y * z) * T(L(T(u,w),z,y),w)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(25(a,2),13568(a,1,2,2,1))].">
      <j1 rule="para" parents="25 13568"/>
    </justification>
  </clause>

  <clause id="13582">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(438(a,1),13581(a,1,2))].">
      <j1 rule="para" parents="438 13581"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11327,a(flip),b,13582,a)].">
      <j1 rule="hyper" parents="64 11327 13582"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(109(a,1),13582(a,1,2,2))].">
      <j1 rule="para" parents="109 13582"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,u))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(111(a,1),13582(a,1,2,2,2,1))].">
      <j1 rule="para" parents="111 13582"/>
    </justification>
  </clause>

  <clause id="13586">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(231(a,1),13582(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 13582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = x \ T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a(flip),b,13584,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 13584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(129,a,13584,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13584 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(6895(a,1),13584(a,1,2,2,1))].">
      <j1 rule="para" parents="6895 13584"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) = T(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(250(a,1),13588(a,1,2,2,1))].">
      <j1 rule="para" parents="250 13588"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(13587(a,2),4106(a,1))].">
      <j1 rule="para" parents="13587 4106"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,x \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,8145,a(flip),b,13426,a),flip(a)].">
      <j1 rule="hyper" parents="319 8145 13426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      T(K(K(x,y) * z,z \ 1),K(x,y)) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(13161(a,2),13594(a,1,1))].">
      <j1 rule="para" parents="13161 13594"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(9341,a,13451,a),flip(a)].">
      <j1 rule="hyper" parents="9341 13451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[para(6895(a,1),13485(a,1,2,2))].">
      <j1 rule="para" parents="6895 13485"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(11229,a,13597,a),flip(a)].">
      <j1 rule="hyper" parents="11229 13597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13597(a,1),11229(a,1))].">
      <j1 rule="para" parents="13597 11229"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,13598,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13598 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13598(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      K(x,y / T(z,z \ u)) = K(x,y / (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(3349(a,1),13598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3349 13598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13605">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5300(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="5300 13598"/>
    </justification>
  </clause>

  <clause id="13606">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(447(a,1),13600(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="447 13600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5300(a,1),13600(a,1,2))].">
      <j1 rule="para" parents="5300 13600"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(w,z),z))
    ]]></literal>
    <justification jstring="[para(5886(a,1),13600(a,1,2,2))].">
      <j1 rule="para" parents="5886 13600"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      T(x,y / (((z * u) / z) * K(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[para(5633(a,1),13600(a,1,2,2))].">
      <j1 rule="para" parents="5633 13600"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      K(x,y / T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13605(a,1),12451(a,1))].">
      <j1 rule="para" parents="13605 12451"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(y / z,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[para(4937(a,1),13607(a,1,2,1))].">
      <j1 rule="para" parents="4937 13607"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ ((z / u) * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((z / u) * K(u,w)) / y) = v5
    ]]></literal>
    <justification jstring="[para(13607(a,1),11225(a,1,2,1))].">
      <j1 rule="para" parents="13607 11225"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      K(x,y / (z / (z / (z / u)))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(318(a,1),13604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="318 13604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13543,a(flip),b,13613,a)].">
      <j1 rule="hyper" parents="64 13543 13613"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      K(x,y / ((z \ u) \ u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(78(a,1),13614(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="78 13614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      K(x,y / T(1 / L(z,u,u \ 1),a(u \ 1,u,z))) = K(x,y / (z \ a(u \ 1,u,z)))
    ]]></literal>
    <justification jstring="[para(3958(a,1),13615(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3958 13615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5300(a,1),13599(a,1,2))].">
      <j1 rule="para" parents="5300 13599"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(3362(a,1),13606(a,1,2,2))].">
      <j1 rule="para" parents="3362 13606"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      K(x,T(T(y,z),T(u,z)) / w) = K(x,(T(y,u) * K(z,y)) / w)
    ]]></literal>
    <justification jstring="[para(23(a,1),13514(a,1,2,1))].">
      <j1 rule="para" parents="23 13514"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,T(y,z))) = T(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(9255(a,1),13521(a,1,2,2))].">
      <j1 rule="para" parents="9255 13521"/>
    </justification>
  </clause>

  <clause id="13621">
    <literal><![CDATA[
      T(x,y / (z * (u / z))) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11178,a(flip),b,13620,a),flip(a)].">
      <j1 rule="hyper" parents="64 11178 13620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13528(a,2),10156(a,1))].">
      <j1 rule="para" parents="13528 10156"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13579(a,2),10156(a,1))].">
      <j1 rule="para" parents="13579 10156"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11190,a(flip),b,13618,a)].">
      <j1 rule="hyper" parents="64 11190 13618"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,u),w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),13625(a,1,2,2))].">
      <j1 rule="para" parents="23 13625"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13424(a,1),13493(a,1))].">
      <j1 rule="para" parents="13424 13493"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(7033(a,1),13431(a,1,2))].">
      <j1 rule="para" parents="7033 13431"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13493,a,13628,a),flip(a)].">
      <j1 rule="hyper" parents="13493 13628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13628(a,1),13493(a,1))].">
      <j1 rule="para" parents="13628 13493"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(127,a,13629,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 13629 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      T(x,K(1 / y,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(81(a,1),13629(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="81 13629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,13631,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 13631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13631(a,2),4106(a,1))].">
      <j1 rule="para" parents="13631 4106"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13454,a,13633,a)].">
      <j1 rule="hyper" parents="13454 13633"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12442,a,b,13633,a)].">
      <j1 rule="hyper" parents="64 12442 13633"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(13633(a,1),7394(a,1,1))].">
      <j1 rule="para" parents="13633 7394"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13453,a,b,13635,a),flip(a)].">
      <j1 rule="hyper" parents="319 13453 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(5084(a,1),13635(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5084 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(7049(a,1),13635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7049 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13642">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(y \ K(y,u),z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(13635(a,1),7386(a,1,1))].">
      <j1 rule="para" parents="13635 7386"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13635(a,2),13454(a,1))].">
      <j1 rule="para" parents="13635 13454"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(12284,a,13639,a)].">
      <j1 rule="hyper" parents="12284 13639"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13639,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13639 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(206,a,13645,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 13645 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z,u \ 1) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,u \ 1) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(13645(a,1),11225(a,1,2,1))].">
      <j1 rule="para" parents="13645 11225"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(12319,a,13636,a)].">
      <j1 rule="hyper" parents="12319 13636"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(11269,a,13640,a),flip(a)].">
      <j1 rule="hyper" parents="11269 13640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13640(a,1),11269(a,1))].">
      <j1 rule="para" parents="13640 11269"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(11956(a,1),13640(a,2,2,1))].">
      <j1 rule="para" parents="11956 13640"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13458,a(flip),b,13649,a)].">
      <j1 rule="hyper" parents="64 13458 13649"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(6213(a,1),13649(a,1,2))].">
      <j1 rule="para" parents="6213 13649"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13456,a(flip),b,13644,a),flip(a)].">
      <j1 rule="hyper" parents="319 13456 13644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(11250,a,13654,a)].">
      <j1 rule="hyper" parents="11250 13654"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(10156,a,13654,a)].">
      <j1 rule="hyper" parents="10156 13654"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13654,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13654 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(78(a,1),13655(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="78 13655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13658,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13658 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(11997(a,1),13660(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11997 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      T(x,T((y \ z) \ K(y,u),w) * v5) = T(x,T(T(y,u) \ z,w) \ v5)
    ]]></literal>
    <justification jstring="[para(11999(a,1),13660(a,1,2,1,1))].">
      <j1 rule="para" parents="11999 13660"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      T(T(x,T(y,z) \ u),w * (w * x)) = T(x,w * (w * (T(y \ 1,z) * u)))
    ]]></literal>
    <justification jstring="[para(13660(a,1),12977(a,1,1))].">
      <j1 rule="para" parents="13660 12977"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,13646,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 13646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(12286,a,13666,a)].">
      <j1 rule="hyper" parents="12286 13666"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4314(a,1),13652(a,2,2))].">
      <j1 rule="para" parents="4314 13652"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(4437(a,1),13667(a,2,1))].">
      <j1 rule="para" parents="4437 13667"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13453(a,1),13650(a,1))].">
      <j1 rule="para" parents="13453 13650"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6804(a,1),13641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6804 13641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(206,a,13672,a(flip),b,4213,a),flip(a)].">
      <j1 rule="hyper" parents="206 13672 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4214,a(flip),b,13673,a),flip(a)].">
      <j1 rule="hyper" parents="319 4214 13673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(z \ y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(9320,a,13674,a)].">
      <j1 rule="hyper" parents="9320 13674"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13456,a(flip),b,13648,a),flip(a)].">
      <j1 rule="hyper" parents="319 13456 13648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      K(x,y * (K(z \ 1,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(2917(a,1),13676(a,1,2,2,1))].">
      <j1 rule="para" parents="2917 13676"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13471,a(flip),b,13677,a)].">
      <j1 rule="hyper" parents="64 13471 13677"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(12174(a,1),13678(a,1,2,1))].">
      <j1 rule="para" parents="12174 13678"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(x,L(T(y,z) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10133,a(flip),b,13656,a),flip(a)].">
      <j1 rule="hyper" parents="319 10133 13656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13656(a,2),10156(a,1))].">
      <j1 rule="para" parents="13656 10156"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) * u,w,v5)) = K(x,L(T(y,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(81(a,1),13680(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="81 13680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13682(a,1),13117(a,1))].">
      <j1 rule="para" parents="13682 13117"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      T(x,(y * y) * ((z / (z / u)) \ w)) = T(x,y * (y * (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12968,a(flip),b,13501,a),flip(a)].">
      <j1 rule="hyper" parents="319 12968 13501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13460,a(flip),b,13653,a),flip(a)].">
      <j1 rule="hyper" parents="319 13460 13653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7988(a,1),13685(a,1,2))].">
      <j1 rule="para" parents="7988 13685"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      K(x,(y * K(y * z,z \ 1)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13422,a(flip),b,13686,a)].">
      <j1 rule="hyper" parents="64 13422 13686"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (((u \ 1) \ 1) \ z)))
    ]]></literal>
    <justification jstring="[para(4817(a,1),13686(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4817 13686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      T(x,y * (y * ((z / (z / u)) \ w))) = T(x,y * (y * (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(12980,a,13684,a)].">
      <j1 rule="hyper" parents="12980 13684"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      K(x,K(y,z) * T(K(z,y) \ u,w)) = K(x,K(z,y) * T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(4356(a,1),13459(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4356 13459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(13630,a,13464,a)].">
      <j1 rule="hyper" parents="13630 13464"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      T(x,((y / (z \ K(z,y))) / y) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(111(a,1),13479(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 13479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * T(z,y)) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13566,a(flip),b,13482,a)].">
      <j1 rule="hyper" parents="64 13566 13482"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,(K(y,y \ z) * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(13349(a,1),13483(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13349 13483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13695">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13582,a(flip),b,13560,a)].">
      <j1 rule="hyper" parents="64 13582 13560"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(9330,a,13695,a),flip(a)].">
      <j1 rule="hyper" parents="9330 13695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      T(x,(y * T(T(z,u),u)) * w) = T(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(129,a,13696,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13696 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),13696(a,1,2,1))].">
      <j1 rule="para" parents="109 13696"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(4130(a,1),13696(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      T(x,(T(y,z) * z) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13699,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13699 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(5974(a,1),13699(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5974 13699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      K(x,(T(y \ z,K(y,u)) * T(y,u)) * w) = K(x,(T(y,u) * (z / y)) * w)
    ]]></literal>
    <justification jstring="[para(6396(a,1),13699(a,1,2,1,1))].">
      <j1 rule="para" parents="6396 13699"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      K(x,((y \ z) * (y * K(u,y))) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[para(7626(a,1),13699(a,1,2,1))].">
      <j1 rule="para" parents="7626 13699"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      T(x,(y * (T(y,z \ y) / z)) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(3119(a,1),13701(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3119 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      T(x,(y * T(z \ u,z)) * w) = T(x,(y * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(111(a,1),13698(a,1,2,1,2,1))].">
      <j1 rule="para" parents="111 13698"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(4130(a,1),13698(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4130 13698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      T(x,(y * R(z \ u,z,z \ u)) * w) = T(x,(y * (T(u,z \ u) / z)) * w)
    ]]></literal>
    <justification jstring="[para(3192(a,1),13707(a,1,2,1,2))].">
      <j1 rule="para" parents="3192 13707"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13700,a(flip),b,13704,a)].">
      <j1 rule="hyper" parents="64 13700 13704"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * T(u,w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13586,a(flip),b,13589,a)].">
      <j1 rule="hyper" parents="64 13586 13589"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(13591,a,13712,a),flip(a)].">
      <j1 rule="hyper" parents="13591 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(13712(a,1),13591(a,1))].">
      <j1 rule="para" parents="13712 13591"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(129,a,13713,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13713 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) * w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),13713(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(232(a,1),13713(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="232 13713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13717(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 13717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5466(a,2),13718(a,1,2))].">
      <j1 rule="para" parents="5466 13718"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (K(z,u) * w))) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(129,a,13719,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13719 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(4218(a,1),13719(a,1,2,2))].">
      <j1 rule="para" parents="4218 13719"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(4292(a,1),13719(a,1,2,2,2))].">
      <j1 rule="para" parents="4292 13719"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,11137,a,b,13721,a)].">
      <j1 rule="hyper" parents="319 11137 13721"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13672,a(flip),b,13721,a),flip(a)].">
      <j1 rule="hyper" parents="319 13672 13721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,13721,a,b,4518,a)].">
      <j1 rule="hyper" parents="129 13721 4518"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(12363(a,1),13721(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12363 13721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(206,a,13726,a,b,4030,a(flip))].">
      <j1 rule="hyper" parents="206 13726 4030"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      K(x,y \ T(z,z * u)) = K(x,(y \ z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(12363(a,1),13724(a,1,2))].">
      <j1 rule="para" parents="12363 13724"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,13725,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13725 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(12770(a,2),13727(a,1,2))].">
      <j1 rule="para" parents="12770 13727"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(12774(a,1),13727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12774 13727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(4117,a,13728,a)].">
      <j1 rule="hyper" parents="4117 13728"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(13728(a,1),4117(a,1))].">
      <j1 rule="para" parents="13728 4117"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(12242,a,13735,a),flip(a)].">
      <j1 rule="hyper" parents="12242 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13674,a(flip),b,13735,a),flip(a)].">
      <j1 rule="hyper" parents="319 13674 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(5172(a,1),13735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5172 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      K((x / y) * K(y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5163(a,1),13735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5163 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8357(a,1),13739(a,1,1))].">
      <j1 rule="para" parents="8357 13739"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      K(x,y) * (x * (K(z,u) * K(z,u))) = T(x * (K(z,u) * K(z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(130,a,13741,a(flip),b,4011,a(flip))].">
      <j1 rule="hyper" parents="130 13741 4011"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5289,a,13733,a)].">
      <j1 rule="hyper" parents="5289 13733"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4055(a,1),13733(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4055 13733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4214,a,b,13744,a),flip(a)].">
      <j1 rule="hyper" parents="319 4214 13744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,13744,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13744 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(3304(a,1),13744(a,1,2,2,1))].">
      <j1 rule="para" parents="3304 13744"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(w / z,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),13734(a,1,2,2,1))].">
      <j1 rule="para" parents="6270 13734"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(12242,a,13737,a)].">
      <j1 rule="hyper" parents="12242 13737"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(11292,a,13749,a),flip(a)].">
      <j1 rule="hyper" parents="11292 13749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      (x \ K(y \ K(z,u),w)) \ (x \ 1) = K(w,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(13749(a,1),12018(a,1,1,2))].">
      <j1 rule="para" parents="13749 12018"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(13749(a,1),12181(a,1))].">
      <j1 rule="para" parents="13749 12181"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9303,a(flip),b,13738,a),flip(a)].">
      <j1 rule="hyper" parents="64 9303 13738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5300(a,2),13740(a,1,1))].">
      <j1 rule="para" parents="5300 13740"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(2757(a,2),13743(a,2,2,2))].">
      <j1 rule="para" parents="2757 13743"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[hyper(4227,a,13745,a)].">
      <j1 rule="hyper" parents="4227 13745"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      K(x \ ((y * z) / y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(231(a,1),13757(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 13757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(4169(a,1),13750(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4169 13750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      K(x \ K(y * (z \ u),z),w) = K(x \ K(z,y * u),w)
    ]]></literal>
    <justification jstring="[para(8261(a,1),13750(a,1,1,2))].">
      <j1 rule="para" parents="8261 13750"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      K(x \ K((y * K(z,z \ u)) \ w,y * K(z,u)),v5) = K(x \ K(y * K(z,z \ u),w),v5)
    ]]></literal>
    <justification jstring="[para(11139(a,1),13750(a,1,1,2))].">
      <j1 rule="para" parents="11139 13750"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      T(T(x,y / ((z * u) / z)),K(y / T(u,z),w)) = T(x,T(y / ((z * u) / z),w))
    ]]></literal>
    <justification jstring="[para(13755(a,1),6392(a,1,2))].">
      <j1 rule="para" parents="13755 6392"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9381,a(flip),b,13758,a),flip(a)].">
      <j1 rule="hyper" parents="64 9381 13758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(12351,a,13764,a),flip(a)].">
      <j1 rule="hyper" parents="12351 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11158,a(flip),b,13764,a),flip(a)].">
      <j1 rule="hyper" parents="64 11158 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12999,a(flip),b,13766,a)].">
      <j1 rule="hyper" parents="64 12999 13766"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(81(a,1),13768(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="81 13768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z / (y \ 1),R(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(411(a,1),13768(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="411 13768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,K(x,w \ (z * (w / u)))) = v5
    ]]></literal>
    <justification jstring="[para(13769(a,1),12644(a,1,3))].">
      <j1 rule="para" parents="13769 12644"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      K(x,y \ T(z,z * u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13727,a(flip),b,13729,a),flip(a)].">
      <j1 rule="hyper" parents="319 13727 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),13772(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 13772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(110(a,1),13773(a,1,2,2))].">
      <j1 rule="para" parents="110 13773"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      K(x,y \ (T((z * (1 / u)) \ z,w) \ z)) = K(x,y \ T(z * (1 / T(u,w)),z))
    ]]></literal>
    <justification jstring="[para(13368(a,2),13774(a,1,2,2,1))].">
      <j1 rule="para" parents="13368 13774"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11157,a(flip),b,13760,a),flip(a)].">
      <j1 rule="hyper" parents="319 11157 13760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13749,a,b,13776,a)].">
      <j1 rule="hyper" parents="64 13749 13776"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11217,a,b,13777,a)].">
      <j1 rule="hyper" parents="64 11217 13777"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) = K(y \ T(x,1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(12424,a,13778,a),flip(a)].">
      <j1 rule="hyper" parents="12424 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      K(x \ T(y,1 / z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13753,a,13779,a),flip(a)].">
      <j1 rule="hyper" parents="13753 13779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(78(a,1),13780(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 13780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(13781(a,1),10106(a,1,2,3))].">
      <j1 rule="para" parents="13781 10106"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11324,a,b,13722,a)].">
      <j1 rule="hyper" parents="64 11324 13722"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      K(x,y \ K(z,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(4751,a,13752,a)].">
      <j1 rule="hyper" parents="4751 13752"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13752(a,1),4751(a,1))].">
      <j1 rule="para" parents="13752 4751"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13675,a,b,13754,a)].">
      <j1 rule="hyper" parents="64 13675 13754"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(81(a,1),13783(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 13783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(129,a,13787,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13787 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(3270(a,1),13787(a,1,2,2))].">
      <j1 rule="para" parents="3270 13787"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,10846,a(flip),b,13789,a),flip(a)].">
      <j1 rule="hyper" parents="319 10846 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z / u)) = K(x,(u \ T(z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11184,a(flip),b,13789,a),flip(a)].">
      <j1 rule="hyper" parents="64 11184 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,T(z,u \ 1)))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[para(5055(a,1),13789(a,2,2,2))].">
      <j1 rule="para" parents="5055 13789"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(9482,a,13786,a)].">
      <j1 rule="hyper" parents="9482 13786"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(9330,a,13791,a),flip(a)].">
      <j1 rule="hyper" parents="9330 13791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(13791(a,1),9330(a,1))].">
      <j1 rule="para" parents="13791 9330"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(3270(a,2),13795(a,1,2,1))].">
      <j1 rule="para" parents="3270 13795"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u * (z / u)) / y) * w) = v5
    ]]></literal>
    <justification jstring="[para(9255(a,1),13796(a,1,2,1,1))].">
      <j1 rule="para" parents="9255 13796"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11150,a(flip),b,13747,a)].">
      <j1 rule="hyper" parents="64 11150 13747"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(3263(a,1),13798(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3263 13798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12908,a,b,13799,a)].">
      <j1 rule="hyper" parents="64 12908 13799"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),13799(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 13799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3041(a,2),13799(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3041 13799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(3103(a,2),13799(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3103 13799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13801(a,2,2,1))].">
      <j1 rule="para" parents="10 13801"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11150,a(flip),b,13804,a),flip(a)].">
      <j1 rule="hyper" parents="64 11150 13804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(129,a,13807,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 13807 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * T(w * u,u))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[para(9251(a,1),13807(a,1,2,2,1))].">
      <j1 rule="para" parents="9251 13807"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(11967(a,1),13807(a,1,2,2,1))].">
      <j1 rule="para" parents="11967 13807"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(12052(a,1),13807(a,1,2,2,1))].">
      <j1 rule="para" parents="12052 13807"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ (z * u)) = T(x,(T(u,z) * z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9310,a(flip),b,13808,a),flip(a)].">
      <j1 rule="hyper" parents="64 9310 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12350,a,13765,a),flip(a)].">
      <j1 rule="hyper" parents="12350 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(11961(a,1),13813(a,1,1,2))].">
      <j1 rule="para" parents="11961 13813"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      T(x,x * (y * K(x * y,z))) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[hyper(131,a,13815,a(flip),b,4470,a(flip))].">
      <j1 rule="hyper" parents="131 13815 4470"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      T(x,(T(y,z) * z) / u) = T(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(7245,a,13812,a),flip(a)].">
      <j1 rule="hyper" parents="7245 13812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4310,a,13742,a),flip(a)].">
      <j1 rule="hyper" parents="4310 13742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(13125,a,13790,a)].">
      <j1 rule="hyper" parents="13125 13790"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,9464,a(flip),b,13793,a)].">
      <j1 rule="hyper" parents="319 9464 13793"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(3822(a,1),13820(a,1,1))].">
      <j1 rule="para" parents="3822 13820"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(7169,a,13821,a),flip(a)].">
      <j1 rule="hyper" parents="7169 13821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(232(a,1),13822(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="232 13822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13249,a,b,13824,a)].">
      <j1 rule="hyper" parents="64 13249 13824"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(y * (T(x,y) * z),x),T(u,z))
    ]]></literal>
    <justification jstring="[para(12197(a,1),13825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12197 13825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      T(x,y * (y * (T(z \ 1,u) * w))) = T(x,y * (y * (T(z,u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12977,a(flip),b,13665,a),flip(a)].">
      <j1 rule="hyper" parents="64 12977 13665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4692,a(flip),b,13811,a)].">
      <j1 rule="hyper" parents="64 4692 13811"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13810,a(flip),b,13828,a),flip(a)].">
      <j1 rule="hyper" parents="64 13810 13828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      T(R(x * K(y,K(z,u)),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6705(a,1),13436(a,1,1,1,2))].">
      <j1 rule="para" parents="6705 13436"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(5521,a,13638,a),flip(a)].">
      <j1 rule="hyper" parents="5521 13638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(7392(a,1),13831(a,1,2,1))].">
      <j1 rule="para" parents="7392 13831"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(5521,a,13642,a),flip(a)].">
      <j1 rule="hyper" parents="5521 13642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7385(a,1),13833(a,1,2,1))].">
      <j1 rule="para" parents="7385 13833"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ K(u,K(y * K(u,z),z))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(6752(a,1),13834(a,2,2))].">
      <j1 rule="para" parents="6752 13834"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[para(12044(a,1),13816(a,1,1,2))].">
      <j1 rule="para" parents="12044 13816"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(11788,a,13836,a)].">
      <j1 rule="hyper" parents="11788 13836"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(12043(a,2),13837(a,2,2))].">
      <j1 rule="para" parents="12043 13837"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10959,a,13839,a),flip(a)].">
      <j1 rule="hyper" parents="10959 13839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13840(a,1,2,2,1))].">
      <j1 rule="para" parents="10 13840"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(111(a,1),13841(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 13841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ (x \ (x * (z * y))),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(13843(a,1),11261(a,1,2))].">
      <j1 rule="para" parents="13843 11261"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      (x * K(y,z)) \ T(u * (K(y,z) * x),K(y,z)) = T(u,T(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6800(a,1),13432(a,1,2,1,2))].">
      <j1 rule="para" parents="6800 13432"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      T(T(x,y / T(z,u)),K(y / T(z,u),w)) = T(x,T(y / ((u * z) / u),w))
    ]]></literal>
    <justification jstring="[para(13600(a,1),13763(a,1,1))].">
      <j1 rule="para" parents="13600 13763"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(6394,a,13847,a),flip(a)].">
      <j1 rule="hyper" parents="6394 13847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      T(x,T((y / z) * K(z,u),w)) = T(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9383,a(flip),b,13848,a)].">
      <j1 rule="hyper" parents="64 9383 13848"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T(z / T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13054,a,b,13849,a)].">
      <j1 rule="hyper" parents="64 13054 13849"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      K(x,T((y * z) * (1 / y),K(y,z) / y) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11992(a,1),13527(a,1,2,1,1))].">
      <j1 rule="para" parents="11992 13527"/>
    </justification>
  </clause>

  <clause id="13852">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) * K(y,y \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(5174(a,1),13477(a,2,2,1))].">
      <j1 rule="para" parents="5174 13477"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(5174(a,1),13567(a,2,2,2))].">
      <j1 rule="para" parents="5174 13567"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(11955(a,1),13572(a,2,2,2,2))].">
      <j1 rule="para" parents="11955 13572"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(8163(a,1),13854(a,2,2,2))].">
      <j1 rule="para" parents="8163 13854"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(1588(a,1),13855(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1588 13855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,11112,a(flip),b,13856,a)].">
      <j1 rule="hyper" parents="319 11112 13856"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      K(x,(y * K(y * z,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13832,a(flip),b,13687,a)].">
      <j1 rule="hyper" parents="64 13832 13687"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      K(x,(y * K(y,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11297,a(flip),b,13858,a)].">
      <j1 rule="hyper" parents="64 11297 13858"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(4019(a,2),13859(a,1,2,1))].">
      <j1 rule="para" parents="4019 13859"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * T(z,y)) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(3252(a,1),13860(a,1,2,1))].">
      <j1 rule="para" parents="3252 13860"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(y * (x * z),x),T(u,z))
    ]]></literal>
    <justification jstring="[para(6095(a,1),13826(a,2,1,2))].">
      <j1 rule="para" parents="6095 13826"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(109(a,1),13861(a,1,2,2,1))].">
      <j1 rule="para" parents="109 13861"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(109(a,1),13864(a,1,2,2,2,2))].">
      <j1 rule="para" parents="109 13864"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(6854(a,1),13865(a,2,2))].">
      <j1 rule="para" parents="6854 13865"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13799,a(flip),b,13866,a)].">
      <j1 rule="hyper" parents="64 13799 13866"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      K(x,T(y * z,(y * z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(6549(a,1),13867(a,1,2,2,2))].">
      <j1 rule="para" parents="6549 13867"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w) * (T(z,u) \ w)) = K(x,((u / (u / z)) \ w) * y)
    ]]></literal>
    <justification jstring="[hyper(13502,a,13783,a),flip(a)].">
      <j1 rule="hyper" parents="13502 13783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(9330,a,13870,a),flip(a)].">
      <j1 rule="hyper" parents="9330 13870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,y / (1 / L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(11971(a,1),13616(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11971 13616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z / (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11981,a(flip),b,13770,a),flip(a)].">
      <j1 rule="hyper" parents="319 11981 13770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,12166,a(flip),b,13875,a),flip(a)].">
      <j1 rule="hyper" parents="319 12166 13875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      K(x * ((y * x) \ (z * (y * x))),y) = K(z * x,y)
    ]]></literal>
    <justification jstring="[hyper(13232,a,13877,a)].">
      <j1 rule="hyper" parents="13232 13877"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      K(x * T(y,z * x),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),13878(a,1,1,2))].">
      <j1 rule="para" parents="22 13878"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      K(T(x,y * z) * z,y) = K(z * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13574,a(flip),b,13879,a),flip(a)].">
      <j1 rule="hyper" parents="64 13574 13879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      K(T((x \ y) \ z,u * K(x \ y,x)) * K(x \ y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4510(a,1),13880(a,2,1))].">
      <j1 rule="para" parents="4510 13880"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (u \ z)))
    ]]></literal>
    <justification jstring="[para(7996(a,1),13688(a,2,2))].">
      <j1 rule="para" parents="7996 13688"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      K(x,T(y / z,T((u \ z) / z,T(u,w)))) = K(x,T(y / z,y / (u \ z)))
    ]]></literal>
    <justification jstring="[para(6896(a,1),13885(a,1,2))].">
      <j1 rule="para" parents="6896 13885"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(7818(a,1),13886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7818 13886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,7142,a(flip),b,13887,a),flip(a)].">
      <j1 rule="hyper" parents="319 7142 13887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13218,a(flip),b,13888,a)].">
      <j1 rule="hyper" parents="64 13218 13888"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      K(x,T(y,T(y,z) / z) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(3264(a,1),13890(a,1,2,2,1))].">
      <j1 rule="para" parents="3264 13890"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ K(u,K(y,z))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(5990(a,1),13835(a,1,2,2,2))].">
      <j1 rule="para" parents="5990 13835"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ K(y,K(z,u))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(6748(a,2),13892(a,1,2,2))].">
      <j1 rule="para" parents="6748 13892"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,K(y,z)) * u) \ 1) = K(x,(K(z \ 1,y) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(9213(a,1),13894(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9213 13894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,K(y,z)) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,5087,a(flip),b,13895,a),flip(a)].">
      <j1 rule="hyper" parents="319 5087 13895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,11145,a(flip),b,13896,a)].">
      <j1 rule="hyper" parents="64 11145 13896"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(5257,a,13897,a),flip(a)].">
      <j1 rule="hyper" parents="5257 13897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13785,a,13898,a)].">
      <j1 rule="hyper" parents="13785 13898"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(3883(a,1),13898(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3883 13898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13756,a(flip),b,13902,a),flip(a)].">
      <j1 rule="hyper" parents="64 13756 13902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11156,a(flip),b,13903,a)].">
      <j1 rule="hyper" parents="64 11156 13903"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13785,a,13905,a)].">
      <j1 rule="hyper" parents="13785 13905"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13743,a(flip),b,13904,a),flip(a)].">
      <j1 rule="hyper" parents="64 13743 13904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(78(a,1),13907(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="78 13907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13909">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13802,a(flip),b,13908,a),flip(a)].">
      <j1 rule="hyper" parents="64 13802 13908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(5754(a,1),13908(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5754 13908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      K(x,y \ T(z,u)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(13908(a,1),13782(a,1,1))].">
      <j1 rule="para" parents="13908 13782"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(777(a,1),13909(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="777 13909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((z \ 1) * y) \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(10177,a,13912,a)].">
      <j1 rule="hyper" parents="10177 13912"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,4761,a(flip),b,13912,a),flip(a)].">
      <j1 rule="hyper" parents="64 4761 13912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,13037,a(flip),b,13914,a),flip(a)].">
      <j1 rule="hyper" parents="64 13037 13914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(538(a,1),13914(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="538 13914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12763,a(flip),b,13915,a)].">
      <j1 rule="hyper" parents="64 12763 13915"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(12190,a,13917,a),flip(a)].">
      <j1 rule="hyper" parents="12190 13917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      K(x,y * (z \ L(z,u,u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(13918(a,1),12190(a,1))].">
      <j1 rule="para" parents="13918 12190"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13081,a(flip),b,13913,a),flip(a)].">
      <j1 rule="hyper" parents="64 13081 13913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13914,a(flip),b,13920,a)].">
      <j1 rule="hyper" parents="64 13914 13920"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      K(x,L(y \ T(z,u \ 1),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ T(z,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13911(a,1),10155(a,1))].">
      <j1 rule="para" parents="13911 10155"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z),w,v5)) = K(x,L(u / ((y * z) \ y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(13922,a,11281,a)].">
      <j1 rule="hyper" parents="13922 11281"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ T(u,z),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(13922,a,11280,a)].">
      <j1 rule="hyper" parents="13922 11280"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      K(x,y * (z \ T((u \ (z * K(w,v5))) * z,K(v5,w)))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[para(12488(a,1),13580(a,1,2,2,2,1))].">
      <j1 rule="para" parents="12488 13580"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(6599(a,1),13891(a,1,2,1))].">
      <j1 rule="para" parents="6599 13891"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(3264(a,1),13926(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3264 13926"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13668,a(flip),b,13927,a)].">
      <j1 rule="hyper" parents="64 13668 13927"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[para(11052(a,1),13929(a,2,2))].">
      <j1 rule="para" parents="11052 13929"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13799,a(flip),b,13930,a)].">
      <j1 rule="hyper" parents="64 13799 13930"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      T(x * (x \ ((y * (x * z)) / y)),x) \ x = ((y * (z * x)) / y) \ L(x,z,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),13844(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="69 13844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),13932(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11201,a(flip),b,13869,a)].">
      <j1 rule="hyper" parents="64 11201 13869"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(13730(a,1),13935(a,1,2,2))].">
      <j1 rule="para" parents="13730 13935"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,y * z))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(4394(a,1),13936(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4394 13936"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(z,y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(13596(a,1),13937(a,1,2,2))].">
      <j1 rule="para" parents="13596 13937"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,T(z,y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(4019(a,2),13938(a,1,2,2,2))].">
      <j1 rule="para" parents="4019 13938"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,T(z * u,u) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(11313,a,13939,a),flip(a)].">
      <j1 rule="hyper" parents="11313 13939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13523,a(flip),b,13940,a),flip(a)].">
      <j1 rule="hyper" parents="319 13523 13940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6330(a,1),13941(a,1,2))].">
      <j1 rule="para" parents="6330 13941"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(7185,a,13942,a)].">
      <j1 rule="hyper" parents="7185 13942"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T((z * u) \ z,z * u)))
    ]]></literal>
    <justification jstring="[para(4270(a,1),13943(a,2,2,1))].">
      <j1 rule="para" parents="4270 13943"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T((K(y,z) * x) / K(y,z),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(6818(a,1),13428(a,1,1))].">
      <j1 rule="para" parents="6818 13428"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T(T(x,K(y,z)),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(6818(a,1),13945(a,1,2,1,2,1))].">
      <j1 rule="para" parents="6818 13945"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(6074(a,1),13946(a,1,2,1,2))].">
      <j1 rule="para" parents="6074 13946"/>
    </justification>
  </clause>

  <clause id="13948">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(6791(a,1),13947(a,1,2))].">
      <j1 rule="para" parents="6791 13947"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,9307,a(flip),b,13948,a),flip(a)].">
      <j1 rule="hyper" parents="319 9307 13948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      a(T((x \ y) * x,z),u,T(T(y,x),z)) \ (K(y,z) * x) = (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z))
    ]]></literal>
    <justification jstring="[para(13044(a,1),12307(a,1,1))].">
      <j1 rule="para" parents="13044 12307"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      a(T(T(x,y),z),u,T(T(x,y),z)) \ (K(x,z) * y) = (y \ x) \ L(T((y \ x) * y,z),u,T((y \ x) * y,z))
    ]]></literal>
    <justification jstring="[para(13041(a,1),13950(a,1,1))].">
      <j1 rule="para" parents="13041 13950"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z)) = a(T(y,x),u,T(y,x)) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(9678(a,1),13951(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9678 13951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z)) = a(y,u,y) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(9678(a,1),13952(a,2,1))].">
      <j1 rule="para" parents="9678 13952"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z)) = K(y,z) * (a(y,u,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11011,a(flip),b,13953,a),flip(a)].">
      <j1 rule="hyper" parents="319 11011 13953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T(T(y,x),z)) = K(y,z) * (a(y,u,y) \ x)
    ]]></literal>
    <justification jstring="[para(10860(a,1),13955(a,1,2))].">
      <j1 rule="para" parents="10860 13955"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,y) = K(y,z) * (a(y,u,y) \ x)
    ]]></literal>
    <justification jstring="[para(10896(a,1),13957(a,1,2))].">
      <j1 rule="para" parents="10896 13957"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w)) \ ((R(w,v5,v6) * T(u,w)) / T(u,w)) = (T(T(u,w),R(T(x,u),y,z)) * R(T(w,u),v5,v6)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(186(a,1),13421(a,1,1,2))].">
      <j1 rule="para" parents="186 13421"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      (T(T(x,y),R(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ ((R(y,w,v5) * T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(6160(a,1),13960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6160 13960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      (T(T(x,y),R(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),13961(a,2,2))].">
      <j1 rule="para" parents="11 13961"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      (T(T(x,y),L(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(12800(a,1),13962(a,1,1,1))].">
      <j1 rule="para" parents="12800 13962"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      (T(T(x,L(y,z,u)),y) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(3355(a,1),13964(a,1,1,1))].">
      <j1 rule="para" parents="3355 13964"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      (T(T(x,y),L(y,z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(23(a,1),13965(a,1,1,1))].">
      <j1 rule="para" parents="23 13965"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      K(L(x,y,z),u) \ R(x,y,z) = (T(u,x) * R(x,y,z)) / T(u,x)
    ]]></literal>
    <justification jstring="[para(12914(a,1),13966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12914 13966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      K(L(x,y,z),u) \ R(x,y,z) = R(K(x,u) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4631,a(flip),b,13967,a),flip(a)].">
      <j1 rule="hyper" parents="319 4631 13967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      R(K(x,y) \ x,y,z) = K(x,y) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8169(a,1),13968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8169 13968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      K(x,y) \ R(x,y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4235,a(flip),b,13969,a),flip(a)].">
      <j1 rule="hyper" parents="64 4235 13969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      (x / ((y \ x) * y)) \ ((((y \ x) * y) \ 1) \ (((y \ x) * y) \ x)) = R((y \ x) * y,((y \ x) * y) \ 1,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),12300(a,2,3,1,1))].">
      <j1 rule="para" parents="10 12300"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      (x / ((y \ x) * y)) \ ((((y \ x) * y) \ 1) \ (((y \ x) * y) \ x)) = R((y \ x) * y,((y \ x) * y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8093,a(flip),b,13971,a),flip(a)].">
      <j1 rule="hyper" parents="319 8093 13971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      K(x,x \ y) \ ((((x \ y) * x) \ 1) \ (((x \ y) * x) \ y)) = R((x \ y) * x,((x \ y) * x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(4002(a,1),13972(a,1,1))].">
      <j1 rule="para" parents="4002 13972"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      K(x,x \ y) \ ((((x \ y) * x) \ 1) \ K(x,x \ y)) = R((x \ y) * x,((x \ y) * x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(90(a,1),13974(a,1,2,2))].">
      <j1 rule="para" parents="90 13974"/>
    </justification>
  </clause>

  <clause id="13976">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ 1,y) = K(x,x \ y) \ (((x * (x \ y)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(12001(a,1),13975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12001 13975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ 1,y) = K(x,x \ y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),13976(a,2,2,1,1))].">
      <j1 rule="para" parents="10 13976"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ 1,y) = K(x \ y,x) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a(flip),b,13977,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 13977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ 1,y) = T((x \ y) * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,4845,a(flip),b,13978,a),flip(a)].">
      <j1 rule="hyper" parents="319 4845 13978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      T((x \ y) * x,y \ 1) \ y = (((x \ y) * x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(13980(a,1),402(a,1,1))].">
      <j1 rule="para" parents="13980 402"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      (((x \ y) * x) \ 1) * y = (y \ 1) * (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8418,a(flip),b,13981,a),flip(a)].">
      <j1 rule="hyper" parents="64 8418 13981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      K(x,x \ y) * K(y \ 1,y) = (((x \ y) * x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,8236,a,b,13982,a)].">
      <j1 rule="hyper" parents="319 8236 13982"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      (((x \ y) * x) \ 1) * ((y \ 1) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5232,a,13983,a)].">
      <j1 rule="hyper" parents="5232 13983"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ 1) * ((z \ 1) \ 1) = K(((x * y) \ x) \ 1,(((x * y) \ x) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(5071(a,2),13984(a,1,1,1))].">
      <j1 rule="para" parents="5071 13984"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ 1) * ((z \ 1) \ 1) = K(((x * y) \ x) \ 1,z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(319,a,8144,a(flip),b,13985,a),flip(a)].">
      <j1 rule="hyper" parents="319 8144 13985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ 1) * ((z \ 1) \ 1) = K(y,z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(319,a,5026,a(flip),b,13986,a),flip(a)].">
      <j1 rule="hyper" parents="319 5026 13986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ L(y,z,y),u,w) * z) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(11847(a,1),13056(a,1,2))].">
      <j1 rule="para" parents="11847 13056"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L(T((y * (y * z)) / y,y) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(13933(a,1),13989(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13933 13989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L((y * z) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(231(a,1),13990(a,2,2,1,1,1))].">
      <j1 rule="para" parents="231 13990"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13991(a,2),12268(a,1))].">
      <j1 rule="para" parents="13991 12268"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u * x,x)) * u))
    ]]></literal>
    <justification jstring="[para(13311(a,1),12904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13311 12904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u,x)) * u))
    ]]></literal>
    <justification jstring="[para(12750(a,1),13994(a,2,2,2,1))].">
      <j1 rule="para" parents="12750 13994"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),(x \ u) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(12765(a,1),13995(a,2,2))].">
      <j1 rule="para" parents="12765 13995"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * T(1 / (y / z),y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(66(a,1),13055(a,1,2,2))].">
      <j1 rule="para" parents="66 13055"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z / (z * u)))
    ]]></literal>
    <justification jstring="[para(6836(a,1),13944(a,2,2,2))].">
      <j1 rule="para" parents="6836 13944"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(7397(a,1),13999(a,2,2,2))].">
      <j1 rule="para" parents="7397 13999"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13910,a(flip),b,14000,a),flip(a)].">
      <j1 rule="hyper" parents="319 13910 14000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z * u,u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13834,a(flip),b,14001,a),flip(a)].">
      <j1 rule="hyper" parents="319 13834 14001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z,u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,11297,a(flip),b,14002,a),flip(a)].">
      <j1 rule="hyper" parents="319 11297 14002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(z,u) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(4019(a,2),14003(a,2,2,1))].">
      <j1 rule="para" parents="4019 14003"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13931,a(flip),b,14004,a),flip(a)].">
      <j1 rule="hyper" parents="319 13931 14004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),14005(a,1,2,1,2))].">
      <j1 rule="para" parents="10 14005"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(5713(a,1),14006(a,1,2))].">
      <j1 rule="para" parents="5713 14006"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(9264(a,1),14007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9264 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(11(a,1),14008(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 14008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      K(x,T(y / z,(z / u) * z)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(81(a,1),14008(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 14008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),14009(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 14009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7181,a,14011,a)].">
      <j1 rule="hyper" parents="7181 14011"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      K(T(x,y \ z),u) = K(x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(6261,a,14011,a)].">
      <j1 rule="hyper" parents="6261 14011"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      K(x \ y,T(z,x * y)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(4172,a,14011,a),flip(a)].">
      <j1 rule="hyper" parents="4172 14011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,14011,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14011 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      K(x,T(y,z * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(213(a,1),14011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="213 14011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(14011(a,1),7185(a,1))].">
      <j1 rule="para" parents="14011 7185"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      K(x / (y * y),z) = K((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(6990,a,14017,a)].">
      <j1 rule="hyper" parents="6990 14017"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      T(x,T(y,z * z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,14017,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14017 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      K(x,K(y,z * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,14017,a,b,7065,a),flip(a)].">
      <j1 rule="hyper" parents="126 14017 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,14022,a)].">
      <j1 rule="hyper" parents="57 14022"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(9262,a,14023,a)].">
      <j1 rule="hyper" parents="9262 14023"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,(z * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6973,a(flip),b,14023,a),flip(a)].">
      <j1 rule="hyper" parents="64 6973 14023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ (z / (y * u)))) = T(x,z / ((y \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2581(a,1),14021(a,1,2))].">
      <j1 rule="para" parents="2581 14021"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14011,a(flip),b,14012,a)].">
      <j1 rule="hyper" parents="64 14011 14012"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13806,a(flip),b,14012,a),flip(a)].">
      <j1 rule="hyper" parents="64 13806 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(14012(a,1),9326(a,1))].">
      <j1 rule="para" parents="14012 9326"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(14012(a,1),9328(a,1))].">
      <j1 rule="para" parents="14012 9328"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(14012(a,1),12113(a,1))].">
      <j1 rule="para" parents="14012 12113"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(z,u) \ y))
    ]]></literal>
    <justification jstring="[para(13949(a,2),14012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13949 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      K(x / (y * y),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,11960,a(flip),b,14020,a),flip(a)].">
      <j1 rule="hyper" parents="319 11960 14020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      T(x,y * (z * z)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(12980,a,14024,a),flip(a)].">
      <j1 rule="hyper" parents="12980 14024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      T(x,((y * y) * z) / u) = T(x,(z / u) * (y * y))
    ]]></literal>
    <justification jstring="[para(719(a,2),14024(a,1,2))].">
      <j1 rule="para" parents="719 14024"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      T(x,((y * z) \ u) * (z * z)) = T(x,R(y / z,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(686(a,1),14024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="686 14024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,11966,a(flip),b,14025,a),flip(a)].">
      <j1 rule="hyper" parents="319 11966 14025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(9296,a,14027,a),flip(a)].">
      <j1 rule="hyper" parents="9296 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u * z)) = K(x,(z * u) / y)
    ]]></literal>
    <justification jstring="[hyper(6993,a,14027,a),flip(a)].">
      <j1 rule="hyper" parents="6993 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z * y)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(6989,a,14027,a),flip(a)].">
      <j1 rule="hyper" parents="6989 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7776,a,b,14027,a)].">
      <j1 rule="hyper" parents="319 7776 14027"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(131,a,14027,a,b,9,a)].">
      <j1 rule="hyper" parents="131 14027 9"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      T(x,K(y / (z * z),u) * w) = T(x,K(u,z \ (z \ y)) * w)
    ]]></literal>
    <justification jstring="[para(14033(a,2),13437(a,1,2,1))].">
      <j1 rule="para" parents="14033 13437"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      T(x,y * (y * (z / (y * u)))) = T(x,z / ((1 / y) * u))
    ]]></literal>
    <justification jstring="[para(703(a,1),14034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="703 14034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      T(x,(y * y) * (z \ T(u,y \ (y \ z)))) = T(x,u / (z / (y * y)))
    ]]></literal>
    <justification jstring="[para(14037(a,1),11180(a,1,2,2,2))].">
      <j1 rule="para" parents="14037 11180"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(14041(a,1),7079(a,1,1,2))].">
      <j1 rule="para" parents="14041 7079"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      K(x,T(y / z,z * (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(11362(a,1),14010(a,1,2))].">
      <j1 rule="para" parents="11362 14010"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      T(x,(y / T(z,u * (u * y))) * (u * u)) = T(x,((u * u) \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12971,a(flip),b,14035,a),flip(a)].">
      <j1 rule="hyper" parents="64 12971 14035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      K(x * ((y \ z) * y),T(u,z)) = K(((y \ z) * y) * x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),14038(a,1,2,2))].">
      <j1 rule="para" parents="10 14038"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(8203(a,1),14038(a,1,1))].">
      <j1 rule="para" parents="8203 14038"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,y \ u),z * (u / y))) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(9548(a,2),14039(a,1,2,1))].">
      <j1 rule="para" parents="9548 14039"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,z \ u),y * (u / z))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(12338(a,2),14040(a,1,2,1))].">
      <j1 rule="para" parents="12338 14040"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(127,a,12947,a(flip),b,14042,a)].">
      <j1 rule="hyper" parents="127 12947 14042"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),u) \ T(K(w,v5) * L(x,y,K(z,u)),u) = K(w,T(v5,L(u * x,y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(13313(a,2),14056(a,2,2,2))].">
      <j1 rule="para" parents="13313 14056"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      K(x,T(y / z,T(u,z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(14018,a,14050,a)].">
      <j1 rule="hyper" parents="14018 14050"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14058(a,1),9929(a,1,1))].">
      <j1 rule="para" parents="14058 9929"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * K(y,y \ z))) = T(x,z / ((1 / (y \ z)) * y))
    ]]></literal>
    <justification jstring="[para(4002(a,1),14047(a,1,2,2,2))].">
      <j1 rule="para" parents="4002 14047"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7254,a,14049,a),flip(a)].">
      <j1 rule="hyper" parents="7254 14049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(9119,a,14060,a)].">
      <j1 rule="hyper" parents="9119 14060"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(7064,a,14063,a)].">
      <j1 rule="hyper" parents="7064 14063"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6980,a,14063,a)].">
      <j1 rule="hyper" parents="6980 14063"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6977,a,14063,a)].">
      <j1 rule="hyper" parents="6977 14063"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      K(T(x,y),K(z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6762,a,14063,a)].">
      <j1 rule="hyper" parents="6762 14063"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6742,a,b,14063,a),flip(a)].">
      <j1 rule="hyper" parents="319 6742 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14063(a,2),6732(a,1))].">
      <j1 rule="para" parents="14063 6732"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14063(a,2),6780(a,1))].">
      <j1 rule="para" parents="14063 6780"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(9269(a,1),14063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9269 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5007(a,1),14064(a,1,2))].">
      <j1 rule="para" parents="5007 14064"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6139(a,1),14064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6139 14064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(14064(a,1),7240(a,1,1))].">
      <j1 rule="para" parents="14064 7240"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = R(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(14064(a,1),8927(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14064 8927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(9271(a,1),14064(a,1,2))].">
      <j1 rule="para" parents="9271 14064"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      (x \ K(y,T(z,u))) * K(y,K(z,w)) = x \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(14064(a,1),12884(a,1,2))].">
      <j1 rule="para" parents="14064 12884"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      K(K(x,y),T(z,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6746,a,b,14065,a)].">
      <j1 rule="hyper" parents="64 6746 14065"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(14065(a,1),8000(a,1,2,1))].">
      <j1 rule="para" parents="14065 8000"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,14066,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14066 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      K(x,T(y,z)) / K(x,T(T(y,u),z)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8011,a,b,14066,a)].">
      <j1 rule="hyper" parents="64 8011 14066"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14066(a,1),6196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14066 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(6953(a,1),14066(a,1,2))].">
      <j1 rule="para" parents="6953 14066"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(14066(a,1),9305(a,1,1))].">
      <j1 rule="para" parents="14066 9305"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,14068,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14068 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(6109(a,1),14068(a,1,2))].">
      <j1 rule="para" parents="6109 14068"/>
    </justification>
  </clause>

  <clause id="14097">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(9276(a,2),14068(a,1,2))].">
      <j1 rule="para" parents="9276 14068"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a,b,14075,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 14075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,14075,a(flip),b,14056,a),flip(a)].">
      <j1 rule="hyper" parents="131 14075 14056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,14075,a(flip),b,6435,a)].">
      <j1 rule="hyper" parents="131 14075 6435"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      K(K(x,y),K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,14075,a(flip),b,6774,a),flip(a)].">
      <j1 rule="hyper" parents="126 14075 6774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(14075(a,1),6124(a,1,2))].">
      <j1 rule="para" parents="14075 6124"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ 1) = u \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14075(a,1),12003(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14075 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(57,a,14102,a)].">
      <j1 rule="hyper" parents="57 14102"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      K(K(x,y) / z,u) = K(z \ K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(6986,a,14105,a)].">
      <j1 rule="hyper" parents="6986 14105"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6908,a,14105,a),flip(a)].">
      <j1 rule="hyper" parents="6908 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6277,a,14105,a),flip(a)].">
      <j1 rule="hyper" parents="6277 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(6262,a,14105,a)].">
      <j1 rule="hyper" parents="6262 14105"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13595,a(flip),b,14105,a),flip(a)].">
      <j1 rule="hyper" parents="64 13595 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9272,a(flip),b,14105,a),flip(a)].">
      <j1 rule="hyper" parents="64 9272 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,14105,a(flip),b,4357,a),flip(a)].">
      <j1 rule="hyper" parents="131 14105 4357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,14105,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="131 14105 22"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,14105,a(flip),b,6801,a)].">
      <j1 rule="hyper" parents="128 14105 6801"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,14105,a(flip),b,7130,a),flip(a)].">
      <j1 rule="hyper" parents="127 14105 7130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14105(a,1),229(a,1,2,2))].">
      <j1 rule="para" parents="14105 229"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(14105(a,1),6081(a,1,1))].">
      <j1 rule="para" parents="14105 6081"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(14105(a,1),6385(a,1,1))].">
      <j1 rule="para" parents="14105 6385"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(14105(a,1),6407(a,2,2))].">
      <j1 rule="para" parents="14105 6407"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(14105(a,1),6908(a,1))].">
      <j1 rule="para" parents="14105 6908"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      K(x,y * z) \ K(x,K(y,z)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(9348,a,14108,a)].">
      <j1 rule="hyper" parents="9348 14108"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(9300,a,14108,a),flip(a)].">
      <j1 rule="hyper" parents="9300 14108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,14108,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14108 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      K(((x \ y) * x) / (K(z,u) * x),w) = K((x * K(z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12862,a(flip),b,14108,a)].">
      <j1 rule="hyper" parents="64 12862 14108"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      K(x,T(K(y,z) / u,w)) = K(x,T(u \ K(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6913,a(flip),b,14108,a)].">
      <j1 rule="hyper" parents="64 6913 14108"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),14108(a,1,2))].">
      <j1 rule="para" parents="25 14108"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(5173(a,1),14108(a,1,2))].">
      <j1 rule="para" parents="5173 14108"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(5148(a,1),14108(a,1,2))].">
      <j1 rule="para" parents="5148 14108"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6386(a,1),14108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6386 14108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6402(a,1),14108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6402 14108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(14108(a,1),6985(a,1))].">
      <j1 rule="para" parents="14108 6985"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(14108(a,1),9296(a,1))].">
      <j1 rule="para" parents="14108 9296"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(14108(a,1),9326(a,1))].">
      <j1 rule="para" parents="14108 9326"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14108(a,1),9328(a,1))].">
      <j1 rule="para" parents="14108 9328"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),14111(a,1,1))].">
      <j1 rule="para" parents="5173 14111"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      K(x * (y * K(x,z)),u) = K(T(x,z) * y,u)
    ]]></literal>
    <justification jstring="[para(6489(a,1),14111(a,1,1))].">
      <j1 rule="para" parents="6489 14111"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(14111(a,1),6994(a,1))].">
      <j1 rule="para" parents="14111 6994"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9273,a,14136,a),flip(a)].">
      <j1 rule="hyper" parents="9273 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5742,a,14136,a),flip(a)].">
      <j1 rule="hyper" parents="5742 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      (x * K(y,z)) \ T(u * (K(y,z) * x),K(y,z)) = T(u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13845,a,b,14136,a)].">
      <j1 rule="hyper" parents="64 13845 14136"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7159,a(flip),b,14136,a)].">
      <j1 rule="hyper" parents="64 7159 14136"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,6812,a,b,14136,a)].">
      <j1 rule="hyper" parents="41 6812 14136"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="23 14136"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(14136(a,1),393(a,1))].">
      <j1 rule="para" parents="14136 393"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      T(x,R(K(y,z) \ u,K(y,z),w)) = T(x,(u * w) / (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(668(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="668 14136"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(5173(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="5173 14136"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(5148(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="5148 14136"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6386(a,1),14136(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6386 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(7069(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="7069 14136"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14136(a,1),9273(a,1))].">
      <j1 rule="para" parents="14136 9273"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7811,a(flip),b,14161,a)].">
      <j1 rule="hyper" parents="64 7811 14161"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14161(a,1),291(a,1,2))].">
      <j1 rule="para" parents="14161 291"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(14161(a,1),6399(a,2))].">
      <j1 rule="para" parents="14161 6399"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14082(a,1),7090(a,1,1))].">
      <j1 rule="para" parents="14082 7090"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(111(a,1),14087(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 14087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(14087(a,1),7139(a,1,1))].">
      <j1 rule="para" parents="14087 7139"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(14087(a,1),9260(a,1,1))].">
      <j1 rule="para" parents="14087 9260"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(9269(a,1),14087(a,1,2))].">
      <j1 rule="para" parents="9269 14087"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      T(x,K(y / z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(111(a,1),14095(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14095(a,1),7246(a,1,1))].">
      <j1 rule="para" parents="14095 7246"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(130,a,14099,a(flip),b,6935,a)].">
      <j1 rule="hyper" parents="130 14099 6935"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      (x \ T(y,z)) \ K(y,K(z,u)) = ((x \ y) * T(K(y,z),u)) \ 1
    ]]></literal>
    <justification jstring="[para(14099(a,1),12387(a,1,2))].">
      <j1 rule="para" parents="14099 12387"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6099,a,b,14128,a),flip(a)].">
      <j1 rule="hyper" parents="319 6099 14128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14128(a,2),6173(a,1))].">
      <j1 rule="para" parents="14128 6173"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9328,a,14142,a),flip(a)].">
      <j1 rule="hyper" parents="9328 14142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) = K(T(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(9296,a,14142,a),flip(a)].">
      <j1 rule="hyper" parents="9296 14142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(7184,a,14142,a)].">
      <j1 rule="hyper" parents="7184 14142"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,6853,a(flip),b,14142,a),flip(a)].">
      <j1 rule="hyper" parents="319 6853 14142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(u,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,14142,a(flip),b,6108,a)].">
      <j1 rule="hyper" parents="131 14142 6108"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      K(x,T(y,z)) * T(z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,14142,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="130 14142 6838"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(14142(a,1),9300(a,1))].">
      <j1 rule="para" parents="14142 9300"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(14142(a,1),9701(a,1,1))].">
      <j1 rule="para" parents="14142 9701"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(14142(a,1),9898(a,1,2))].">
      <j1 rule="para" parents="14142 9898"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7263,a,14167,a),flip(a)].">
      <j1 rule="hyper" parents="7263 14167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5742,a,14167,a),flip(a)].">
      <j1 rule="hyper" parents="5742 14167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      K(T(x,y),z) \ T(z,T(u,x)) = T(T(z,u),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(127,a,14167,a(flip),b,6279,a)].">
      <j1 rule="hyper" parents="127 14167 6279"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,T(z,w))) = u
    ]]></literal>
    <justification jstring="[para(14167(a,1),6401(a,1))].">
      <j1 rule="para" parents="14167 6401"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(14167(a,1),7207(a,2,2))].">
      <j1 rule="para" parents="14167 7207"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      T(x,y) \ T(z,T(u,x)) = K(z,u) * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(14167(a,1),12406(a,1,2))].">
      <j1 rule="para" parents="14167 12406"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(x \ T(y,z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7939,a(flip),b,14189,a)].">
      <j1 rule="hyper" parents="64 7939 14189"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5173(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="5173 14130"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5148(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="5148 14130"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(6050(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="6050 14130"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(6489(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="6489 14130"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,z) = w
    ]]></literal>
    <justification jstring="[para(6914(a,2),14130(a,1))].">
      <j1 rule="para" parents="6914 14130"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6816(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="6816 14130"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7109(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="7109 14130"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(7191(a,1),14130(a,1))].">
      <j1 rule="para" parents="7191 14130"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(9253(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="9253 14130"/>
    </justification>
  </clause>

  <clause id="14224">
    <literal><![CDATA[
      K(x,y * L(z \ u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * z) \ (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(10089(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="10089 14130"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(12365(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="12365 14130"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(6816(a,1),14144(a,1,1))].">
      <j1 rule="para" parents="6816 14144"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      K((x / y) * K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) / y,u) = w
    ]]></literal>
    <justification jstring="[para(12119(a,1),14144(a,1,1))].">
      <j1 rule="para" parents="12119 14144"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5148(a,1),14174(a,1,2))].">
      <j1 rule="para" parents="5148 14174"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      T(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(6050(a,1),14174(a,1,2))].">
      <j1 rule="para" parents="6050 14174"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6392(a,1),14174(a,1,2))].">
      <j1 rule="para" parents="6392 14174"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6816(a,1),14174(a,1,2))].">
      <j1 rule="para" parents="6816 14174"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u * K(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(9257(a,1),14174(a,1))].">
      <j1 rule="para" parents="9257 14174"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(12365(a,1),14174(a,1,2))].">
      <j1 rule="para" parents="12365 14174"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14071(a,1),6732(a,1))].">
      <j1 rule="para" parents="14071 6732"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14071(a,1),6780(a,1))].">
      <j1 rule="para" parents="14071 6780"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(14071(a,1),12043(a,2,2))].">
      <j1 rule="para" parents="14071 12043"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,K(z,1 / z) / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,10215,a,b,14076,a)].">
      <j1 rule="hyper" parents="319 10215 14076"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(x / w,u / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,10195,a,b,14076,a)].">
      <j1 rule="hyper" parents="319 10195 14076"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(7520,a,14089,a),flip(a)].">
      <j1 rule="hyper" parents="7520 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      (x \ y) * K(x,K(z,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(6788,a,14089,a),flip(a)].">
      <j1 rule="hyper" parents="6788 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6787,a,14089,a)].">
      <j1 rule="hyper" parents="6787 14089"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12776,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="319 12776 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (w * u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,10186,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="319 10186 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6782,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="319 6782 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(130,a,14089,a,b,6781,a)].">
      <j1 rule="hyper" parents="130 14089 6781"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,4918,a(flip),b,14089,a)].">
      <j1 rule="hyper" parents="127 4918 14089"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(14089(a,1),4421(a,1))].">
      <j1 rule="para" parents="14089 4421"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      K(x,y) * (z * K(x,K(y,u))) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[para(14089(a,1),8552(a,1,2))].">
      <j1 rule="para" parents="14089 8552"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(14096(a,1),6789(a,1))].">
      <j1 rule="para" parents="14096 6789"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(14096(a,2),6789(a,1))].">
      <j1 rule="para" parents="14096 6789"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8229,a(flip),b,14097,a)].">
      <j1 rule="hyper" parents="64 8229 14097"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      K((x * K(y,z)) \ 1,u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5191,a,b,14107,a)].">
      <j1 rule="hyper" parents="64 5191 14107"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      K((x / y) \ K(z,u),L(w,K(z,u),y)) = K((K(z,u) * y) / x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12793,a(flip),b,14107,a),flip(a)].">
      <j1 rule="hyper" parents="64 12793 14107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12909,a,b,14110,a)].">
      <j1 rule="hyper" parents="319 12909 14110"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(13650,a,14115,a),flip(a)].">
      <j1 rule="hyper" parents="13650 14115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13454,a,14115,a)].">
      <j1 rule="hyper" parents="13454 14115"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13605,a(flip),b,14115,a),flip(a)].">
      <j1 rule="hyper" parents="319 13605 14115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13457,a,b,14115,a)].">
      <j1 rule="hyper" parents="64 13457 14115"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13456,a(flip),b,14115,a),flip(a)].">
      <j1 rule="hyper" parents="64 13456 14115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u * z)) = K(x,u * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[para(8188(a,1),14115(a,2,2))].">
      <j1 rule="para" parents="8188 14115"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(10115(a,1),14115(a,2,2))].">
      <j1 rule="para" parents="10115 14115"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(14115(a,1),13454(a,1))].">
      <j1 rule="para" parents="14115 13454"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14115(a,2),13617(a,1))].">
      <j1 rule="para" parents="14115 13617"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(14115(a,1),13634(a,1))].">
      <j1 rule="para" parents="14115 13634"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a,b,14116,a)].">
      <j1 rule="hyper" parents="319 4356 14116"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      x \ (T(x,y) * K(z,u)) = K(u,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4288,a,b,14116,a)].">
      <j1 rule="hyper" parents="319 4288 14116"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,T(z,w)) \ K(y,x) = v5
    ]]></literal>
    <justification jstring="[para(14116(a,2),6165(a,1))].">
      <j1 rule="para" parents="14116 6165"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      R(K(x,y) \ (z / K(u,w)),K(x,y),K(u,w)) = T(z / (K(u,w) * K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(14117(a,1),669(a,2,1,2))].">
      <j1 rule="para" parents="14117 669"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u * (x \ K(y,z)),K(x,w)) = T(u,K(w,x) * (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(14119(a,1),13430(a,1,2,1,2))].">
      <j1 rule="para" parents="14119 13430"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(14129(a,1),7072(a,2,1))].">
      <j1 rule="para" parents="14129 7072"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      K(x * K(y,y \ z),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(13503,a,14134,a),flip(a)].">
      <j1 rule="hyper" parents="13503 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(11272,a,14134,a),flip(a)].">
      <j1 rule="hyper" parents="11272 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(11271,a,14134,a),flip(a)].">
      <j1 rule="hyper" parents="11271 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      K(x * K(y,z),y * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(7353,a,14134,a),flip(a)].">
      <j1 rule="hyper" parents="7353 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7348,a,14134,a),flip(a)].">
      <j1 rule="hyper" parents="7348 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13735,a,b,14134,a),flip(a)].">
      <j1 rule="hyper" parents="319 13735 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      K(K(x,y) * z,u) * w = K(z * K(x,y),u) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,14134,a,b,11,a)].">
      <j1 rule="hyper" parents="130 14134 11"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      K(x * K(y,z),x \ y) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12514,a(flip),b,14134,a),flip(a)].">
      <j1 rule="hyper" parents="64 12514 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) = u / T(u,K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11237,a(flip),b,14134,a),flip(a)].">
      <j1 rule="hyper" parents="64 11237 14134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      K(x * K(y,z),T(u,(K(y,z) * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14134(a,1),6245(a,1))].">
      <j1 rule="para" parents="14134 6245"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(14134(a,1),11271(a,1))].">
      <j1 rule="para" parents="14134 11271"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      K(x * K(y * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(14134(a,1),11272(a,1))].">
      <j1 rule="para" parents="14134 11272"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * K(w,u * K(y,z)),v5) = v6
    ]]></literal>
    <justification jstring="[para(14134(a,2),13736(a,1,1,2))].">
      <j1 rule="para" parents="14134 13736"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[para(5178(a,1),14280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5178 14280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      K(x / (y / z),y) = K(x / (z \ y),y)
    ]]></literal>
    <justification jstring="[para(5241(a,1),14280(a,1,1))].">
      <j1 rule="para" parents="5241 14280"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * z)) = K(x,u * (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(8163(a,1),14140(a,2,2))].">
      <j1 rule="para" parents="8163 14140"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(8906(a,1),14140(a,2,2))].">
      <j1 rule="para" parents="8906 14140"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14011,a(flip),b,14143,a),flip(a)].">
      <j1 rule="hyper" parents="319 14011 14143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      x \ (y * (K((y \ x) / (z / y),u) * (y \ x))) = K(((y \ x) * y) / z,T(u,x / y))
    ]]></literal>
    <justification jstring="[hyper(12855,a,14143,a(flip))].">
      <j1 rule="hyper" parents="12855 14143"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13735,a,b,14150,a),flip(a)].">
      <j1 rule="hyper" parents="319 13735 14150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      K(K(x,y) \ (z / y),u) = K(z / T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,13740,a(flip),b,14150,a),flip(a)].">
      <j1 rule="hyper" parents="319 13740 14150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      T(x,y * K(z \ u,z)) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(13627,a,14155,a),flip(a)].">
      <j1 rule="hyper" parents="13627 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      T(x,y * K(z,z \ u)) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(13494,a,14155,a),flip(a)].">
      <j1 rule="hyper" parents="13494 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(13490,a,14155,a),flip(a)].">
      <j1 rule="hyper" parents="13490 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13489,a,14155,a)].">
      <j1 rule="hyper" parents="13489 14155"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,14155,a(flip),b,13435,a),flip(a)].">
      <j1 rule="hyper" parents="131 14155 13435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(5045(a,1),14155(a,2,2))].">
      <j1 rule="para" parents="5045 14155"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(14155(a,1),13489(a,1))].">
      <j1 rule="para" parents="14155 13489"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ K(z,y)),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(14157(a,1),12962(a,1,2,2,1))].">
      <j1 rule="para" parents="14157 12962"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      K(x,T((y * z) * (1 / y),y \ K(y,z)) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(14157(a,1),13851(a,1,2,1))].">
      <j1 rule="para" parents="14157 13851"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(7128(a,1),14162(a,1,2,1))].">
      <j1 rule="para" parents="7128 14162"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13726,a,b,14165,a),flip(a)].">
      <j1 rule="hyper" parents="319 13726 14165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(u / z) \ y) = T(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(14178(a,1),7139(a,1,1))].">
      <j1 rule="para" parents="14178 7139"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y,K(w * u,z) * x) = v5
    ]]></literal>
    <justification jstring="[para(14181(a,1),13493(a,1,2,1,2))].">
      <j1 rule="para" parents="14181 13493"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(14182(a,1),6824(a,1))].">
      <j1 rule="para" parents="14182 6824"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14011,a(flip),b,14193,a)].">
      <j1 rule="hyper" parents="64 14011 14193"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,14196,a(flip),b,6838,a),flip(a)].">
      <j1 rule="hyper" parents="130 14196 6838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14315">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6089,a,b,14243,a),flip(a)].">
      <j1 rule="hyper" parents="319 6089 14243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12363,a(flip),b,14243,a),flip(a)].">
      <j1 rule="hyper" parents="319 12363 14243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4922,a(flip),b,14243,a),flip(a)].">
      <j1 rule="hyper" parents="319 4922 14243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14318">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(14243(a,1),330(a,1))].">
      <j1 rule="para" parents="14243 330"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      T(R(K(x,K(y,z)) \ u,K(w,v5),w),K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14243(a,2),13830(a,1,1,1))].">
      <j1 rule="para" parents="14243 13830"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[para(6727(a,1),14247(a,1,1))].">
      <j1 rule="para" parents="6727 14247"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(4922(a,1),14259(a,2,2))].">
      <j1 rule="para" parents="4922 14259"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(14259(a,2),11126(a,1))].">
      <j1 rule="para" parents="14259 11126"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14261(a,2),13617(a,1))].">
      <j1 rule="para" parents="14261 13617"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10096(a,2),14268(a,1,1))].">
      <j1 rule="para" parents="10096 14268"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      K((x * y) * K(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,9293,a,b,14279,a),flip(a)].">
      <j1 rule="hyper" parents="319 9293 14279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,14134,a,b,14281,a)].">
      <j1 rule="hyper" parents="319 14134 14281"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      K(x * K(y,z),x \ z) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12514,a(flip),b,14281,a),flip(a)].">
      <j1 rule="hyper" parents="64 12514 14281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      T(x * K(y,z),K(K(z,y) * x,u) * w) = T(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(14281(a,2),5800(a,1,2,1))].">
      <j1 rule="para" parents="14281 5800"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      K((x / y) * K(z,x),u) = K(T(x,z) / y,u)
    ]]></literal>
    <justification jstring="[para(12057(a,1),14281(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12057 14281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      K(x,K(y * (z \ u),(y * (z \ u)) \ u) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(14289(a,2),13470(a,2,2,1))].">
      <j1 rule="para" parents="14289 13470"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),14290(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 14290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(127,a,14301,a,b,10,a)].">
      <j1 rule="hyper" parents="127 14301 10"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      T(x / (y * K(z,u)),K(u,z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      (y * K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(14301(a,2),393(a,1))].">
      <j1 rule="para" parents="14301 393"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * K(u,z)) = T(x,y * T(y \ K(z,u),w))
    ]]></literal>
    <justification jstring="[para(4934(a,2),14301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4934 14301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      T(x,K(y,y \ z) * (u * (z / y))) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(5178(a,1),14301(a,2,2))].">
      <j1 rule="para" parents="5178 14301"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(12057(a,1),14301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12057 14301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) = T(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(12363(a,1),14301(a,2,2))].">
      <j1 rule="para" parents="12363 14301"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(4922(a,1),14309(a,2,2))].">
      <j1 rule="para" parents="4922 14309"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      T(x,K(y,z) \ T(u,y)) = T(x,y \ (u * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6089(a,2),14309(a,2,2))].">
      <j1 rule="para" parents="6089 14309"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      K(x * (y * (z \ y)),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * (z \ y)) * x,u) = w
    ]]></literal>
    <justification jstring="[para(14313(a,1),9296(a,1))].">
      <j1 rule="para" parents="14313 9296"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      K(K(x,y) * (T(x,y) * z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(4041(a,1),14328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4041 14328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      K(x \ (y * (z \ x)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13768,a(flip),b,14333,a)].">
      <j1 rule="hyper" parents="64 13768 14333"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ (z * (y * x)),L(x,y,y \ 1)) = K(z / (1 / y),L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1594(a,1),14347(a,1,1,2,2))].">
      <j1 rule="para" parents="1594 14347"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = v5
    ]]></literal>
    <justification jstring="[para(14347(a,1),11269(a,1,2,1))].">
      <j1 rule="para" parents="14347 11269"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(111(a,1),14070(a,1,2,2))].">
      <j1 rule="para" parents="111 14070"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6102(a,2),14070(a,1,2))].">
      <j1 rule="para" parents="6102 14070"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(9288(a,1),14070(a,1,2))].">
      <j1 rule="para" parents="9288 14070"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(2673(a,1),14324(a,1,2))].">
      <j1 rule="para" parents="2673 14324"/>
    </justification>
  </clause>

  <clause id="14354">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(3695(a,1),14324(a,1,2))].">
      <j1 rule="para" parents="3695 14324"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(x,v5))) = w
    ]]></literal>
    <justification jstring="[para(14063(a,1),14351(a,1))].">
      <j1 rule="para" parents="14063 14351"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      T((L(K(x,x \ K(y,z)),u,w) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(429,a,3939,a,b,14114,a)].">
      <j1 rule="hyper" parents="429 3939 14114"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(40,a,5176,a,b,14133,a)].">
      <j1 rule="hyper" parents="40 5176 14133"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      K(x,(T(y,z) \ (y * u)) * w) \ K(x,K(K(y,z) \ u,w)) = K(w * (T(y,z) \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(4426(a,1),14133(a,1,2,2))].">
      <j1 rule="para" parents="4426 14133"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) \ K(x,K(L(y,z,K(u,w)),z * K(u,w))) = K((z * K(u,w)) * L(y,z,K(u,w)),x)
    ]]></literal>
    <justification jstring="[para(13263(a,1),14133(a,1,1,2))].">
      <j1 rule="para" parents="13263 14133"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)),w,v5)) = K(x,L(T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(6386(a,1),14139(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6386 14139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      K(x,K(y / (z / u),u \ z) * (w * (y / (z / u)))) = K(x,w * T((z / u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7111(a,1),14141(a,2,2,2))].">
      <j1 rule="para" parents="7111 14141"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      K(T(x * y,x) * (z * K(T(x * y,x),u)),w) = K(T(T(x * y,u),T(x,y)) * z,w)
    ]]></literal>
    <justification jstring="[para(3135(a,2),14152(a,2,1,1))].">
      <j1 rule="para" parents="3135 14152"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      T(x * K(y,z),T(u / x,w)) = T(x * K(y,z),T(x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6896,a(flip),b,14160,a)].">
      <j1 rule="hyper" parents="64 6896 14160"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      T(x,K(y,(z * z) \ u) * ((w / u) * (z * z))) = T(x,w / T((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(688(a,1),14169(a,1,2,2))].">
      <j1 rule="para" parents="688 14169"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u / T(z * K(w,y),y))
    ]]></literal>
    <justification jstring="[para(5991(a,1),14169(a,1,2,1))].">
      <j1 rule="para" parents="5991 14169"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      K(x,T(y,z)) \ (u * z) = K(x,y) \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(14176(a,1),7256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14176 7256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * T(z,K(x,y)) = ((z * K(x,y)) * u) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,11404,a(flip),b,14185,a),flip(a)].">
      <j1 rule="hyper" parents="64 11404 14185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14374">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,y)) = y \ (K(u,z) \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,14198,a(flip),b,4383,a),flip(a)].">
      <j1 rule="hyper" parents="127 14198 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),14199(a,1,1,2))].">
      <j1 rule="para" parents="23 14199"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      T(x,y) * K(z / x,u) = K(x \ z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6156(a,1),14199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6156 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(6377(a,1),14205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6377 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(14246(a,1),330(a,1,2))].">
      <j1 rule="para" parents="14246 330"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,14248,a(flip),b,4284,a)].">
      <j1 rule="hyper" parents="131 14248 4284"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      K((K(x,T(y,z * u)) * z) \ 1,T(w,u)) = K(T(z,u) \ K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(12946,a,14255,a)].">
      <j1 rule="hyper" parents="12946 14255"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      K(x,T(K(y,z) \ (K(y,z) / u),w) * K(z,y \ z)) = K(x,(K(y,z) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[para(4269(a,2),14258(a,2,2))].">
      <j1 rule="para" parents="4269 14258"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      T(T(x,K(y,z / T(u,w))),(K(u,w) * (z / u)) \ y) = T(x,y / (K(u,w) * (z / u)))
    ]]></literal>
    <justification jstring="[para(14260(a,1),7139(a,1,1,2))].">
      <j1 rule="para" parents="14260 7139"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(5683(a,1),14262(a,1,2))].">
      <j1 rule="para" parents="5683 14262"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      K(x,y) \ K(y,T(x,z)) = y \ T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[para(5939(a,1),14269(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5939 14269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(10063(a,2),14277(a,1,1,2))].">
      <j1 rule="para" parents="10063 14277"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * ((y \ x) * y),u)
    ]]></literal>
    <justification jstring="[para(8188(a,1),14278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8188 14278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (y / z))) = T(x,u * (z \ y))
    ]]></literal>
    <justification jstring="[para(5178(a,1),14298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5178 14298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      K(T((x \ y) \ z,K(y,x) * u) * K(x \ y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(14298(a,1),13881(a,1,1,1))].">
      <j1 rule="para" parents="14298 13881"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      T(x / y,K(y,x) * z) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,6209,a,b,14299,a)].">
      <j1 rule="hyper" parents="41 6209 14299"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      K(x / y,K(y,x) * z) = (x / y) \ T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(127,a,14391,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 14391 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(127,a,14317,a(flip),b,4101,a),flip(a)].">
      <j1 rule="hyper" parents="127 14317 4101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * T(L(z / y,u,w),y))
    ]]></literal>
    <justification jstring="[para(4177(a,1),14323(a,1,2,1))].">
      <j1 rule="para" parents="4177 14323"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      T(x,(y / (z * K(u,w))) * K(z,T(z \ w,u))) = T(x,y / T(z * K(u,w),z \ w))
    ]]></literal>
    <justification jstring="[para(14329(a,1),13607(a,1,2,2))].">
      <j1 rule="para" parents="14329 13607"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,y * (z * K(u,y)))) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(5886(a,1),14340(a,1,2,1))].">
      <j1 rule="para" parents="5886 14340"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      K(x,x * (K(y,z) \ (u * y))) \ T(x,u * T(y,z)) = R(x,K(y,z) \ (u * y),x)
    ]]></literal>
    <justification jstring="[para(14343(a,1),4461(a,1,2))].">
      <j1 rule="para" parents="14343 4461"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(4330(a,1),14346(a,1,1))].">
      <j1 rule="para" parents="4330 14346"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),14398(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="231 14398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(6742(a,1),14359(a,1,1))].">
      <j1 rule="para" parents="6742 14359"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,(z \ T(T(u,w),w)) * y) = K(x,y * (z \ T(T(u,w),w)))
    ]]></literal>
    <justification jstring="[para(13744(a,1),14359(a,1,1,2))].">
      <j1 rule="para" parents="13744 14359"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,T(z,u) * x) = K(y,x * T(z,u))
    ]]></literal>
    <justification jstring="[para(14065(a,1),14359(a,1,1))].">
      <j1 rule="para" parents="14065 14359"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),14385(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4540(a,1),14399(a,1,1))].">
      <j1 rule="para" parents="4540 14399"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) * K(y,z * ((u \ x) * u)) = K(y,((u \ x) * u) * z)
    ]]></literal>
    <justification jstring="[para(9286(a,1),14400(a,1,1))].">
      <j1 rule="para" parents="9286 14400"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * T(x,u)) = K(y,T(x,u) * z)
    ]]></literal>
    <justification jstring="[para(14067(a,1),14400(a,1,1))].">
      <j1 rule="para" parents="14067 14400"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13669,a,b,14404,a)].">
      <j1 rule="hyper" parents="64 13669 14404"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      K(T(x,y) / (((z \ 1) / y) * y),u) = K(T(z,y) * x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13553,a(flip),b,14407,a)].">
      <j1 rule="hyper" parents="64 13553 14407"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      x \ K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * (x \ 1) = w
    ]]></literal>
    <justification jstring="[para(11948(a,1),14103(a,1))].">
      <j1 rule="para" parents="11948 14103"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(13735(a,1),14145(a,1))].">
      <j1 rule="para" parents="13735 14145"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(13738(a,2),14145(a,1))].">
      <j1 rule="para" parents="13738 14145"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * K(y,z \ (y * u))) = v5
    ]]></literal>
    <justification jstring="[para(6592(a,2),14148(a,1,2,1))].">
      <j1 rule="para" parents="6592 14148"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14259(a,1),14148(a,1))].">
      <j1 rule="para" parents="14259 14148"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14258(a,2),14148(a,1))].">
      <j1 rule="para" parents="14258 14148"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u / T(z,y),w)) = v5
    ]]></literal>
    <justification jstring="[para(7069(a,1),14153(a,1,2,1))].">
      <j1 rule="para" parents="7069 14153"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(13437(a,1),14171(a,1))].">
      <j1 rule="para" parents="13437 14171"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14301(a,1),14171(a,1))].">
      <j1 rule="para" parents="14301 14171"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(6748(a,1),14173(a,1,1))].">
      <j1 rule="para" parents="6748 14173"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,(y / z) \ T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(12372(a,2),14220(a,1,2))].">
      <j1 rule="para" parents="12372 14220"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(14261(a,2),14220(a,1))].">
      <j1 rule="para" parents="14261 14220"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      K(x,T(y,(z / u) * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,L(w,u,u \ z) * z)) = v5
    ]]></literal>
    <justification jstring="[para(9549(a,1),14223(a,1,2,2))].">
      <j1 rule="para" parents="9549 14223"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12133(a,2),14223(a,1,2))].">
      <j1 rule="para" parents="12133 14223"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14011(a,2),14223(a,1))].">
      <j1 rule="para" parents="14011 14223"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(14012(a,2),14223(a,1))].">
      <j1 rule="para" parents="14012 14223"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(14293(a,2),14223(a,1))].">
      <j1 rule="para" parents="14293 14223"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      K(K(x,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(14296(a,2),14226(a,1))].">
      <j1 rule="para" parents="14296 14226"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      T(x,(y * z) / T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(5158(a,2),14231(a,1,2))].">
      <j1 rule="para" parents="5158 14231"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * w) * R(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(105(a,1),14236(a,1,2,2))].">
      <j1 rule="para" parents="105 14236"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(10465(a,2),14236(a,1))].">
      <j1 rule="para" parents="10465 14236"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * w) \ (z * w))) = v5
    ]]></literal>
    <justification jstring="[para(12803(a,2),14252(a,1,2))].">
      <j1 rule="para" parents="12803 14252"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(11955(a,2),14350(a,1,2))].">
      <j1 rule="para" parents="11955 14350"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(11983(a,1),14353(a,1))].">
      <j1 rule="para" parents="11983 14353"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4607(a,2),14435(a,1))].">
      <j1 rule="para" parents="4607 14435"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(12028(a,2),14435(a,1))].">
      <j1 rule="para" parents="12028 14435"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(13872(a,2),14436(a,1))].">
      <j1 rule="para" parents="13872 14436"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11137(a,2),14413(a,1))].">
      <j1 rule="para" parents="11137 14413"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * u) * K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(6616(a,1),14419(a,1))].">
      <j1 rule="para" parents="6616 14419"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14421,a,11214,a)].">
      <j1 rule="hyper" parents="14421 11214"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(L(z,u,w),y) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(10096(a,2),14421(a,1,2,1))].">
      <j1 rule="para" parents="10096 14421"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,14442,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14442 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11215,a,b,14442,a)].">
      <j1 rule="hyper" parents="64 11215 14442"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4243(a,1),14442(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4243 14442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,K(z,y) \ ((T(y,z) \ z) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13191,a(flip),b,14444,a)].">
      <j1 rule="hyper" parents="64 13191 14444"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14421,a,14445,a)].">
      <j1 rule="hyper" parents="14421 14445"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      K(K(x,x * y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(14427,a,11159,a)].">
      <j1 rule="hyper" parents="14427 11159"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      K(K(x * y,y \ 1) \ z,u) = K(K(y \ 1,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10077(a,1),14449(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10077 14449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      K(x,T(y,z)) * K(T(y,u),T(x,z)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(6169,a,14088,a)].">
      <j1 rule="hyper" parents="6169 14088"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14089(a,1),14100(a,1,1))].">
      <j1 rule="para" parents="14089 14100"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w) * K(v5,v6))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(128,a,12901,a,b,14121,a)].">
      <j1 rule="hyper" parents="128 12901 14121"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14172(a,2),44(a,1))].">
      <j1 rule="para" parents="14172 44"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(z,y)) = u * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(6703(a,1),14172(a,1,1))].">
      <j1 rule="para" parents="6703 14172"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      T(T(x,K(y,z \ y)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6306(a,1),14179(a,2,2))].">
      <j1 rule="para" parents="6306 14179"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      T(T(x,K(y,y \ z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(9322,a,14180,a)].">
      <j1 rule="hyper" parents="9322 14180"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(y,T(u,x)) = T(T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(6102(a,1),14207(a,1,1))].">
      <j1 rule="para" parents="6102 14207"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      x \ T(T(y,z),x) = K(y,z) * (T(x,y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6315,a(flip),b,14210,a)].">
      <j1 rule="hyper" parents="64 6315 14210"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      K(K(x,y),z) * (T(u \ y,K(x,u)) \ K(x,y)) = (u \ y) \ T(T(K(x,y),z),u \ y)
    ]]></literal>
    <justification jstring="[para(6968(a,1),14461(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6968 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,14189,a,b,14212,a)].">
      <j1 rule="hyper" parents="319 14189 14212"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      T(K(x,((y * K(z,u)) * w) * v5),v5 \ T(v5 * ((y * K(z,u)) * w),x)) = (v5 \ T(v5 * ((y * K(z,u)) * w),x)) \ T((y * K(z,u)) * w,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(417,a,14275,a,b,12141,a)].">
      <j1 rule="hyper" parents="417 14275 12141"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      (K(x * K(y,z),u) * w) \ (K(K(y,z) * x,u) * T(w,v5)) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(127,a,14282,a,b,4922,a)].">
      <j1 rule="hyper" parents="127 14282 4922"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      T(x,K(y,T(y \ z,u)) * (w * T(y \ z,u))) = T(x,w * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(447(a,1),14303(a,2,2,2))].">
      <j1 rule="para" parents="447 14303"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      K(x / K(y,z),K(y,z)) \ T(u,x / K(y,z)) = (x / K(y,z)) \ (u * (K(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(111(a,1),14315(a,2,2,2))].">
      <j1 rule="para" parents="111 14315"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),14315(a,1,1))].">
      <j1 rule="para" parents="6748 14315"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      K(x * T(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[para(4922(a,1),14327(a,1,1))].">
      <j1 rule="para" parents="4922 14327"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),x * y) = K(x * (z * y),y * x)
    ]]></literal>
    <justification jstring="[hyper(8226,a,14469,a)].">
      <j1 rule="hyper" parents="8226 14469"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      K(x,(y \ T(T(z,K(u,w) * v5),x)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[para(14335(a,1),5970(a,2,2,1))].">
      <j1 rule="para" parents="14335 5970"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      T(x,y) * K(z,L(T(u,x),w,v5)) = K(z,L(u,w,v5)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(14362(a,1),6188(a,1,2))].">
      <j1 rule="para" parents="14362 6188"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      x \ (K(y,z) \ T(x,x \ z)) = z \ (x * (T(z,y) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13053,a(flip),b,14374,a),flip(a)].">
      <j1 rule="hyper" parents="64 13053 14374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      T(x,L(y / K(z \ u,w),K(z \ u,w),T(z,v5))) = T(x,(y * T(z,v5)) / (T(z,v5) * K(u / z,w)))
    ]]></literal>
    <justification jstring="[para(14376(a,2),12828(a,2,2,2))].">
      <j1 rule="para" parents="14376 12828"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(3820,a,14381,a),flip(a)].">
      <j1 rule="hyper" parents="3820 14381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * T(x \ u,w)) / T(x,K(y,z))) = x * T(u / x,w)
    ]]></literal>
    <justification jstring="[para(447(a,1),14381(a,2,2))].">
      <j1 rule="para" parents="447 14381"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ (T(K(x,y),z) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(14386(a,1),9771(a,1,1))].">
      <j1 rule="para" parents="14386 9771"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      K(x / y,K(y,x) * z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,14392,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 14392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      K(x / y,(y / T(x,y)) * z) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[para(10806(a,1),14478(a,1,2))].">
      <j1 rule="para" parents="10806 14478"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(x,y))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(6816(a,1),14393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6816 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = u
    ]]></literal>
    <justification jstring="[para(14403(a,2),6040(a,1))].">
      <j1 rule="para" parents="14403 6040"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14448,a(flip),b,14446,a),flip(a)].">
      <j1 rule="hyper" parents="64 14448 14446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      K(x,K(y \ 1,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14421,a,14482,a)].">
      <j1 rule="hyper" parents="14421 14482"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,K(y,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(4285(a,1),14482(a,1,2))].">
      <j1 rule="para" parents="4285 14482"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1)) \ w) = K(x,K(y,u * z) \ w)
    ]]></literal>
    <justification jstring="[para(11973(a,1),14482(a,1,2,1))].">
      <j1 rule="para" parents="11973 14482"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      K(x,K(y \ 1,z * y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11144,a(flip),b,14483,a),flip(a)].">
      <j1 rule="hyper" parents="319 11144 14483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,T(T(x,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(6474,a,14451,a)].">
      <j1 rule="hyper" parents="6474 14451"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,T(T(x,z),u * w)) = K(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(14013(a,1),14451(a,1,2))].">
      <j1 rule="para" parents="14013 14451"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      K(x,y) * (x * K(z,K(u,w))) = T(x * K(z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[hyper(319,a,4081,a,b,14453,a)].">
      <j1 rule="hyper" parents="319 4081 14453"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,3813,a(flip),b,14453,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3813 14453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      (x * (T(y,z) * K(u,K(w,v5)))) \ (x * (y * K(u,K(w,v5)))) = K(z,y * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(14453(a,1),5150(a,1,1,2))].">
      <j1 rule="para" parents="14453 5150"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) / K(y,z) = T(x,w) / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(14453(a,2),6772(a,1,1))].">
      <j1 rule="para" parents="14453 6772"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = L(u * K(y,T(x,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(14457(a,1),9245(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14457 9245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(y,u \ x) = T(T(y,x / u),T(x,z))
    ]]></literal>
    <justification jstring="[para(5705(a,1),14460(a,1,2))].">
      <j1 rule="para" parents="5705 14460"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4285(a,1),14484(a,2,2))].">
      <j1 rule="para" parents="4285 14484"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      K(x,T(T((y \ 1) \ z,u),y) \ w) = K(x,T(z / (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13486,a(flip),b,14495,a),flip(a)].">
      <j1 rule="hyper" parents="64 13486 14495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      (T(x,K(y,z)) * (K(x,K(y,z)) \ T(u,w))) / T(x,K(y,z)) = T((x * u) / T(x,K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(14490(a,1),4419(a,1,1,2))].">
      <j1 rule="para" parents="14490 4419"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(x * u,w) = T(T(x,K(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(6784(a,1),14490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6784 14490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(u,x),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(23(a,1),14201(a,1,2))].">
      <j1 rule="para" parents="23 14201"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      K(T(T(x * y,x),z) * u,T(w,y * x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * T(T(x * y,x),z),w) = v5
    ]]></literal>
    <justification jstring="[para(9264(a,1),14201(a,1,2))].">
      <j1 rule="para" parents="9264 14201"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) * K((x \ y) \ 1,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(6866(a,1),14202(a,1,1))].">
      <j1 rule="para" parents="6866 14202"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K((x \ 1) * y,T(u,w))) = T(z / ((x \ 1) * y),T(x \ y,u))
    ]]></literal>
    <justification jstring="[hyper(14208,a,12474,a)].">
      <j1 rule="hyper" parents="14208 12474"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      K(x,K(y / z,u) * (w * ((z / y) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((z / y) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(4645(a,1),14215(a,1,2,1))].">
      <j1 rule="para" parents="4645 14215"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (K(w,z) * y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(K(w,z) * y,z)) = v5
    ]]></literal>
    <justification jstring="[para(5837(a,1),14215(a,1,2,1))].">
      <j1 rule="para" parents="5837 14215"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (u * (K(w,z) * y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(K(w,z) * y,z \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(6516(a,1),14215(a,1,2,1))].">
      <j1 rule="para" parents="6516 14215"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13457(a,2),14215(a,1))].">
      <j1 rule="para" parents="13457 14215"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * (u * K(z * y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,z) * z,w) * u) = v5
    ]]></literal>
    <justification jstring="[para(9316(a,1),14218(a,1,2,2,2))].">
      <j1 rule="para" parents="9316 14218"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      K(x * ((y \ z) * y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14222,a,14388,a),flip(a)].">
      <j1 rule="hyper" parents="14222 14388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      K(((x \ y) * x) * z,u) = K(z * T(y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14052,a(flip),b,14509,a)].">
      <j1 rule="hyper" parents="64 14052 14509"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      K(((x \ y) * x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,14192,a(flip),b,14511,a),flip(a)].">
      <j1 rule="hyper" parents="319 14192 14511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      K(T(x * y,x) * z,u) = K((y * x) * z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14512(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 14512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) * a(w,v5,K(T(z,y) * u,x)) = K(x,L(((y \ z) * y) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(14512(a,1),10106(a,1,2,3))].">
      <j1 rule="para" parents="14512 10106"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14259(a,1),14225(a,1))].">
      <j1 rule="para" parents="14259 14225"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(z * (y / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * K(y,w)) * T(y / z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12222(a,1),14228(a,1,2,2))].">
      <j1 rule="para" parents="12222 14228"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(13437(a,1),14233(a,1))].">
      <j1 rule="para" parents="13437 14233"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * (v5 / w)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / T(w,a(y,z,u))) = v6
    ]]></literal>
    <justification jstring="[para(12604(a,2),14266(a,1,2,1))].">
      <j1 rule="para" parents="12604 14266"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      K(x,y * K(z,u \ (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(w * u,z)) = v5
    ]]></literal>
    <justification jstring="[para(12739(a,1),14414(a,1,2,2))].">
      <j1 rule="para" parents="12739 14414"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      T(x,(y * z) / T(y,u)) = T(x,K(y,u) \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(14428,a,13817,a),flip(a)].">
      <j1 rule="hyper" parents="14428 13817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      T(x,(y * z) / T(y,u)) = T(x,y \ (z * T(y,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14344,a(flip),b,14520,a),flip(a)].">
      <j1 rule="hyper" parents="319 14344 14520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      T(x,y \ ((y \ z) * T(y,u))) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14521(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      K(x,x * (y \ ((y \ z) * T(y,u)))) \ T(x,z / T(y,u)) = R(x,y \ ((y \ z) * T(y,u)),x)
    ]]></literal>
    <justification jstring="[para(14522(a,1),4461(a,1,2))].">
      <j1 rule="para" parents="14522 4461"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[hyper(14430,a,13226,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14430 13226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(14079(a,1),14432(a,1))].">
      <j1 rule="para" parents="14079 14432"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      K(x,y * K(z,(u * z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u * w,z)) = v5
    ]]></literal>
    <justification jstring="[para(12507(a,2),14440(a,1,2,2))].">
      <j1 rule="para" parents="12507 14440"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13721(a,1),14440(a,1))].">
      <j1 rule="para" parents="13721 14440"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      K(x,(y \ z) * K(u \ (w * (v5 \ 1)),z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = v6
    ]]></literal>
    <justification jstring="[para(3907(a,1),14515(a,1,2,2))].">
      <j1 rule="para" parents="3907 14515"/>
    </justification>
  </clause>

  <clause id="14529">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u \ w,z)) = v5
    ]]></literal>
    <justification jstring="[para(11482(a,2),14527(a,1))].">
      <j1 rule="para" parents="11482 14527"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4616,a(flip),b,14257,a),flip(a)].">
      <j1 rule="hyper" parents="319 4616 14257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14532">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(7563,a,14531,a)].">
      <j1 rule="hyper" parents="7563 14531"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * ((z \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(11269,a,14263,a)].">
      <j1 rule="hyper" parents="11269 14263"/>
    </justification>
  </clause>

  <clause id="14535">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14215,a,14534,a),flip(a)].">
      <j1 rule="hyper" parents="14215 14534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14534(a,1),14215(a,1))].">
      <j1 rule="para" parents="14534 14215"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,14535,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14535 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(8471(a,2),14535(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8471 14535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,((w \ u) * w) * K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(14537(a,1),14171(a,1))].">
      <j1 rule="para" parents="14537 14171"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) = K(x,u * (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11214,a(flip),b,14291,a)].">
      <j1 rule="hyper" parents="64 11214 14291"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14507,a,14540,a),flip(a)].">
      <j1 rule="hyper" parents="14507 14540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),14541(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 14541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / z))) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),14541(a,2,2,2))].">
      <j1 rule="para" parents="23 14541"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13857,a(flip),b,14542,a)].">
      <j1 rule="hyper" parents="64 13857 14542"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      K(x,y * T(T(z / u,T(w,u)) * v5,K(u \ z,w) * v5)) = K(x,y * ((K(u \ z,w) * v5) * (z / u)))
    ]]></literal>
    <justification jstring="[para(6215(a,1),14542(a,1,2,2,1))].">
      <j1 rule="para" parents="6215 14542"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14442,a(flip),b,14292,a)].">
      <j1 rule="hyper" parents="64 14442 14292"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14325,a,14546,a),flip(a)].">
      <j1 rule="hyper" parents="14325 14546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (u / (1 / z)))) = K(x,y / T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,4703,a,b,14547,a)].">
      <j1 rule="hyper" parents="64 4703 14547"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / T(z \ 1,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13379,a(flip),b,14547,a),flip(a)].">
      <j1 rule="hyper" parents="64 13379 14547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),14547(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 14547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3041(a,2),14547(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3041 14547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14552">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6810,a,14302,a)].">
      <j1 rule="hyper" parents="6810 14302"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,u) * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9338,a,b,14308,a)].">
      <j1 rule="hyper" parents="64 9338 14308"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12682,a(flip),b,14326,a),flip(a)].">
      <j1 rule="hyper" parents="64 12682 14326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      K(x,y) * K(a(z,u,y),x) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(131,a,12588,a(flip),b,14555,a)].">
      <j1 rule="hyper" parents="131 12588 14555"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      T(x,y) / T(x,a(z,u,y)) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(5230,a,14556,a)].">
      <j1 rule="hyper" parents="5230 14556"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      T(x,y) / (a(x,z,K(u,y)) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12626(a,2),14557(a,1,2))].">
      <j1 rule="para" parents="12626 14557"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      T(x,y) / (a(K(x,y),z,u) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12521(a,2),14558(a,1,2,1))].">
      <j1 rule="para" parents="12521 14558"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(37,a,4359,a,b,14559,a)].">
      <j1 rule="hyper" parents="37 4359 14559"/>
    </justification>
  </clause>

  <clause id="14561">
    <literal><![CDATA[
      T(K(x,L(y,z,u)) * y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,5920,a,b,14560,a)].">
      <j1 rule="hyper" parents="64 5920 14560"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(K(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(2844(a,1),14561(a,1,1))].">
      <j1 rule="para" parents="2844 14561"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(x,z,K(u,y)) \ x
    ]]></literal>
    <justification jstring="[para(12521(a,1),14562(a,2,1))].">
      <j1 rule="para" parents="12521 14562"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12626,a(flip),b,14563,a),flip(a)].">
      <j1 rule="hyper" parents="319 12626 14563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      T(x,(y / z) * (y / z)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(4348(a,1),14339(a,1,2))].">
      <j1 rule="para" parents="4348 14339"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      T(T(x,y),(z \ u) * (z \ u)) = T(x,(u / z) * ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(12979,a,14565,a),flip(a)].">
      <j1 rule="hyper" parents="12979 14565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ (w * (u / z)) = K(x,y) \ (w * T(u / z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(14143(a,1),14372(a,1,1))].">
      <j1 rule="para" parents="14143 14372"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      K(x,T(T(y,z),u * w)) * T(z,v5) = T(z,v5) * K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14042,a,b,14375,a),flip(a)].">
      <j1 rule="hyper" parents="319 14042 14375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(K(y * z,x) * y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13862,a,b,14387,a)].">
      <j1 rule="hyper" parents="64 13862 14387"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(T(u * z,u),w) * x) = K(y,x * T(T(u * z,u),w))
    ]]></literal>
    <justification jstring="[para(9269(a,1),14402(a,1,1,2))].">
      <j1 rule="para" parents="9269 14402"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(T(u,z) * z,w) * x) = K(y,x * T(T(u,z) * z,w))
    ]]></literal>
    <justification jstring="[para(9306(a,1),14402(a,1,1,2))].">
      <j1 rule="para" parents="9306 14402"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,u) = K(K(x * y,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(11367,a,14450,a),flip(a)].">
      <j1 rule="hyper" parents="11367 14450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(14463(a,1),6986(a,1))].">
      <j1 rule="para" parents="14463 6986"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) = K(T(y,z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(14574,a,13749,a),flip(a)].">
      <j1 rule="hyper" parents="14574 13749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      K((x / y) \ K(z \ K(u,w),y),v5) = K(T(y,z \ K(w,u \ w)) / x,v5)
    ]]></literal>
    <justification jstring="[para(13777(a,1),14575(a,1,1,2))].">
      <j1 rule="para" parents="13777 14575"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,4022,a(flip),b,14489,a)].">
      <j1 rule="hyper" parents="36 4022 14489"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(14411,a,14577,a)].">
      <j1 rule="hyper" parents="14411 14577"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a(flip),b,14577,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 14577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      K(K(x,K(y,z)) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14296,a,b,14577,a)].">
      <j1 rule="hyper" parents="64 14296 14577"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(1187(a,1),14577(a,1,1))].">
      <j1 rule="para" parents="1187 14577"/>
    </justification>
  </clause>

  <clause id="14583">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,K(w,v5))) = x * T(y * K(u,K(w,v5)),z)
    ]]></literal>
    <justification jstring="[para(14577(a,1),4912(a,1,1,2))].">
      <j1 rule="para" parents="14577 4912"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(6418(a,1),14577(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6418 14577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K(x / (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(8891(a,1),14577(a,1,1))].">
      <j1 rule="para" parents="8891 14577"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(14172(a,1),14578(a,1,1))].">
      <j1 rule="para" parents="14172 14578"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(14580(a,1),4345(a,1))].">
      <j1 rule="para" parents="14580 4345"/>
    </justification>
  </clause>

  <clause id="14588">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4049,a,14579,a)].">
      <j1 rule="hyper" parents="4049 14579"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(37,a,14284,a(flip),b,14579,a(flip))].">
      <j1 rule="hyper" parents="37 14284 14579"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(14579(a,2),4117(a,1))].">
      <j1 rule="para" parents="14579 4117"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14300,a(flip),b,14588,a)].">
      <j1 rule="hyper" parents="64 14300 14588"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13607,a(flip),b,14588,a)].">
      <j1 rule="hyper" parents="64 13607 14588"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1187(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="1187 14588"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) / w) = T(x,y / w)
    ]]></literal>
    <justification jstring="[para(1191(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="1191 14588"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(4636(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="4636 14588"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(4922(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="4922 14588"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5360(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="5360 14588"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8172(a,1),14588(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8172 14588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8891(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="8891 14588"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5)))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10186(a,1),14588(a,1,2))].">
      <j1 rule="para" parents="10186 14588"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13445,a(flip),b,14589,a),flip(a)].">
      <j1 rule="hyper" parents="64 13445 14589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) * w) = T(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7447(a,1),14589(a,1,2))].">
      <j1 rule="para" parents="7447 14589"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14172(a,1),14589(a,1,2))].">
      <j1 rule="para" parents="14172 14589"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(5173(a,1),14582(a,1,1,2))].">
      <j1 rule="para" parents="5173 14582"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(6386(a,1),14582(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6386 14582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      K((x \ K(y \ z,u)) * (y \ T(z,K(w,v5))),v6) = K(x \ T(y \ T(z,K(w,v5)),u),v6)
    ]]></literal>
    <justification jstring="[para(14582(a,1),12189(a,1,1,1,2))].">
      <j1 rule="para" parents="14582 12189"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ u,w) = K(T(x,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6386(a,1),14584(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6386 14584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,12443,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="64 12443 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(6386(a,1),14592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6386 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u * K(y,z),w) \ v5)
    ]]></literal>
    <justification jstring="[para(5965(a,1),14592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5965 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6386(a,1),14593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6386 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(6400(a,1),14593(a,1,2,2))].">
      <j1 rule="para" parents="6400 14593"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y / T(w * K(z,u),v5))
    ]]></literal>
    <justification jstring="[para(5965(a,1),14593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5965 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      T(x,y / T(z,u / w)) = T(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(6402(a,1),14593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6402 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(6386(a,1),14594(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6386 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(6386(a,1),14595(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6386 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      T(x,(K(y,z) * (u / z)) * w) = T(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(7069(a,1),14596(a,1,2,1))].">
      <j1 rule="para" parents="7069 14596"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      T(x,((y * z) * K(u,L(w,y,z))) * v5) = T(x,((K(u,w) * y) * z) * v5)
    ]]></literal>
    <justification jstring="[para(12849(a,1),14596(a,1,2,1))].">
      <j1 rule="para" parents="12849 14596"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u / (1 / z))) = T(x,(u / (1 / z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12480,a,b,14597,a)].">
      <j1 rule="hyper" parents="64 12480 14597"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      T(x,y * T(T(z,K(u,w)),v5)) = T(x,y * T(z,v5))
    ]]></literal>
    <justification jstring="[para(23(a,1),14597(a,1,2,2))].">
      <j1 rule="para" parents="23 14597"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      T(x,y * (K(z,u) \ w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(5173(a,1),14597(a,1,2,2))].">
      <j1 rule="para" parents="5173 14597"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      T(x,y * T(z,T(u,w))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(6386(a,1),14597(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6386 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * (w * u)) = T(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(12201(a,1),14597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12201 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(4644(a,1),14587(a,1,1))].">
      <j1 rule="para" parents="4644 14587"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(4757(a,1),14587(a,1,1))].">
      <j1 rule="para" parents="4757 14587"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      K(K(x,K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(6783(a,2),14587(a,1,1))].">
      <j1 rule="para" parents="6783 14587"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(6727(a,1),14587(a,1,1))].">
      <j1 rule="para" parents="6727 14587"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(x,y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(9187(a,1),14587(a,1,1))].">
      <j1 rule="para" parents="9187 14587"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(14244(a,1),14587(a,1,1))].">
      <j1 rule="para" parents="14244 14587"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      K(x * (y * K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (K(z,u) * y),w) = v5
    ]]></literal>
    <justification jstring="[para(8172(a,1),14590(a,1,1))].">
      <j1 rule="para" parents="8172 14590"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      K(x * K(T(y,z),u),w) = K(x * K(y,u),w)
    ]]></literal>
    <justification jstring="[para(6102(a,2),14586(a,1,1,2))].">
      <j1 rule="para" parents="6102 14586"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      T(x,y * (T(z,K(u,w)) * v5)) = T(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[para(4636(a,1),14601(a,1,2,2))].">
      <j1 rule="para" parents="4636 14601"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      T(x,y * (T(z,K(u,w)) \ v5)) = T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(6418(a,1),14601(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6418 14601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) = T(x,y * K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7308(a,1),14601(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7308 14601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,14301,a,b,14604,a),flip(a)].">
      <j1 rule="hyper" parents="319 14301 14604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = v5
    ]]></literal>
    <justification jstring="[para(14604(a,2),14305(a,1))].">
      <j1 rule="para" parents="14604 14305"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(12305(a,2),14608(a,1,1))].">
      <j1 rule="para" parents="12305 14608"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      K(T(x * y,x) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(14610(a,1),6453(a,1))].">
      <j1 rule="para" parents="14610 6453"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      K(T(x * y,y) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(14610(a,1),7229(a,1))].">
      <j1 rule="para" parents="14610 7229"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11109,a,b,14614,a),flip(a)].">
      <j1 rule="hyper" parents="319 11109 14614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      T(x,T(y,z) / T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14614(a,1),11161(a,1))].">
      <j1 rule="para" parents="14614 11161"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      T(T(x,y),z \ T(u,x)) = T(T(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(5873,a,14618,a),flip(a)].">
      <j1 rule="hyper" parents="5873 14618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11178,a(flip),b,14618,a),flip(a)].">
      <j1 rule="hyper" parents="64 11178 14618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(12305(a,2),14618(a,1,2))].">
      <j1 rule="para" parents="12305 14618"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13517,a(flip),b,14619,a),flip(a)].">
      <j1 rule="hyper" parents="64 13517 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      R(T(x / y,y * T(z,u)),y,T(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      (y * T(z,T(u,w))) \ (x * T(z,T(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(14625(a,1),884(a,1,1))].">
      <j1 rule="para" parents="14625 884"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      T(x,y * T(z / T(T(u,w),z),u)) = T(x,y * (T(T(u,w),z) \ z))
    ]]></literal>
    <justification jstring="[para(3133(a,1),14625(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3133 14625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(u * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(14410,a,14636,a)].">
      <j1 rule="hyper" parents="14410 14636"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      K((T(x,y) / z) * K(x,u),w) = K(T(T(x,y),u) / z,w)
    ]]></literal>
    <justification jstring="[hyper(14227,a,14636,a),flip(a)].">
      <j1 rule="hyper" parents="14227 14636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14155,a,b,14640,a)].">
      <j1 rule="hyper" parents="64 14155 14640"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),K(z,y) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13997,a,b,14640,a)].">
      <j1 rule="hyper" parents="64 13997 14640"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      (x \ T(y,x)) \ (x \ (y * T(x,T(y,z)))) = T(T(x,T(y,z)),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6381,a,b,14647,a)].">
      <j1 rule="hyper" parents="64 6381 14647"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      K(((K(x,T(y,z)) * u) * w) / a(x,u,K(w,T(y,z))),v5) = K((u * w) * K(y,x),v5)
    ]]></literal>
    <justification jstring="[para(12526(a,2),14653(a,1,1))].">
      <j1 rule="para" parents="12526 14653"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      T(x,T(K(y,T(z,u)) * w,v5)) = K(x,v5) * T(x * K(v5,x),K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(131,a,14655,a(flip),b,7604,a),flip(a)].">
      <j1 rule="hyper" parents="131 14655 7604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      T(x,K(T(y,z),u) * w) = T(x,K(u,y) * w)
    ]]></literal>
    <justification jstring="[para(6102(a,2),14655(a,1,2,1))].">
      <j1 rule="para" parents="6102 14655"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ T(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(T(y,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(14655(a,1),14517(a,1))].">
      <j1 rule="para" parents="14655 14517"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      T(x,K(y / z,u) * w) = T(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13444,a(flip),b,14660,a),flip(a)].">
      <j1 rule="hyper" parents="64 13444 14660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(6392(a,1),14628(a,1,1,2))].">
      <j1 rule="para" parents="6392 14628"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      K(T(x,T(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(6392(a,1),14629(a,1,1,1))].">
      <j1 rule="para" parents="6392 14629"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(5822(a,1),14631(a,1,1,1))].">
      <j1 rule="para" parents="5822 14631"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K(x * (y \ K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(12275,a,14585,a),flip(a)].">
      <j1 rule="hyper" parents="12275 14585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ K(u,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(14585(a,1),12275(a,1))].">
      <j1 rule="para" parents="14585 12275"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6402(a,1),14598(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6402 14598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12137,a(flip),b,14600,a),flip(a)].">
      <j1 rule="hyper" parents="64 12137 14600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ (u * K(z,y)) = x * ((u * K(z,y)) / x)
    ]]></literal>
    <justification jstring="[para(14607(a,2),4258(a,1,1))].">
      <j1 rule="para" parents="14607 4258"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u / w)) = T(x,y \ K(w \ u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12353,a(flip),b,14617,a),flip(a)].">
      <j1 rule="hyper" parents="319 12353 14617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      T(x,y * (T(z,u * w) \ v5)) = T(x,y * (T(z,w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(9253(a,1),14638(a,1,2,2,1))].">
      <j1 rule="para" parents="9253 14638"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(z \ y,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13611,a(flip),b,14639,a),flip(a)].">
      <j1 rule="hyper" parents="64 13611 14639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14676">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) \ K(w,z))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13609,a(flip),b,14670,a),flip(a)].">
      <j1 rule="hyper" parents="64 13609 14670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(12366(a,1),14670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12366 14670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[para(13576(a,1),14677(a,1,2,2,2))].">
      <j1 rule="para" parents="13576 14677"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(9269(a,1),14634(a,1,1,2))].">
      <j1 rule="para" parents="9269 14634"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * T(z,u))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * (z * K(u,z)),w)) = v6
    ]]></literal>
    <justification jstring="[para(13559(a,1),14646(a,1,2,2))].">
      <j1 rule="para" parents="13559 14646"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * (T(u,w) / x)) = T(T(x,K(y,z)) * (u / x),w)
    ]]></literal>
    <justification jstring="[para(3795(a,1),14498(a,1,2))].">
      <j1 rule="para" parents="3795 14498"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(3795(a,2),14543(a,1,2,2))].">
      <j1 rule="para" parents="3795 14543"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(13542,a,14551,a),flip(a)].">
      <j1 rule="hyper" parents="13542 14551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / ((z * u) / u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13416,a(flip),b,14683,a),flip(a)].">
      <j1 rule="hyper" parents="64 13416 14683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      T(x * T(y,K(z,u) \ x),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(14309(a,2),14552(a,1,1,2))].">
      <j1 rule="para" parents="14309 14552"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,u),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11288,a(flip),b,14615,a),flip(a)].">
      <j1 rule="hyper" parents="64 11288 14615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K(y * x,z),T(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14642(a,1),6244(a,1))].">
      <j1 rule="para" parents="14642 6244"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      K(K(x,y) * (T(y * x,z) / u),w) = K(T(T(y * x,z),y) / u,w)
    ]]></literal>
    <justification jstring="[hyper(14287,a,14654,a)].">
      <j1 rule="hyper" parents="14287 14654"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12353,a(flip),b,14672,a)].">
      <j1 rule="hyper" parents="64 12353 14672"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(129,a,14682,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14682 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      T(x,R(y / y,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,((T(z,y * y) \ u) / w) * (y * y))
    ]]></literal>
    <justification jstring="[para(976(a,1),14036(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="976 14036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14076,a,b,14091,a),flip(a)].">
      <j1 rule="hyper" parents="319 14076 14091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(13634,a,14264,a)].">
      <j1 rule="hyper" parents="13634 14264"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,u) = z \ (K(x,y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14271,a,14374,a)].">
      <j1 rule="hyper" parents="14271 14374"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      x \ (K(y,z) \ T(x,x \ z)) = (x * (T(z,y) / x)) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,12479,a(flip),b,14695,a),flip(a)].">
      <j1 rule="hyper" parents="64 12479 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      (x * (T(y,z) / x)) / y = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,14473,a(flip),b,14696,a),flip(a)].">
      <j1 rule="hyper" parents="64 14473 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(14441,a,12374,a)].">
      <j1 rule="hyper" parents="14441 12374"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,14321,a,b,14698,a)].">
      <j1 rule="hyper" parents="36 14321 14698"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(6818(a,2),14699(a,1,1))].">
      <j1 rule="para" parents="6818 14699"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12476,a(flip),b,14700,a)].">
      <j1 rule="hyper" parents="64 12476 14700"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ z = K(z,T(y,u)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(6102(a,1),14701(a,1,1,2))].">
      <j1 rule="para" parents="6102 14701"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(12359(a,1),14701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12359 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(4374,a,14703,a)].">
      <j1 rule="hyper" parents="4374 14703"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = (x \ T(z,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,13343,a,b,14704,a)].">
      <j1 rule="hyper" parents="64 13343 14704"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      (x \ T(K(y,z),u)) \ K(y,z) = (x \ K(y,z)) \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14244,a(flip),b,14704,a),flip(a)].">
      <j1 rule="hyper" parents="64 14244 14704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      (x * K(y,T(z \ u,z))) \ (z \ u) = K(u / z,y) * (x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(6850(a,1),14702(a,2,1))].">
      <j1 rule="para" parents="6850 14702"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = w
    ]]></literal>
    <justification jstring="[para(6748(a,1),14456(a,1,1))].">
      <j1 rule="para" parents="6748 14456"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,4611,a(flip),b,14544,a),flip(a)].">
      <j1 rule="hyper" parents="319 4611 14544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(14544(a,2),14354(a,1))].">
      <j1 rule="para" parents="14544 14354"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      T(x,L(K(y,z),z * u,w) * (w * (z * u))) = T(x,w * (z * (u * K(y,z))))
    ]]></literal>
    <justification jstring="[para(5683(a,1),14626(a,2,2,2))].">
      <j1 rule="para" parents="5683 14626"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(14679,a,11625,a)].">
      <j1 rule="hyper" parents="14679 11625"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(14679,a,xx)].">
      <j1 rule="hyper" parents="14679"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      K((x * y) \ T(x,z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(5417(a,2),14679(a,1))].">
      <j1 rule="para" parents="5417 14679"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      K(x,K(y,(z * (u * w)) / (z * w))) = K(x,K(y,L(u,w,z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),14692(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11 14692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      (x \ T(y,z)) \ K(y,K(z,u)) = ((x \ y) * K(y,T(z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(6099(a,2),14186(a,2,1,2))].">
      <j1 rule="para" parents="6099 14186"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(319,a,1368,a,b,14209,a)].">
      <j1 rule="hyper" parents="319 1368 14209"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(z \ w,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(14366(a,1),13748(a,1,2,2))].">
      <j1 rule="para" parents="14366 13748"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      (T(x,K(y,L(z,u,w)) * v5) * K(y,L(T(z,x),u,w))) / (K(y,L(z,u,w)) * x) = K(x,v5 * K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(128,a,14472,a,b,9256,a)].">
      <j1 rule="hyper" parents="128 14472 9256"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),T(w * T(y,K(z,u)),K(z,u))),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(14475(a,1),13433(a,1,1,2,1))].">
      <j1 rule="para" parents="14475 13433"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14487,a(flip),b,14488,a),flip(a)].">
      <j1 rule="hyper" parents="64 14487 14488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7122,a,14725,a)].">
      <j1 rule="hyper" parents="7122 14725"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,14725,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14725 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(129,a,14726,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14726 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ w) = T(u \ z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[para(14726(a,1),6727(a,1,1))].">
      <j1 rule="para" parents="14726 6727"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(14312,a,14727,a)].">
      <j1 rule="hyper" parents="14312 14727"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z \ u) * y) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(14727(a,1),9260(a,1,1))].">
      <j1 rule="para" parents="14727 9260"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(14727(a,1),9339(a,1,1))].">
      <j1 rule="para" parents="14727 9339"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (T(u,z) / z)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[para(14727(a,1),11089(a,1,1))].">
      <j1 rule="para" parents="14727 11089"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      T(T(x,K(y,z * (u / z))),y / ((z \ u) / z)) = T(x,((z \ u) / z) \ y)
    ]]></literal>
    <justification jstring="[para(14727(a,1),11129(a,1,1))].">
      <j1 rule="para" parents="14727 11129"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,u \ w)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(14727(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="14727 13423"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      T(x,K(y,z * u)) \ T(w * x,K(y,z \ u)) = T(w,x * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(14727(a,1),13949(a,1,1))].">
      <j1 rule="para" parents="14727 13949"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),14730(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 14730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u * (z \ 1)) * y) = T(x,y * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(14730(a,1),10430(a,1,1))].">
      <j1 rule="para" parents="14730 10430"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) / K(x,y) = T(K(x,y) * u,w) / T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(14241(a,1),14492(a,1,1,1))].">
      <j1 rule="para" parents="14241 14492"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      T(x,(y / z) * ((y / z) * u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(12979,a,14566,a),flip(a)].">
      <j1 rule="hyper" parents="12979 14566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14741">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) \ v5) = T(x,T(y \ K(u,z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13663,a(flip),b,14613,a),flip(a)].">
      <j1 rule="hyper" parents="64 13663 14613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      ((x \ K(y,z)) \ K(y,T(z,u))) * K(y,K(z,w)) = (x \ T(K(y,z),u)) \ K(y,T(z,w))
    ]]></literal>
    <justification jstring="[para(14706(a,1),12884(a,1,1))].">
      <j1 rule="para" parents="14706 12884"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      (x \ T(y,z)) \ K(y,K(z,u)) = (x \ T(y,T(z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(12363(a,1),14718(a,2,1))].">
      <j1 rule="para" parents="12363 14718"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      (x \ T(y,z)) \ K(y,K(z,u)) = (x \ y) \ K(z,T(T(y,u),x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12887,a,b,14747,a),flip(a)].">
      <j1 rule="hyper" parents="319 12887 14747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(6907(a,1),14720(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6907 14720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(11163(a,1),14749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11163 14749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,14314,a(flip),b,14750,a),flip(a)].">
      <j1 rule="hyper" parents="319 14314 14750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * (y * u))) = T(x,(((z / y) \ 1) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12306,a(flip),b,14740,a),flip(a)].">
      <j1 rule="hyper" parents="64 12306 14740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      (x \ y) \ K(z,T(T(y,u),x)) = K(y,K(z,u)) * ((x \ T(y,z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14409,a,14748,a),flip(a)].">
      <j1 rule="hyper" parents="14409 14748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      T(x,R(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4356(a,1),14164(a,1,2,1))].">
      <j1 rule="para" parents="4356 14164"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7014,a(flip),b,14239,a),flip(a)].">
      <j1 rule="hyper" parents="319 7014 14239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(14253,a,14755,a)].">
      <j1 rule="hyper" parents="14253 14755"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,L(w,u,z))) = K(x,K(w,(y * z) / (z * u)))
    ]]></literal>
    <justification jstring="[para(22(a,2),14756(a,1,2,1,1))].">
      <j1 rule="para" parents="22 14756"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(14416,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(14443,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14264,a(flip),b,14694,a),flip(a)].">
      <j1 rule="hyper" parents="64 14264 14694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5532,a,b,14760,a)].">
      <j1 rule="hyper" parents="64 5532 14760"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(4019(a,2),14761(a,2,2,2))].">
      <j1 rule="para" parents="4019 14761"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(12279,a,14762,a)].">
      <j1 rule="hyper" parents="12279 14762"/>
    </justification>
  </clause>

  <clause id="14764">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13599,a,14763,a)].">
      <j1 rule="hyper" parents="13599 14763"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(12250,a,14764,a),flip(a)].">
      <j1 rule="hyper" parents="12250 14764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(L(x,w,v5),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(10156,a,14764,a)].">
      <j1 rule="hyper" parents="10156 14764"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14549,a(flip),b,14764,a),flip(a)].">
      <j1 rule="hyper" parents="64 14549 14764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(81(a,1),14764(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="81 14764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(11266,a,14765,a)].">
      <j1 rule="hyper" parents="11266 14765"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,14769,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14769 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,y * K(z,u)),K(z,u)),K(u,z)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13430,a,b,14770,a)].">
      <j1 rule="hyper" parents="64 13430 14770"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      T(x,y * T(1 / z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,14768,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14768 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / T(y / z,y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13998,a(flip),b,14768,a),flip(a)].">
      <j1 rule="hyper" parents="64 13998 14768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4623,a(flip),b,14768,a)].">
      <j1 rule="hyper" parents="64 4623 14768"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(12023(a,1),14772(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12023 14772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      T(x,y * T(z \ 1,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,14774,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14774 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      T(x,y / T((z * z) \ u,w)) = T(x,y * T(u \ (z * z),w))
    ]]></literal>
    <justification jstring="[para(591(a,1),14777(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="591 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y * T(w \ K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(11997(a,1),14777(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11997 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      T(x,y * T((z * K(u * z,w)) \ 1,u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[para(12045(a,1),14777(a,2,2,2))].">
      <j1 rule="para" parents="12045 14777"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13679,a(flip),b,14767,a)].">
      <j1 rule="hyper" parents="64 13679 14767"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13693,a(flip),b,14782,a),flip(a)].">
      <j1 rule="hyper" parents="64 13693 14782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      K(x,((((y \ (z * u)) \ 1) \ y) \ y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[para(6543(a,1),14782(a,1,2,1))].">
      <j1 rule="para" parents="6543 14782"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10133,a(flip),b,14766,a),flip(a)].">
      <j1 rule="hyper" parents="319 10133 14766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(z \ K(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14616,a(flip),b,14780,a)].">
      <j1 rule="hyper" parents="64 14616 14780"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = K(x,L(y * T(z \ u,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(12458,a,14785,a)].">
      <j1 rule="hyper" parents="12458 14785"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      T(x,y * T(K(z,u) / w,v5)) = T(x,y * T(w \ K(z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14776,a(flip),b,14786,a)].">
      <j1 rule="hyper" parents="64 14776 14786"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      T(x,L(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(12837,a,14754,a)].">
      <j1 rule="hyper" parents="12837 14754"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(4356(a,1),14032(a,2,2,2))].">
      <j1 rule="para" parents="4356 14032"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      T(x,y * (y * (z \ T(u,y \ (y \ z))))) = T(x,u / (z / (y * y)))
    ]]></literal>
    <justification jstring="[hyper(12980,a,14048,a)].">
      <j1 rule="hyper" parents="12980 14048"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      T(x,(y / T(z,u * (u * y))) * (u * u)) = T(x,z \ ((u * u) * y))
    ]]></literal>
    <justification jstring="[para(638(a,1),14051(a,2,2))].">
      <j1 rule="para" parents="638 14051"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      K(x \ K(T(y,x * z),u),T(w,z)) = K(T(x,z) \ K(y,u),w)
    ]]></literal>
    <justification jstring="[hyper(5248,a,14382,a)].">
      <j1 rule="hyper" parents="5248 14382"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      K(x \ K(y,T(z,x * u)),T(w,u)) = K(T(x,u) \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(6102(a,1),14795(a,1,1,2))].">
      <j1 rule="para" parents="6102 14795"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      K(T(x,y) \ K(z,u),w) = K(x \ K(z,u),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(14634,a,14796,a),flip(a)].">
      <j1 rule="hyper" parents="14634 14796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14800">
    <literal><![CDATA[
      K((x / y) \ K(z,u),T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ K(z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(14797(a,1),11316(a,1))].">
      <j1 rule="para" parents="14797 11316"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),14408(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 14408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,12166,a(flip),b,14801,a),flip(a)].">
      <j1 rule="hyper" parents="319 12166 14801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(14499,a,14802,a)].">
      <j1 rule="hyper" parents="14499 14802"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,9290,a(flip),b,14804,a),flip(a)].">
      <j1 rule="hyper" parents="319 9290 14804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14053,a(flip),b,14805,a)].">
      <j1 rule="hyper" parents="64 14053 14805"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(7015(a,1),14458(a,1,1))].">
      <j1 rule="para" parents="7015 14458"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(6791(a,1),14807(a,1,1))].">
      <j1 rule="para" parents="6791 14807"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(6901(a,1),14459(a,1,1))].">
      <j1 rule="para" parents="6901 14459"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,9362,a(flip),b,14554,a),flip(a)].">
      <j1 rule="hyper" parents="319 9362 14554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      T(x,y) * K(z,T(T(u,x),w * v5)) = K(z,T(u,v5 * w)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6860(a,1),14568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6860 14568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      T(x,y * T(z / T(T(u,w),z),u)) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13788,a(flip),b,14652,a),flip(a)].">
      <j1 rule="hyper" parents="319 13788 14652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ T(w,z))) = T(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[para(6640(a,1),14814(a,1,2,2))].">
      <j1 rule="para" parents="6640 14814"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(x,z)) = T(T(x,T(y,z)),x \ y)
    ]]></literal>
    <justification jstring="[para(7078(a,1),14657(a,1,2))].">
      <j1 rule="para" parents="7078 14657"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      K(T(T(x * y,z),x) / u,w) = K(T(y * x,T(z,y)) / u,w)
    ]]></literal>
    <justification jstring="[para(12513(a,1),14688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12513 14688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      K(T(T(x * y,z),x) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(y * x,z) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(14817(a,2),14665(a,1))].">
      <j1 rule="para" parents="14817 14665"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(14818,a,13824,a)].">
      <j1 rule="hyper" parents="14818 13824"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),14819(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 14819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(14819(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14819 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      K(T((x * y) * (K(y,x) / y),K(y,x) / y) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(12320(a,1),14819(a,2,1,1))].">
      <j1 rule="para" parents="12320 14819"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,14077,a,b,14820,a),flip(a)].">
      <j1 rule="hyper" parents="319 14077 14820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,14821,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 14821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(14821(a,2),5187(a,1))].">
      <j1 rule="para" parents="14821 5187"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),14824(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 14824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11135,a(flip),b,14826,a),flip(a)].">
      <j1 rule="hyper" parents="319 11135 14826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(12496(a,1),14826(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12496 14826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(232(a,1),14827(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 14827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(12839,a,14829,a)].">
      <j1 rule="hyper" parents="12839 14829"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(35,a,14092,a,b,14823,a(flip))].">
      <j1 rule="hyper" parents="35 14092 14823"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),14831(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 14831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) * a(w,v5,K(y \ (u * z),x)) = K(x,L(y \ T(z * u,u),v5,w))
    ]]></literal>
    <justification jstring="[para(14832(a,1),10106(a,1,2,3))].">
      <j1 rule="para" parents="14832 10106"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      (x * K(y,z / u)) \ (u \ z) = K(z / u,y) * (x \ (u \ z))
    ]]></literal>
    <justification jstring="[para(6858(a,1),14707(a,1,1,2))].">
      <j1 rule="para" parents="6858 14707"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      T(x,y / ((K(z / u,w) * (u \ (u \ z))) \ (u \ z))) = T(x,y / (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(14834(a,1),11191(a,1,2,2,1))].">
      <j1 rule="para" parents="14834 11191"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(11268,a,14733,a)].">
      <j1 rule="hyper" parents="11268 14733"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(14836(a,1),14732(a,1))].">
      <j1 rule="para" parents="14836 14732"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u * (z \ 1))) = T(x,(u * (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(6797(a,1),14738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6797 14738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      T(x,(((y / z) \ 1) \ y) * (z \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14752(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(K(x,T(y,u)) * u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12947,a(flip),b,14811,a),flip(a)].">
      <j1 rule="hyper" parents="64 12947 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6839(a,1),14840(a,2,1))].">
      <j1 rule="para" parents="6839 14840"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6110(a,1),14841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6110 14841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(14027(a,1),14841(a,1,1))].">
      <j1 rule="para" parents="14027 14841"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,9345,a(flip),b,14842,a),flip(a)].">
      <j1 rule="hyper" parents="319 9345 14842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(12248,a,14842,a(flip))].">
      <j1 rule="hyper" parents="12248 14842"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      T(x * K(x * y,z),y) \ T(x,T(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(14842(a,2),9512(a,1,1))].">
      <j1 rule="para" parents="14842 9512"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = K(x \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(14014(a,1),14843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14014 14843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(319,a,9334,a(flip),b,14844,a),flip(a)].">
      <j1 rule="hyper" parents="319 9334 14844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      T(x,y / (z * ((u * K(u * z,w)) / z))) = T(x,y / (T(u,z) * K(z * u,w)))
    ]]></literal>
    <justification jstring="[para(14844(a,1),13621(a,2,2,2))].">
      <j1 rule="para" parents="14844 13621"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      (x * y) / (K(z * K(z * u,w),T(x,u)) * y) = T(x,T(z * u,w) / T(u,z))
    ]]></literal>
    <justification jstring="[para(14845(a,2),6163(a,2,2))].">
      <j1 rule="para" parents="14845 6163"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      T(x,T(T(y * K(y * z,u),z),y * z)) = T(x,T(z,y) \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14845(a,1),14206(a,1,2,1))].">
      <j1 rule="para" parents="14845 14206"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = T(x,y) * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,14376,a,b,14847,a),flip(a)].">
      <j1 rule="hyper" parents="319 14376 14847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      T(x * K(x * y,z),y) \ T(x,T(y,T(z,u))) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(14167(a,2),14846(a,1,2))].">
      <j1 rule="para" parents="14167 14846"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5471,a(flip),b,14848,a)].">
      <j1 rule="hyper" parents="64 5471 14848"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,y / (z * y))) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(14854(a,2),12789(a,2,2,1))].">
      <j1 rule="para" parents="14854 12789"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      T(T(x,K(y,(z * z) * T(u,z))),y * ((z * z) * (T(u,z \ 1) \ 1))) = T(x,((z * z) * (T(u,z \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(12976(a,1),14838(a,1,1,2,2))].">
      <j1 rule="para" parents="12976 14838"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (u / y)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(25(a,2),14054(a,1,2))].">
      <j1 rule="para" parents="25 14054"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (u / z)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(25(a,2),14055(a,1,2))].">
      <j1 rule="para" parents="25 14055"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      K(x,y * K(z,u \ (z * w))) = K(x,K(z,u \ w) * y)
    ]]></literal>
    <justification jstring="[hyper(14412,a,13480,a)].">
      <j1 rule="hyper" parents="14412 13480"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14859(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      T(x,y / ((1 / (z \ y)) * z)) = T(x,(z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(4097(a,1),14061(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4097 14061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      K(K(x,y) * T((y \ x) \ z,K(x,y) * u),u) = K((x / y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(14286,a,14390,a)].">
      <j1 rule="hyper" parents="14286 14390"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * ((u \ x) * u)) = K(y,((u \ x) * u) * z)
    ]]></literal>
    <justification jstring="[para(14075(a,1),14405(a,1,1))].">
      <j1 rule="para" parents="14075 14405"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(z,K(x,u)) * K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(14535(a,1),14865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14535 14865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,14406,a(flip),b,14867,a),flip(a)].">
      <j1 rule="hyper" parents="319 14406 14867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,14868,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 14868 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14868(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 14868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14869(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 14869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      T(x,((K(y * z,y) * u) * T(y,z)) * w) = T(x,T(R(y,z,y) * u,T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(4748(a,1),14871(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4748 14871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      T(x,T(R(y,z,u) * w,L(y,z,u)) * v5) = T(x,(w * R(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(12800(a,1),14871(a,1,2,1))].">
      <j1 rule="para" parents="12800 14871"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      T(x,K(y,T(y \ z,u)) * ((y \ z) * T(T(y \ z,u),u))) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(4407(a,1),14466(a,1,2,2))].">
      <j1 rule="para" parents="4407 14466"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),(y \ z) \ (T(y,u) \ z)) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[hyper(12034,a,14524,a)].">
      <j1 rule="hyper" parents="12034 14524"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),K(u,T(y,z))) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[para(6419(a,1),14875(a,1,2))].">
      <j1 rule="para" parents="6419 14875"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      K(x,K(y,T(z \ ((y \ u) \ 1),w))) = K(y,K(x,u * z))
    ]]></literal>
    <justification jstring="[hyper(14355,a,14876,a)].">
      <j1 rule="hyper" parents="14355 14876"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      K(x,K(y,z \ ((x \ u) \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(14069,a,14877,a)].">
      <j1 rule="hyper" parents="14069 14877"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      K(x,K(y,z * (x \ u))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(14430,a,14878,a)].">
      <j1 rule="hyper" parents="14430 14878"/>
    </justification>
  </clause>

  <clause id="14881">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(z * y,x),T(u,z))
    ]]></literal>
    <justification jstring="[para(9295(a,1),14569(a,2,1))].">
      <j1 rule="para" parents="9295 14569"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(4946(a,1),14611(a,2,1))].">
      <j1 rule="para" parents="4946 14611"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7224,a,b,14883,a),flip(a)].">
      <j1 rule="hyper" parents="319 7224 14883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      T(x,T(K(y,T(z,u)) * w,v5)) = T(x,T(K(z,y) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,7603,a(flip),b,14659,a),flip(a)].">
      <j1 rule="hyper" parents="319 7603 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[para(12945(a,1),14885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12945 14885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14301,a,b,14886,a),flip(a)].">
      <j1 rule="hyper" parents="319 14301 14886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(14539,a,14887,a(flip))].">
      <j1 rule="hyper" parents="14539 14887"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,y \ (z \ y)) / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),14684(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 14684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),y / ((u \ z) / u)) = T(x,((u \ z) / u) \ y)
    ]]></literal>
    <justification jstring="[para(9282(a,1),14734(a,1,1,2))].">
      <j1 rule="para" parents="9282 14734"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / ((u \ z) / u)) = T(x,((u \ z) / u) \ y)
    ]]></literal>
    <justification jstring="[para(14087(a,1),14890(a,1,1))].">
      <j1 rule="para" parents="14087 14890"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,u * w)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(14727(a,1),14735(a,1,2))].">
      <j1 rule="para" parents="14727 14735"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,w * u)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(14728(a,1),14735(a,1,2))].">
      <j1 rule="para" parents="14728 14735"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      T(x,K(y,z * u)) \ T(w * x,K(y,z * u)) = T(w,x * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(14727(a,1),14736(a,1,2))].">
      <j1 rule="para" parents="14727 14736"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      T(K(x,y) * z,u) / T(K(x,y),w) = T(K(x,T(y,w)) * z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5186,a,14739,a),flip(a)].">
      <j1 rule="hyper" parents="5186 14739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14787(a,2),13624(a,1))].">
      <j1 rule="para" parents="14787 13624"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      T(x,y \ T(T(z,z * y) * y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(13154(a,1),14851(a,1,2))].">
      <j1 rule="para" parents="13154 14851"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,12304,a(flip),b,14881,a),flip(a)].">
      <j1 rule="hyper" parents="319 12304 14881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      K(K(T(x,y),z) * y,T(u,z * T(x,y))) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(9192,a,14899,a)].">
      <j1 rule="hyper" parents="9192 14899"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(6840(a,1),14900(a,1,1))].">
      <j1 rule="para" parents="6840 14900"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(13493,a,14893,a),flip(a)].">
      <j1 rule="hyper" parents="13493 14893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(14902(a,1),13627(a,1))].">
      <j1 rule="para" parents="14902 13627"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13949,a(flip),b,14895,a),flip(a)].">
      <j1 rule="hyper" parents="64 13949 14895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u * w)) = T(x,T(y,u \ w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14300,a(flip),b,14904,a),flip(a)].">
      <j1 rule="hyper" parents="64 14300 14904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      T(x,T(y,z \ u) \ w) = T(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14300,a(flip),b,14905,a),flip(a)].">
      <j1 rule="hyper" parents="64 14300 14905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      T(x,T(y,z * z) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(213(a,1),14906(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="213 14906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      T(x,y \ ((z * z) \ y)) = T(x,(z * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11223,a(flip),b,14907,a),flip(a)].">
      <j1 rule="hyper" parents="64 11223 14907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      T(x,(((y * y) \ y) * ((y * y) \ y)) * z) = T(T(x,z),(y * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11964,a,b,14908,a)].">
      <j1 rule="hyper" parents="64 11964 14908"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      T(x,((y * y) \ y) * (((y * y) \ y) * z)) = T(T(x,z),(y * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(12980,a,14909,a)].">
      <j1 rule="hyper" parents="12980 14909"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      T(x,((y * y) \ y) * L(y \ z,y,y)) = T(T(x,z),(y * y) \ 1)
    ]]></literal>
    <justification jstring="[para(471(a,1),14910(a,1,2,2))].">
      <j1 rule="para" parents="471 14910"/>
    </justification>
  </clause>

  <clause id="14913">
    <literal><![CDATA[
      T(x,L(y \ L(y \ z,y,y),y,y)) = T(T(x,z),(y * y) \ 1)
    ]]></literal>
    <justification jstring="[para(471(a,1),14912(a,1,2))].">
      <j1 rule="para" parents="471 14912"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      T(x,y \ L(y \ z,y,y)) = T(T(x,z),(y * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(11978,a,14913,a)].">
      <j1 rule="hyper" parents="11978 14913"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      T(x,y \ L(y \ z,y,y)) = T(T(x,z),y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,12174,a(flip),b,14914,a),flip(a)].">
      <j1 rule="hyper" parents="319 12174 14914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12111,a(flip),b,14915,a),flip(a)].">
      <j1 rule="hyper" parents="64 12111 14915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(410,a,14917,a)].">
      <j1 rule="hyper" parents="410 14917"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      T(T(x,y \ (y \ z)),u) = T(T(x,z),y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(14917(a,1),14918(a,1,1))].">
      <j1 rule="para" parents="14917 14918"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      T(T(x,y * z),y \ (y \ u)) = T(T(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14919(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      T(K(x,y) * z,u) / K(x,T(y,w)) = T(K(x,T(y,w)) * z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6099(a,2),14896(a,1,2))].">
      <j1 rule="para" parents="6099 14896"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6169,a,14921,a),flip(a)].">
      <j1 rule="hyper" parents="6169 14921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9493,a,b,14922,a)].">
      <j1 rule="hyper" parents="64 9493 14922"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(365(a,1),14319(a,1,1))].">
      <j1 rule="para" parents="365 14319"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14490,a(flip),b,14924,a)].">
      <j1 rule="hyper" parents="64 14490 14924"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      T(x,K(y,L(z,z * u,w)) * (w * (z * u))) = T(x,w * (z * (u * K(y,z))))
    ]]></literal>
    <justification jstring="[para(10096(a,1),14711(a,1,2,1))].">
      <j1 rule="para" parents="10096 14711"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u * (x \ K(y,z)),K(x,w)) = T(u,T(x,w) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(4314(a,1),14273(a,2,2))].">
      <j1 rule="para" parents="4314 14273"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z / y) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(13137(a,1),14332(a,1,2,1))].">
      <j1 rule="para" parents="13137 14332"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * ((w / u) * (z * z))) = T(x,w / T((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(11946(a,1),14370(a,1,2,1))].">
      <j1 rule="para" parents="11946 14370"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,5970,a(flip),b,14471,a)].">
      <j1 rule="hyper" parents="64 5970 14471"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * (u / (u / z)),w)) = T(x,(u * K(z,w)) / T(u / z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14886,a,b,14674,a)].">
      <j1 rule="hyper" parents="64 14886 14674"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(u / y,w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13626,a(flip),b,14686,a)].">
      <j1 rule="hyper" parents="64 13626 14686"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      K(x,y \ T(K(z,u \ w) * u,u \ w)) = K(x,y \ (w / T(w / u,z)))
    ]]></literal>
    <justification jstring="[para(6390(a,1),14722(a,1,2,2))].">
      <j1 rule="para" parents="6390 14722"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(5973(a,1),14934(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5973 14934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      T(x,y / (z * (K(z * u,w) * (u / z)))) = T(x,y / (T(u,z) * K(z * u,w)))
    ]]></literal>
    <justification jstring="[para(12906(a,1),14849(a,1,2,2,2))].">
      <j1 rule="para" parents="12906 14849"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(y / T(y / z,w),u))
    ]]></literal>
    <justification jstring="[para(7204(a,1),14931(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7204 14931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(T(z \ y,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,9086,a(flip),b,14937,a),flip(a)].">
      <j1 rule="hyper" parents="319 9086 14937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      R(K(x,y) \ (z * K(u,w)),K(x,y),K(w,u)) = T(z / (K(w,u) * K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(5174(a,1),14272(a,1,1,2))].">
      <j1 rule="para" parents="5174 14272"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(14311,a,14894,a),flip(a)].">
      <j1 rule="hyper" parents="14311 14894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z * y,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(14894(a,1),14311(a,1))].">
      <j1 rule="para" parents="14894 14311"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11238,a(flip),b,14941,a),flip(a)].">
      <j1 rule="hyper" parents="319 11238 14941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      (x \ T(y * x,K(z * u,w) * v5)) * (T(y,x) \ 1) = K(x * y,K(u \ z,w) * v5)
    ]]></literal>
    <justification jstring="[para(14941(a,1),13194(a,1,1,2))].">
      <j1 rule="para" parents="14941 13194"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z \ u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z \ u,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(14943(a,1),11225(a,1,2,1))].">
      <j1 rule="para" parents="14943 11225"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      K(x,K(y,z) \ (x * (u * y))) \ T(x,u * T(y,z)) = R(x,K(y,z) \ (u * y),x)
    ]]></literal>
    <justification jstring="[para(8782(a,2),14397(a,1,1))].">
      <j1 rule="para" parents="8782 14397"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(y * z,w))) = K(x,T(T(z,y) * y,w) * u)
    ]]></literal>
    <justification jstring="[hyper(14508,a,13699,a),flip(a)].">
      <j1 rule="hyper" parents="14508 13699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      K(x,T(T(y,z) * z,u) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(14218,a,14947,a),flip(a)].">
      <j1 rule="hyper" parents="14218 14947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),K(x,y) / x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(11992(a,1),14822(a,1,1,1,1))].">
      <j1 rule="para" parents="11992 14822"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x \ K(x,y)) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(14157(a,1),14949(a,1,1,1))].">
      <j1 rule="para" parents="14157 14949"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      T(x,((K(y * z,y) * u) * T(y,z)) * w) = T(x,T(R(y,z,y) * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14603,a(flip),b,14872,a),flip(a)].">
      <j1 rule="hyper" parents="319 14603 14872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      R(K(x,y) * (z * K(u,w)),K(y,x),K(w,u)) = T(z / (K(w,u) * K(y,x)),K(y,x))
    ]]></literal>
    <justification jstring="[para(4356(a,1),14940(a,1,1))].">
      <j1 rule="para" parents="4356 14940"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      x \ (y * ((y \ x) * K((z / y) \ (y \ x),u))) = K(((y \ x) * y) / z,T(u,x / y))
    ]]></literal>
    <justification jstring="[para(4984(a,1),14294(a,1,2,2))].">
      <j1 rule="para" parents="4984 14294"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      K(T(x * y,x) * (z * K(y * x,u)),w) = K(T(T(x * y,u),T(x,y)) * z,w)
    ]]></literal>
    <justification jstring="[para(9291(a,1),14364(a,1,1,2,2))].">
      <j1 rule="para" parents="9291 14364"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      K(T(T(x * y,z),T(x,y)) * u,w) = K((y * x) * (u * K(y * x,z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14513,a(flip),b,14955,a),flip(a)].">
      <j1 rule="hyper" parents="64 14513 14955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      K(T(T(x * y,z),T(x,y)) * u,w) = K(T(y * x,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14152,a(flip),b,14956,a),flip(a)].">
      <j1 rule="hyper" parents="319 14152 14956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      K(T(T(x * y,x),z) * u,w) = K(T(y * x,z) * u,w)
    ]]></literal>
    <justification jstring="[para(3135(a,1),14957(a,1,1,1))].">
      <j1 rule="para" parents="3135 14957"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      K(T(x * y,z) * u,T(w,x * y)) = K(u * T(T(y * x,y),z),w)
    ]]></literal>
    <justification jstring="[hyper(14500,a,14958,a),flip(a)].">
      <j1 rule="hyper" parents="14500 14958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      K(x * T(T(y * z,y),u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * T(z * y,u),w) = v5
    ]]></literal>
    <justification jstring="[para(14959(a,1),14201(a,1))].">
      <j1 rule="para" parents="14959 14201"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(14960,a,13574,a)].">
      <j1 rule="hyper" parents="14960 13574"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14806,a,b,14961,a)].">
      <j1 rule="hyper" parents="64 14806 14961"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      K(x * (y * z),z * x) = K(x * (z * y),x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14470,a(flip),b,14962,a)].">
      <j1 rule="hyper" parents="64 14470 14962"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(127,a,14962,a(flip),b,6998,a)].">
      <j1 rule="hyper" parents="127 14962 6998"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      K((((x * y) \ z) * y) * (z / (y * ((x * y) \ z))),u) = K(((x * y) \ z) * (y * x),u)
    ]]></literal>
    <justification jstring="[para(103(a,1),14962(a,1,1,2))].">
      <j1 rule="para" parents="103 14962"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      K(x * (((y \ z) * (z \ y)) * (1 / (z \ y))),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(1401(a,1),14963(a,2,1,2))].">
      <j1 rule="para" parents="1401 14963"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),(K(z,u) * (w / z)) \ y) = T(x,y / (K(z,u) * (w / z)))
    ]]></literal>
    <justification jstring="[para(14178(a,1),14384(a,1,1))].">
      <j1 rule="para" parents="14178 14384"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      T(x,K(y \ z,y) * (u / (y * K(w,z)))) = T(x,u / T(y * K(w,z),y \ z))
    ]]></literal>
    <justification jstring="[hyper(14641,a,14395,a)].">
      <j1 rule="hyper" parents="14641 14395"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),z \ w)) = T(x,K(w,z) * (y / (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(13627,a,14968,a),flip(a)].">
      <j1 rule="hyper" parents="13627 14968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14971">
    <literal><![CDATA[
      K(K(x,y),z) * (T(u \ y,K(x,u)) \ K(x,y)) = (u \ y) \ T(K(x,T(y,z)),u \ y)
    ]]></literal>
    <justification jstring="[para(6099(a,2),14462(a,2,2,1))].">
      <j1 rule="para" parents="6099 14462"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(6816(a,1),14480(a,1,2,2))].">
      <j1 rule="para" parents="6816 14480"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      K(x,T(L(y,K(z,K(u,w)),v5),K(z,K(u,w)))) = K(x,y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5440,a(flip),b,14491,a)].">
      <j1 rule="hyper" parents="64 5440 14491"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      K(x,L(y,K(z,K(u,w)),v5)) = K(x,y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(14130,a,14973,a)].">
      <j1 rule="hyper" parents="14130 14973"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12940,a,14974,a),flip(a)].">
      <j1 rule="hyper" parents="12940 14974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14977">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14974(a,1),5681(a,1))].">
      <j1 rule="para" parents="14974 5681"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(14267,a,14975,a)].">
      <j1 rule="hyper" parents="14267 14975"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      K(x,K(K(y,z),u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(14220,a,14975,a)].">
      <j1 rule="hyper" parents="14220 14975"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(13617,a,14975,a)].">
      <j1 rule="hyper" parents="13617 14975"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14261,a,b,14975,a)].">
      <j1 rule="hyper" parents="64 14261 14975"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1187(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="1187 14975"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(1191(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="1191 14975"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4922(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="4922 14975"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(6418(a,1),14975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6418 14975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8172(a,1),14975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8172 14975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8891(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="8891 14975"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10186(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="10186 14975"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7447(a,1),14978(a,1,2))].">
      <j1 rule="para" parents="7447 14978"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9187(a,1),14978(a,1,2))].">
      <j1 rule="para" parents="9187 14978"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(9188(a,1),14978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9188 14978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / K(y,z))) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(9629(a,1),14978(a,1,2))].">
      <j1 rule="para" parents="9629 14978"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      K(x,(T(y,K(z,u)) * w) * v5) = K(x,(y * w) * v5)
    ]]></literal>
    <justification jstring="[para(12832(a,1),14978(a,1,2))].">
      <j1 rule="para" parents="12832 14978"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14172(a,1),14978(a,1,2))].">
      <j1 rule="para" parents="14172 14978"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,11227,a,b,14980,a)].">
      <j1 rule="hyper" parents="319 11227 14980"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(6402(a,1),14980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6402 14980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      K(x,y / ((z * u) * K(w,L(v5,z,u)))) = K(x,y / ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(12849(a,1),14980(a,1,2,2))].">
      <j1 rule="para" parents="12849 14980"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(6402(a,1),14982(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6402 14982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      K(x,y \ ((z * u) * K(w,L(v5,z,u)))) = K(x,y \ ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(12849(a,1),14982(a,1,2,2))].">
      <j1 rule="para" parents="12849 14982"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) = K(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(6386(a,1),14983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6386 14983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(6402(a,1),14983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6402 14983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15003">
    <literal><![CDATA[
      K(x,((y * z) * K(u,L(w,y,z))) / v5) = K(x,((K(u,w) * y) * z) / v5)
    ]]></literal>
    <justification jstring="[para(12849(a,1),14983(a,1,2,1))].">
      <j1 rule="para" parents="12849 14983"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,u) * y) / w) = v5
    ]]></literal>
    <justification jstring="[para(14983(a,1),14825(a,1))].">
      <j1 rule="para" parents="14983 14825"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13578,a(flip),b,14984,a)].">
      <j1 rule="hyper" parents="64 13578 14984"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      K(x,y * L(T(z,K(u,w)),v5,v6)) = K(x,y * L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),14984(a,1,2,2))].">
      <j1 rule="para" parents="25 14984"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      K(x,y * (K(z,u) \ w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(5173(a,1),14984(a,1,2,2))].">
      <j1 rule="para" parents="5173 14984"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(12365(a,1),14984(a,1,2,2))].">
      <j1 rule="para" parents="12365 14984"/>
    </justification>
  </clause>

  <clause id="15009">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14790,a(flip),b,14985,a),flip(a)].">
      <j1 rule="hyper" parents="64 14790 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(1187(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="1187 14977"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(4922(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="4922 14977"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(5360(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="5360 14977"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5925(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="5925 14977"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,K(w,v5)) \ z) = u
    ]]></literal>
    <justification jstring="[para(6418(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="6418 14977"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(6782(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="6782 14977"/>
    </justification>
  </clause>

  <clause id="15018">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(10186(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="10186 14977"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(12327(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="12327 14977"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12776(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="12776 14977"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(14259(a,2),14977(a,1))].">
      <j1 rule="para" parents="14259 14977"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(14242(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="14242 14977"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(7447(a,1),15013(a,1,2))].">
      <j1 rule="para" parents="7447 15013"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(1187(a,1),14988(a,1,2,2))].">
      <j1 rule="para" parents="1187 14988"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(1191(a,1),14988(a,1,2,2))].">
      <j1 rule="para" parents="1191 14988"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7299(a,1),14988(a,1,2,2))].">
      <j1 rule="para" parents="7299 14988"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,K(v5,v6))))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(10186(a,1),14988(a,1,2,2))].">
      <j1 rule="para" parents="10186 14988"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,9306,a(flip),b,14990,a),flip(a)].">
      <j1 rule="hyper" parents="319 9306 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,(u / ((y \ z) * y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13484,a(flip),b,14990,a),flip(a)].">
      <j1 rule="hyper" parents="64 13484 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11114,a(flip),b,14990,a),flip(a)].">
      <j1 rule="hyper" parents="64 11114 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z) * w) = K(x,(T(z,u) \ y) * w)
    ]]></literal>
    <justification jstring="[para(111(a,1),14990(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(9251(a,1),15028(a,1,2,1))].">
      <j1 rule="para" parents="9251 15028"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(14147,a,14995,a)].">
      <j1 rule="hyper" parents="14147 14995"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,14140,a,b,14995,a),flip(a)].">
      <j1 rule="hyper" parents="319 14140 14995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(9269(a,1),14995(a,1,2,2))].">
      <j1 rule="para" parents="9269 14995"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      K(x,(T(y,z) * K(u,y)) / w) = K(x,T(T(y,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13619,a(flip),b,15001,a)].">
      <j1 rule="hyper" parents="64 13619 15001"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11120,a(flip),b,15001,a),flip(a)].">
      <j1 rule="hyper" parents="64 11120 15001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14259,a,b,15033,a),flip(a)].">
      <j1 rule="hyper" parents="319 14259 15033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(15033(a,2),14265(a,1))].">
      <j1 rule="para" parents="15033 14265"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14261,a,b,15034,a)].">
      <j1 rule="hyper" parents="64 14261 15034"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      K(x,K(y,z * u) \ w) = K(x,w * K(u * z,y))
    ]]></literal>
    <justification jstring="[para(9288(a,1),15034(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9288 15034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,K(u,z) * T(y,w))
    ]]></literal>
    <justification jstring="[para(14841(a,1),15038(a,1,2))].">
      <j1 rule="para" parents="14841 15038"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(14421,a,15041,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14421 15041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(15041(a,2),14421(a,1))].">
      <j1 rule="para" parents="15041 14421"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(y,u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(111(a,1),15044(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="111 15044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(15044(a,2),14421(a,1))].">
      <j1 rule="para" parents="15044 14421"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(7109(a,1),15010(a,1,2,2))].">
      <j1 rule="para" parents="7109 15010"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(9253(a,1),15010(a,1,2,2))].">
      <j1 rule="para" parents="9253 15010"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      K(x,y * (K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(5173(a,1),15011(a,1,2,2))].">
      <j1 rule="para" parents="5173 15011"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(5175(a,1),15011(a,1,2,2))].">
      <j1 rule="para" parents="5175 15011"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(7109(a,1),15011(a,1,2,2))].">
      <j1 rule="para" parents="7109 15011"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w / T(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(7069(a,1),15011(a,1,2,2))].">
      <j1 rule="para" parents="7069 15011"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) / u)) = v5
    ]]></literal>
    <justification jstring="[para(12119(a,1),15011(a,1,2,2))].">
      <j1 rule="para" parents="12119 15011"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(12365(a,1),15011(a,1,2,2))].">
      <j1 rule="para" parents="12365 15011"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(13578(a,1),15011(a,1))].">
      <j1 rule="para" parents="13578 15011"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      K(x,y / L(T(z,K(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / L(z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(25(a,2),15016(a,1,2,2))].">
      <j1 rule="para" parents="25 15016"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(5822(a,1),15016(a,1,2,2))].">
      <j1 rule="para" parents="5822 15016"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      K(x,y / (K(z,u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w \ T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(12365(a,1),15016(a,1,2,2))].">
      <j1 rule="para" parents="12365 15016"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12000(a,1),15022(a,1,2))].">
      <j1 rule="para" parents="12000 15022"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11323,a(flip),b,14986,a),flip(a)].">
      <j1 rule="hyper" parents="64 11323 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      K(x,y * (z * K(u,u * w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11294,a(flip),b,14986,a),flip(a)].">
      <j1 rule="hyper" parents="64 11294 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12086,a(flip),b,14987,a),flip(a)].">
      <j1 rule="hyper" parents="64 12086 14987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      K(x,((y * z) * K(u,L(w,y,z))) * v5) = K(x,((K(u,w) * y) * z) * v5)
    ]]></literal>
    <justification jstring="[para(12796(a,1),14992(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12796 14992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,((y \ u) * T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13703,a(flip),b,14994,a)].">
      <j1 rule="hyper" parents="64 13703 14994"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,((K(u,z) * y) * w) * v5)
    ]]></literal>
    <justification jstring="[para(5963(a,1),14994(a,1,2,1,1))].">
      <j1 rule="para" parents="5963 14994"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(11130,a,14997,a),flip(a)].">
      <j1 rule="hyper" parents="11130 14997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u \ w)) = K(x,y / T(z,w / u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13605,a,b,14997,a)].">
      <j1 rule="hyper" parents="319 13605 14997"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(14997(a,1),11130(a,1))].">
      <j1 rule="para" parents="14997 11130"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13519,a(flip),b,15002,a),flip(a)].">
      <j1 rule="hyper" parents="64 13519 15002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13516,a(flip),b,15002,a),flip(a)].">
      <j1 rule="hyper" parents="64 13516 15002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(15002(a,1),11127(a,1))].">
      <j1 rule="para" parents="15002 11127"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z * K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(15005(a,1),12291(a,1))].">
      <j1 rule="para" parents="15005 12291"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ (z * K(w,v5))) * z))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13925,a(flip),b,15024,a),flip(a)].">
      <j1 rule="hyper" parents="64 13925 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) / v5))) = K(x,y * (z \ (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,11248,a(flip),b,15024,a),flip(a)].">
      <j1 rule="hyper" parents="64 11248 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      K(x,y * (z \ (u * T(z,K(w,v5))))) = K(x,y * T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(13423(a,1),15024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13423 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(6402(a,1),15025(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6402 15025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(8211(a,2),15032(a,2,2))].">
      <j1 rule="para" parents="8211 15032"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      K(x,(y * z) * K(u,z * y)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(6963,a,15035,a),flip(a)].">
      <j1 rule="hyper" parents="6963 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      K(x,T((K(y,z) * u) * K(y,z),w)) = K(x,K(y,z) * T(K(z,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,13690,a,b,15043,a),flip(a)].">
      <j1 rule="hyper" parents="319 13690 15043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      K(x,K(y,z \ u) \ ((u / z) \ w)) = K(x,T(u / z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13462,a(flip),b,15046,a),flip(a)].">
      <j1 rule="hyper" parents="64 13462 15046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15084">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u \ w,u))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12782,a(flip),b,15064,a),flip(a)].">
      <j1 rule="hyper" parents="64 12782 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      K(x,y * (T(z * u,x) \ K(L(w,u,z),v5))) = K(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,10185,a(flip),b,15064,a),flip(a)].">
      <j1 rule="hyper" parents="64 10185 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),15064(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(5163(a,1),15064(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5163 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) = K(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(12366(a,1),15064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12366 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(13356(a,1),15064(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13356 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * (w \ K(y * u,v5))) = K(x,T(L(y,z,y) * u,v5) / w)
    ]]></literal>
    <justification jstring="[para(11096(a,1),15088(a,1,2,2,2))].">
      <j1 rule="para" parents="11096 15088"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13328(a,1),15081(a,1,2))].">
      <j1 rule="para" parents="13328 15081"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      K(x,y * (z \ ((((z \ u) * y) \ u) * ((z \ u) * y)))) = K(x,T(y * (z \ u),((z \ u) * y) \ u))
    ]]></literal>
    <justification jstring="[para(12489(a,1),15091(a,1,2,2))].">
      <j1 rule="para" parents="12489 15091"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = v6
    ]]></literal>
    <justification jstring="[para(1187(a,1),15018(a,1,2,2))].">
      <j1 rule="para" parents="1187 15018"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(5925(a,1),15018(a,1,2,2))].">
      <j1 rule="para" parents="5925 15018"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = v6
    ]]></literal>
    <justification jstring="[para(6782(a,1),15018(a,1,2,2))].">
      <j1 rule="para" parents="6782 15018"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      K(x,y * (z \ K(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(12776(a,1),15018(a,1,2,2))].">
      <j1 rule="para" parents="12776 15018"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(14453(a,2),15018(a,1,2,2))].">
      <j1 rule="para" parents="14453 15018"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u \ z)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(15020,a,7764,a)].">
      <j1 rule="hyper" parents="15020 7764"/>
    </justification>
  </clause>

  <clause id="15099">
    <literal><![CDATA[
      K(x,y \ K(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6857(a,1),15020(a,1,2,2))].">
      <j1 rule="para" parents="6857 15020"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      K(x,y \ K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u * z,w)) = v5
    ]]></literal>
    <justification jstring="[para(9288(a,1),15020(a,1,2,2))].">
      <j1 rule="para" parents="9288 15020"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z) * w) = v5
    ]]></literal>
    <justification jstring="[para(111(a,1),15023(a,1,2,1,2))].">
      <j1 rule="para" parents="111 15023"/>
    </justification>
  </clause>

  <clause id="15102">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(9288(a,1),15040(a,1,2,1))].">
      <j1 rule="para" parents="9288 15040"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5310(a,1),15061(a,1))].">
      <j1 rule="para" parents="5310 15061"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(7447(a,1),15094(a,1,2,2))].">
      <j1 rule="para" parents="7447 15094"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      K(x,(L(T(y,K(z,u)),w,v5) \ v6) * ((v6 \ L(T(y,K(z,u)),w,v5)) * v6)) = K(x,((v6 * (L(T(y,K(z,u)),w,v5) / v6)) \ v6) * L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(12417(a,1),15006(a,1,2))].">
      <j1 rule="para" parents="12417 15006"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6952,a,b,15009,a)].">
      <j1 rule="hyper" parents="64 6952 15009"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * v6) * ((v6 * (z * K(u,K(w,v5)))) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(3458(a,2),15027(a,1,2,2))].">
      <j1 rule="para" parents="3458 15027"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * (((z * K(u,K(w,v5))) * v6) * T(z * K(u,K(w,v5)),v7)))
    ]]></literal>
    <justification jstring="[para(5630(a,1),15027(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5630 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      K(x,y * (z * T(u,T(w,v5)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6405(a,1),15027(a,1,2,2,2))].">
      <j1 rule="para" parents="6405 15027"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      K(x,y * (z * (u * (w * K(v5,K(v6,v7)))))) = K(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(10186(a,1),15027(a,1,2,2,2))].">
      <j1 rule="para" parents="10186 15027"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      K(x,y * (z * T(u * K(w,K(v5,v6)),v7))) = K(x,y * (z * T(u,v7)))
    ]]></literal>
    <justification jstring="[para(14453(a,2),15027(a,1,2,2,2))].">
      <j1 rule="para" parents="14453 15027"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(3047(a,1),15037(a,1,2,1,1))].">
      <j1 rule="para" parents="3047 15037"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (K(z,u) * (z / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13853,a,b,15062,a)].">
      <j1 rule="hyper" parents="64 13853 15062"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ (y * K(z,z \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12194,a,b,15062,a)].">
      <j1 rule="hyper" parents="64 12194 15062"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(5308(a,2),15062(a,1,2,2))].">
      <j1 rule="para" parents="5308 15062"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(8163(a,1),15062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8163 15062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (z \ u)))) = K(x,y * (w \ (u / z)))
    ]]></literal>
    <justification jstring="[para(12774(a,1),15062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12774 15062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      K(x,y / T(z,z / u)) = K(x,(y / z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14414,a,15069,a),flip(a)].">
      <j1 rule="hyper" parents="14414 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      K(x,y / T(z,z / u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5163(a,1),15120(a,2,2))].">
      <j1 rule="para" parents="5163 15120"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / T(z * u,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15121(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      K(x,y / T(z * u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14550,a(flip),b,15122,a),flip(a)].">
      <j1 rule="hyper" parents="64 14550 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      T(x,y / T(z * u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(129,a,15123,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15123 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      K(x,y / ((z \ u) * z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),15123(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      T(x,y / (z \ T(((K(u,w) * z) * v5) * T(z,K(u,w)),K(w,u)))) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(13430(a,2),15124(a,1,2,2))].">
      <j1 rule="para" parents="13430 15124"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      T(x,y / T((z * K(u,w)) * v5,K(u,w) * z)) = T(x,y / (v5 * (z * K(u,w))))
    ]]></literal>
    <justification jstring="[para(14155(a,2),15124(a,1,2,2))].">
      <j1 rule="para" parents="14155 15124"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14983,a(flip),b,15107,a),flip(a)].">
      <j1 rule="hyper" parents="64 14983 15107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6859,a(flip),b,15128,a),flip(a)].">
      <j1 rule="hyper" parents="319 6859 15128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14223,a,15130,a)].">
      <j1 rule="hyper" parents="14223 15130"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = x \ T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a(flip),b,15130,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,15130,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15130 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14011,a,b,15130,a)].">
      <j1 rule="hyper" parents="64 14011 15130"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      K(x,T(T(((y \ z) * y) \ u,w),u)) = K(x,T((K(y,y \ z) * u) / z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9238,a(flip),b,15130,a),flip(a)].">
      <j1 rule="hyper" parents="64 9238 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4041(a,1),15130(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4041 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4348(a,1),15130(a,1,2,2))].">
      <j1 rule="para" parents="4348 15130"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4522(a,1),15130(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4522 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      K(x,T(y,z * (u / w))) = K(x,T(y,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(14389(a,1),15130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14389 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7241,a,15131,a)].">
      <j1 rule="hyper" parents="7241 15131"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14293,a,b,15131,a)].">
      <j1 rule="hyper" parents="64 14293 15131"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,15131,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="130 15131 6838"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(5241(a,1),15131(a,1,2,2))].">
      <j1 rule="para" parents="5241 15131"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(5487(a,1),15131(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5487 15131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u / (x * K(y,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(15131(a,1),6990(a,1))].">
      <j1 rule="para" parents="15131 6990"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y * K(z,u)) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(15131(a,1),9296(a,1))].">
      <j1 rule="para" parents="15131 9296"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14015,a,b,15134,a)].">
      <j1 rule="hyper" parents="64 14015 15134"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4041(a,1),15134(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4041 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(9188(a,1),15134(a,1,2,2))].">
      <j1 rule="para" parents="9188 15134"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(12832(a,1),15134(a,1,2,2))].">
      <j1 rule="para" parents="12832 15134"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15143(a,1),12205(a,1,1,1))].">
      <j1 rule="para" parents="15143 12205"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / K(z,T(y,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(15143(a,1),13417(a,1,2,2))].">
      <j1 rule="para" parents="15143 13417"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,15145,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="130 15145 6838"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w / (K(y,z) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(15153(a,1),7263(a,1))].">
      <j1 rule="para" parents="15153 7263"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(15133(a,2),4106(a,1))].">
      <j1 rule="para" parents="15133 4106"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      K(x,T(T(y,z),u \ y)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(7162,a,15140,a),flip(a)].">
      <j1 rule="hyper" parents="7162 15140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(3984(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="3984 15163"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * w)) = v5
    ]]></literal>
    <justification jstring="[para(4081(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="4081 15163"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(4356(a,2),15163(a,1,2,2))].">
      <j1 rule="para" parents="4356 15163"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      K(x,T(y,z * T(z \ u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(4038(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="4038 15163"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = v5
    ]]></literal>
    <justification jstring="[para(4646(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="4646 15163"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(4644(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="4644 15163"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(5933(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="5933 15163"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(6099(a,1),15163(a,1))].">
      <j1 rule="para" parents="6099 15163"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,(u * z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(9188(a,1),15163(a,1,2,2))].">
      <j1 rule="para" parents="9188 15163"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z / (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(5241(a,1),15171(a,1,2,2))].">
      <j1 rule="para" parents="5241 15171"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(6099(a,1),15171(a,1))].">
      <j1 rule="para" parents="6099 15171"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(12774(a,1),15171(a,1,2,2))].">
      <j1 rule="para" parents="12774 15171"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(14422,a,15139,a)].">
      <j1 rule="hyper" parents="14422 15139"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * (v5 \ v6))) = K(x,L(T(u,w * (v6 / v5)),y,z))
    ]]></literal>
    <justification jstring="[hyper(10156,a,15142,a),flip(a)].">
      <j1 rule="hyper" parents="10156 15142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,6713,a,b,15147,a)].">
      <j1 rule="hyper" parents="64 6713 15147"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15169,a,14901,a)].">
      <j1 rule="hyper" parents="15169 14901"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,y)) = z * (K(u,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,8357,a(flip),b,15146,a),flip(a)].">
      <j1 rule="hyper" parents="319 8357 15146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(244,a,15146,a(flip),b,8552,a),flip(a)].">
      <j1 rule="hyper" parents="244 15146 8552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(w,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(244,a,15146,a(flip),b,7653,a(flip))].">
      <j1 rule="hyper" parents="244 15146 7653"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3889(a,1),15146(a,1,1))].">
      <j1 rule="para" parents="3889 15146"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6824,a,15183,a)].">
      <j1 rule="hyper" parents="6824 15183"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      T(x,K(y,z)) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * K(u,w),K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(15183(a,1),6824(a,1))].">
      <j1 rule="para" parents="15183 6824"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,4880,a(flip),b,15185,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 4880 15185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      T(K(x,y) \ z,K(u,w)) = K(x,y) \ T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,3813,a(flip),b,15185,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3813 15185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15155,a,b,15156,a)].">
      <j1 rule="hyper" parents="64 15155 15156"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12245,a,15161,a)].">
      <j1 rule="hyper" parents="12245 15161"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12295,a,b,15196,a)].">
      <j1 rule="hyper" parents="64 12295 15196"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9342,a,b,15180,a)].">
      <j1 rule="hyper" parents="64 9342 15180"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(15181(a,1),6131(a,1,2))].">
      <j1 rule="para" parents="15181 6131"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,6755,a,b,15182,a)].">
      <j1 rule="hyper" parents="36 6755 15182"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(14236,a,15200,a)].">
      <j1 rule="hyper" parents="14236 15200"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(7182,a,15200,a)].">
      <j1 rule="hyper" parents="7182 15200"/>
    </justification>
  </clause>

  <clause id="15204">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,15200,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15200 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14726,a,b,15200,a)].">
      <j1 rule="hyper" parents="64 14726 15200"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(4918(a,1),15200(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4918 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(5241(a,1),15200(a,1,2,2))].">
      <j1 rule="para" parents="5241 15200"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(5300(a,2),15200(a,1,2,2))].">
      <j1 rule="para" parents="5300 15200"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(5307(a,2),15200(a,1,2,2))].">
      <j1 rule="para" parents="5307 15200"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(5487(a,1),15200(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5487 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(12774(a,1),15200(a,1,2,2))].">
      <j1 rule="para" parents="12774 15200"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a(flip),b,15202,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 15202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,15202,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15202 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (K(u,w) * z),y) = K((K(u,w) * z) / x,y)
    ]]></literal>
    <justification jstring="[para(15202(a,1),7238(a,1,1))].">
      <j1 rule="para" parents="15202 7238"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(9188(a,1),15202(a,1,2,2))].">
      <j1 rule="para" parents="9188 15202"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(12225(a,1),15202(a,1,2,2))].">
      <j1 rule="para" parents="12225 15202"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(13076(a,1),15202(a,1,2,2))].">
      <j1 rule="para" parents="13076 15202"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(K(u,w) * z) * x) = K(y,x * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(15202(a,1),14400(a,1,1))].">
      <j1 rule="para" parents="15202 14400"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6758,a,b,15203,a),flip(a)].">
      <j1 rule="hyper" parents="319 6758 15203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14727,a,b,15204,a)].">
      <j1 rule="hyper" parents="64 14727 15204"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(4636(a,1),15204(a,1,2,2))].">
      <j1 rule="para" parents="4636 15204"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      T(x,K(y,T(z,u) \ w)) = T(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(6185(a,1),15204(a,1,2,2))].">
      <j1 rule="para" parents="6185 15204"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10115(a,1),15204(a,1,2,2))].">
      <j1 rule="para" parents="10115 15204"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6748,a(flip),b,15205,a),flip(a)].">
      <j1 rule="hyper" parents="319 6748 15205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(w,v5))) = K(w,K(v5,z)) \ T(u,K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(15205(a,1),14468(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15205 14468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14726,a,b,15213,a)].">
      <j1 rule="hyper" parents="64 14726 15213"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      K(x,K(y,z)) * K((K(u,w) * x) \ z,y) = K(z / (K(u,w) * x),y)
    ]]></literal>
    <justification jstring="[para(15213(a,1),7239(a,1,1))].">
      <j1 rule="para" parents="15213 7239"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,15214,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 15214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,(u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(4510(a,1),15214(a,1,2,2))].">
      <j1 rule="para" parents="4510 15214"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(15214(a,2),6824(a,1))].">
      <j1 rule="para" parents="15214 6824"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,K(w,v5) * u)) = T(y,K(K(w,v5) * u,z) * x)
    ]]></literal>
    <justification jstring="[para(15214(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="15214 13423"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(7120,a,15220,a),flip(a)].">
      <j1 rule="hyper" parents="7120 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14238,a,b,15220,a)].">
      <j1 rule="hyper" parents="64 14238 15220"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10194,a(flip),b,15220,a)].">
      <j1 rule="hyper" parents="64 10194 15220"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(K(w,v5) / y,z)) = u
    ]]></literal>
    <justification jstring="[para(15220(a,1),6789(a,1))].">
      <j1 rule="para" parents="15220 6789"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(15220(a,1),7120(a,1))].">
      <j1 rule="para" parents="15220 7120"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,15214,a,b,15222,a),flip(a)].">
      <j1 rule="hyper" parents="319 15214 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      K(x,K(K(y,z) \ u,w)) = K(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(6789,a,15226,a)].">
      <j1 rule="hyper" parents="6789 15226"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      (x \ K(y,z)) * K(x,K(u,w)) = T(x \ K(y,z),K(u,w))
    ]]></literal>
    <justification jstring="[para(15230(a,1),6754(a,1,2))].">
      <j1 rule="para" parents="15230 6754"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      T(x,K(y \ T(z,u),w)) = T(x,K(w,y \ z))
    ]]></literal>
    <justification jstring="[para(4522(a,1),15233(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4522 15233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(14352,a,15238,a)].">
      <j1 rule="hyper" parents="14352 15238"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(1191(a,1),15238(a,1,2,1))].">
      <j1 rule="para" parents="1191 15238"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(10145,a,15247,a)].">
      <j1 rule="hyper" parents="10145 15247"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) * K(x,K(u,w)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,15247,a(flip),b,7126,a)].">
      <j1 rule="hyper" parents="131 15247 7126"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(T(z,w) \ u) * y) = T(x,y * (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(15223(a,1),14731(a,1,1))].">
      <j1 rule="para" parents="15223 14731"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(T(z,w) \ u) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(15224(a,1),9319(a,1,1))].">
      <j1 rule="para" parents="15224 9319"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),((w * (z / w)) \ u) * y) = T(x,y * ((w * (z / w)) \ u))
    ]]></literal>
    <justification jstring="[para(15224(a,1),13533(a,1,1))].">
      <j1 rule="para" parents="15224 13533"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(u / T(z,w)) \ y) = T(x,y / (u / T(z,w)))
    ]]></literal>
    <justification jstring="[para(15224(a,1),14310(a,1,1))].">
      <j1 rule="para" parents="15224 14310"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      (x \ T(y,z)) \ T(u,K(x \ T(y,z),w)) = T((x \ T(y,z)) \ u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[hyper(6408,a,15246,a)].">
      <j1 rule="hyper" parents="6408 15246"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14757,a(flip),b,15248,a),flip(a)].">
      <j1 rule="hyper" parents="64 14757 15248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(15241,a,15238,a(flip))].">
      <j1 rule="hyper" parents="15241 15238"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      L(K(x,K(y,z / (u / w))),v5,v6) = K(y,K(z / (w \ u),L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(15207(a,2),10131(a,1,1))].">
      <j1 rule="para" parents="15207 10131"/>
    </justification>
  </clause>

  <clause id="15264">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1191(a,1),15210(a,1,2,2,1))].">
      <j1 rule="para" parents="1191 15210"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(1464(a,1),15210(a,1,2,2,1))].">
      <j1 rule="para" parents="1464 15210"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(6421(a,1),15210(a,1,2,2,1))].">
      <j1 rule="para" parents="6421 15210"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,v5 * z)) = v6
    ]]></literal>
    <justification jstring="[para(15210(a,2),14236(a,1))].">
      <j1 rule="para" parents="15210 14236"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(7177,a,15217,a),flip(a)].">
      <j1 rule="hyper" parents="7177 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14715,a(flip),b,15217,a),flip(a)].">
      <j1 rule="hyper" parents="319 14715 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = K(x,K(y,a(w,z,z \ u)))
    ]]></literal>
    <justification jstring="[para(902(a,1),15217(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="902 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w / (u * z))) = v5
    ]]></literal>
    <justification jstring="[para(15217(a,1),7177(a,1))].">
      <j1 rule="para" parents="15217 7177"/>
    </justification>
  </clause>

  <clause id="15272">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(7177,a,15218,a)].">
      <j1 rule="hyper" parents="7177 15218"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(4646(a,1),15218(a,1,2,2,1))].">
      <j1 rule="para" parents="4646 15218"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(1187(a,1),15225(a,1,2,2,2))].">
      <j1 rule="para" parents="1187 15225"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,x \ K(y,z))) = (x \ K(y,z)) \ T(u,K(w,K(v5,v6) * x))
    ]]></literal>
    <justification jstring="[hyper(127,a,15243,a(flip),b,7130,a),flip(a)].">
      <j1 rule="hyper" parents="127 15243 7130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(w,K(v5,v6) * y)) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w)) = v7
    ]]></literal>
    <justification jstring="[para(15243(a,1),6815(a,1))].">
      <j1 rule="para" parents="15243 6815"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,K(u,w) * v5)),K(z,v5 \ K(v6,v7))) = T(y,K(v5 \ K(v6,v7),z) * x)
    ]]></literal>
    <justification jstring="[para(15243(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="15243 13423"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(w,L(K(v5,v6) / y,y,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10169,a(flip),b,15261,a),flip(a)].">
      <j1 rule="hyper" parents="64 10169 15261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(15268(a,1),7177(a,1))].">
      <j1 rule="para" parents="15268 7177"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(15268(a,2),7177(a,1))].">
      <j1 rule="para" parents="15268 7177"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(5457(a,1),15272(a,1,2,2,2))].">
      <j1 rule="para" parents="5457 15272"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(6862(a,1),15272(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6862 15272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      K(x,K(y,z / u)) * (w * K(x,y)) = w * K(x,T(y,(u * K(v5,v6)) / z))
    ]]></literal>
    <justification jstring="[para(15282(a,1),14172(a,1,1))].">
      <j1 rule="para" parents="15282 14172"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      T(x,T(T(y * T(z,u),w),(z * y) * v5)) = T(x,T(T(y * T(z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,6447,a(flip),b,15195,a),flip(a)].">
      <j1 rule="hyper" parents="64 6447 15195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(6244,a,15198,a)].">
      <j1 rule="hyper" parents="6244 15198"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,4301,a(flip),b,15199,a),flip(a)].">
      <j1 rule="hyper" parents="319 4301 15199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,4036,a,b,15199,a)].">
      <j1 rule="hyper" parents="35 4036 15199"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((T(T(x,z),z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(15286(a,1),9968(a,2,2,1))].">
      <j1 rule="para" parents="15286 9968"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9204,a,b,15287,a)].">
      <j1 rule="hyper" parents="64 9204 15287"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) * K(u,w)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15287(a,1),13719(a,1,2,2))].">
      <j1 rule="para" parents="15287 13719"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(8362(a,1),15291(a,1,2,2))].">
      <j1 rule="para" parents="8362 15291"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(15286(a,1),15291(a,1,2))].">
      <j1 rule="para" parents="15286 15291"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      K(x,T(T(R(y,z,u),w),w) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),15293(a,2,2))].">
      <j1 rule="para" parents="105 15293"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(251(a,1),15293(a,1,2,1,1))].">
      <j1 rule="para" parents="251 15293"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14986,a,b,15292,a)].">
      <j1 rule="hyper" parents="319 14986 15292"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(12044(a,1),15292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12044 15292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(12363(a,1),15292(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12363 15292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(u,w))) = K(x,y * (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(13356(a,1),15292(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13356 15292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      K(x,y * (K(z * u,z) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,15063,a(flip),b,15296,a),flip(a)].">
      <j1 rule="hyper" parents="319 15063 15296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(u,z)))) = K(x,y * (w / u))
    ]]></literal>
    <justification jstring="[para(4918(a,1),15296(a,2,2,2))].">
      <j1 rule="para" parents="4918 15296"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),15296(a,2,2,2))].">
      <j1 rule="para" parents="4922 15296"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[para(5163(a,1),15296(a,2,2,2))].">
      <j1 rule="para" parents="5163 15296"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15296(a,2),14218(a,1))].">
      <j1 rule="para" parents="15296 14218"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(11619(a,1),15297(a,1,2,2,2))].">
      <j1 rule="para" parents="11619 15297"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(4437(a,2),15304(a,1,2))].">
      <j1 rule="para" parents="4437 15304"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      K(x,(y / ((z \ u) * z)) * (K(w,y / T(u,z)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(15125(a,1),15304(a,1,2,2,1))].">
      <j1 rule="para" parents="15125 15304"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13644(a,2),15306(a,1))].">
      <j1 rule="para" parents="13644 15306"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(w,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(15240(a,2),10145(a,1))].">
      <j1 rule="para" parents="15240 10145"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,w)) = T(x,K(u,w)) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14242,a(flip),b,15245,a),flip(a)].">
      <j1 rule="hyper" parents="64 14242 15245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = (x * K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,12000,a(flip),b,15310,a),flip(a)].">
      <j1 rule="hyper" parents="319 12000 15310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,12020,a(flip),b,15311,a),flip(a)].">
      <j1 rule="hyper" parents="64 12020 15311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,12516,a,b,15312,a)].">
      <j1 rule="hyper" parents="64 12516 15312"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,12089,a,b,15312,a)].">
      <j1 rule="hyper" parents="64 12089 15312"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ 1) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(11948(a,1),15312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11948 15312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(15312(a,1),12091(a,1,2,2,2))].">
      <j1 rule="para" parents="15312 12091"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      T(x,y * T(K(z,u * w) * (w \ 1),u)) = T(x,y / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[para(15312(a,1),14781(a,1,2,2,1))].">
      <j1 rule="para" parents="15312 14781"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(T(K(z,y),(x \ 1) \ 1),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(15315(a,1),6184(a,1,1))].">
      <j1 rule="para" parents="15315 6184"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(249(a,1),15264(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="249 15264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15268,a(flip),b,15273,a)].">
      <j1 rule="hyper" parents="64 15268 15273"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(12773(a,2),15298(a,1,2,2))].">
      <j1 rule="para" parents="12773 15298"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,13190,a(flip),b,15313,a)].">
      <j1 rule="hyper" parents="64 13190 15313"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),15320(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 15320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(232(a,1),15321(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="232 15321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * w))) = K(x,y * (z \ T(w * u,u)))
    ]]></literal>
    <justification jstring="[para(3298(a,1),15321(a,1,2,2,2))].">
      <j1 rule="para" parents="3298 15321"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,K(y,z \ u)) * K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,14359,a,b,15324,a),flip(a)].">
      <j1 rule="hyper" parents="319 14359 15324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(15012,a,13583,a),flip(a)].">
      <j1 rule="hyper" parents="15012 13583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(6402(a,1),15012(a,1,2,2,2))].">
      <j1 rule="para" parents="6402 15012"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(15049,a,13819,a)].">
      <j1 rule="hyper" parents="15049 13819"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / T(v5,T(z,u) \ y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 \ (y / T(z,T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(14612(a,1),15070(a,1,2,2))].">
      <j1 rule="para" parents="14612 15070"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (v5 * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(5175(a,1),15093(a,1,2,2,2))].">
      <j1 rule="para" parents="5175 15093"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      K(x,y * (z \ T(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(6392(a,1),15093(a,1,2,2,2))].">
      <j1 rule="para" parents="6392 15093"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(12020(a,1),15093(a,1,2,2,2))].">
      <j1 rule="para" parents="12020 15093"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / T(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(6392(a,1),15095(a,1,2,2,2))].">
      <j1 rule="para" parents="6392 15095"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(12020(a,1),15095(a,1,2,2,2))].">
      <j1 rule="para" parents="12020 15095"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      K(x,y \ K(z * (u \ w),u)) = K(x,y \ K(w * z,u))
    ]]></literal>
    <justification jstring="[hyper(15100,a,12435,a)].">
      <j1 rule="hyper" parents="15100 12435"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      K(x,y \ K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(w * u,z)) = v5
    ]]></literal>
    <justification jstring="[para(13784(a,1),15100(a,1))].">
      <j1 rule="para" parents="13784 15100"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,z)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(15103,a,13510,a)].">
      <j1 rule="hyper" parents="15103 13510"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(13785,a,15339,a)].">
      <j1 rule="hyper" parents="13785 15339"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u \ w)) = K(x,T(z,w / u) / y)
    ]]></literal>
    <justification jstring="[hyper(15099,a,15340,a)].">
      <j1 rule="hyper" parents="15099 15340"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,u)) = K(x,T(z * K(u,w),u) / y)
    ]]></literal>
    <justification jstring="[para(6002(a,1),15340(a,1,2,2))].">
      <j1 rule="para" parents="6002 15340"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,T(z \ u,w))) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[para(14283(a,1),15340(a,1,2,2))].">
      <j1 rule="para" parents="14283 15340"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,(u / y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13906,a(flip),b,15341,a),flip(a)].">
      <j1 rule="hyper" parents="64 13906 15341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,15340,a(flip),b,15344,a),flip(a)].">
      <j1 rule="hyper" parents="319 15340 15344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13021,a,b,15345,a)].">
      <j1 rule="hyper" parents="64 13021 15345"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15002,a(flip),b,15345,a)].">
      <j1 rule="hyper" parents="64 15002 15345"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(12751(a,1),15347(a,1,2,1))].">
      <j1 rule="para" parents="12751 15347"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(11185(a,2),15348(a,1,2,1))].">
      <j1 rule="para" parents="11185 15348"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(15074,a,15349,a),flip(a)].">
      <j1 rule="hyper" parents="15074 15349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(15173,a,15137,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15173 15137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      K(x,K(y / (z \ u),L(w,u,z))) = K(x,K(w,(y * z) / (z * (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,13182,a(flip),b,15260,a)].">
      <j1 rule="hyper" parents="64 13182 15260"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      K(x,K(T(R(y,K(z,u),w),K(z,u)),L(v5,K(z,u) * w,v6))) = K(x,K(v5,(((K(z,u) * y) * w) * v6) / (v6 * (K(z,u) * w))))
    ]]></literal>
    <justification jstring="[para(6817(a,1),15260(a,1,2,1))].">
      <j1 rule="para" parents="6817 15260"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(4912(a,1),15267(a,1,2,2))].">
      <j1 rule="para" parents="4912 15267"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(x,K(y,(z / T(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,v5 * (z / u))) = v6
    ]]></literal>
    <justification jstring="[para(5163(a,1),15267(a,1,2,2,1))].">
      <j1 rule="para" parents="5163 15267"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x,K(y,z * (u * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = v6
    ]]></literal>
    <justification jstring="[para(14079(a,1),15267(a,1))].">
      <j1 rule="para" parents="14079 15267"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(791(a,2),15294(a,1,2,1))].">
      <j1 rule="para" parents="791 15294"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      K(x,K(y,z * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(88(a,1),15357(a,1,2,2,2))].">
      <j1 rule="para" parents="88 15357"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(105(a,1),15358(a,1,2))].">
      <j1 rule="para" parents="105 15358"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(231(a,1),15360(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="231 15360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(4540(a,1),15361(a,1,2,1))].">
      <j1 rule="para" parents="4540 15361"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13702,a(flip),b,15362,a)].">
      <j1 rule="hyper" parents="64 13702 15362"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      K(x,K(y,z * u) \ ((u / (z \ 1)) \ w)) = K(x,T(u / (z \ 1),y) \ w)
    ]]></literal>
    <justification jstring="[para(11956(a,1),15083(a,1,2,1))].">
      <j1 rule="para" parents="11956 15083"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15303,a(flip),b,15117,a),flip(a)].">
      <j1 rule="hyper" parents="319 15303 15117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      T(x,y * (z / (u / (u / w)))) = T(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(129,a,15366,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15366 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      T(x,T(y,z / T(u,w)) * (z / T(u,w))) = T(x,(z / (w / (w / u))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13546,a(flip),b,15367,a),flip(a)].">
      <j1 rule="hyper" parents="64 13546 15367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15369">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15302,a(flip),b,15118,a),flip(a)].">
      <j1 rule="hyper" parents="64 15302 15118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(u,w))) = K(x,y * (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(15051,a,15119,a)].">
      <j1 rule="hyper" parents="15051 15119"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12357,a(flip),b,15184,a),flip(a)].">
      <j1 rule="hyper" parents="64 12357 15184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15197,a(flip),b,15371,a),flip(a)].">
      <j1 rule="hyper" parents="64 15197 15371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      K(x,L(K(y,z),K(u,w) / w,v5)) * K(K(y,z),x) = a(v5,K(u,w) / (K(z,y) * w),K(K(y,z),x))
    ]]></literal>
    <justification jstring="[para(15372(a,2),8620(a,2,2))].">
      <j1 rule="para" parents="15372 8620"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,T(K(y,z) * u,w)) * K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,13470,a,b,15254,a)].">
      <j1 rule="hyper" parents="319 13470 15254"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      K(x,K(y,((z \ (z * ((1 / z) * u))) * w) * v5)) = K(x,K(y,(L(u / z,z,1 / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(830(a,1),15266(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="830 15266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7035,a,b,15281,a),flip(a)].">
      <j1 rule="hyper" parents="319 7035 15281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(9249(a,1),15290(a,1,2))].">
      <j1 rule="para" parents="9249 15290"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(15379(a,1),9382(a,1,1))].">
      <j1 rule="para" parents="15379 9382"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(14236,a,15319,a)].">
      <j1 rule="hyper" parents="14236 15319"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,z \ u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,11995,a,b,15327,a)].">
      <j1 rule="hyper" parents="64 11995 15327"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14828,a(flip),b,15346,a),flip(a)].">
      <j1 rule="hyper" parents="319 14828 15346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(15279,a,15377,a)].">
      <j1 rule="hyper" parents="15279 15377"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(78(a,1),15381(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="78 15381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,((v6 / (v6 / z)) / u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(15381(a,1),14236(a,1))].">
      <j1 rule="para" parents="15381 14236"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(15384(a,2),15279(a,1))].">
      <j1 rule="para" parents="15384 15279"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w / T(T(u,z),z))) = v5
    ]]></literal>
    <justification jstring="[para(4162(a,1),15053(a,1,2,2,1))].">
      <j1 rule="para" parents="4162 15053"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(4314(a,1),15055(a,1,2,2))].">
      <j1 rule="para" parents="4314 15055"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(15296(a,1),15055(a,1))].">
      <j1 rule="para" parents="15296 15055"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      K(x,y * (z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u \ T(z,u))) = w
    ]]></literal>
    <justification jstring="[para(13787(a,1),15390(a,1))].">
      <j1 rule="para" parents="13787 15390"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(15104,a,13584,a)].">
      <j1 rule="hyper" parents="15104 13584"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * (w / u))) = K(x,y * (T(u \ w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13585,a(flip),b,15393,a)].">
      <j1 rule="hyper" parents="64 13585 15393"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(v5,z) * T(z,w / u)))
    ]]></literal>
    <justification jstring="[para(6836(a,1),15393(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6836 15393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(14253,a,15239,a)].">
      <j1 rule="hyper" parents="14253 15239"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11257,a(flip),b,15325,a),flip(a)].">
      <j1 rule="hyper" parents="64 11257 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),15398(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(15333,a,13792,a)].">
      <j1 rule="hyper" parents="15333 13792"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      K(x,y * (z * K(z * u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u \ T(u * z,w))) = v5
    ]]></literal>
    <justification jstring="[para(12197(a,1),15333(a,1,2,2))].">
      <j1 rule="para" parents="12197 15333"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(15335,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      K(x * (y / T(z,T(u,w))),v5) = K(v5,x * (y / T(z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(15403(a,1),4213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15403 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      K(x * (y / T(z,T(u,w))),v5) = K(x * (y / T(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,4213,a(flip),b,15404,a),flip(a)].">
      <j1 rule="hyper" parents="319 4213 15404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12806,a(flip),b,15396,a),flip(a)].">
      <j1 rule="hyper" parents="64 12806 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(6789,a,15406,a)].">
      <j1 rule="hyper" parents="6789 15406"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14254,a(flip),b,15407,a),flip(a)].">
      <j1 rule="hyper" parents="64 14254 15407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(81(a,1),15408(a,1,2,2,1,2))].">
      <j1 rule="para" parents="81 15408"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10439,a(flip),b,15409,a),flip(a)].">
      <j1 rule="hyper" parents="64 10439 15409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15209,a(flip),b,15410,a),flip(a)].">
      <j1 rule="hyper" parents="64 15209 15410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(6744,a,15411,a)].">
      <j1 rule="hyper" parents="6744 15411"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6742,a,b,15412,a),flip(a)].">
      <j1 rule="hyper" parents="319 6742 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),u)) = K(x,y * T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(4913(a,2),15078(a,1,2,2))].">
      <j1 rule="para" parents="4913 15078"/>
    </justification>
  </clause>

  <clause id="15416">
    <literal><![CDATA[
      K(x,y * (z * (u * (K(w,K(v5,v6)) * v7)))) = K(x,y * (z * (u * v7)))
    ]]></literal>
    <justification jstring="[para(5925(a,1),15111(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5925 15111"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11135,a(flip),b,15114,a),flip(a)].">
      <j1 rule="hyper" parents="64 11135 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15417(a,2,2,1))].">
      <j1 rule="para" parents="12 15417"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      K(x,L(T(y,z * (u / w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * (w \ u)),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(15178(a,1),10156(a,1))].">
      <j1 rule="para" parents="15178 10156"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) * w)),(T(z,v5) \ w) * y) = T(x,y * (T(z,v5) \ w))
    ]]></literal>
    <justification jstring="[para(15223(a,2),15255(a,1,1))].">
      <j1 rule="para" parents="15223 15255"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      K(x,y * (z \ (u \ T(w,u)))) = K(x,y * (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15370,a(flip),b,15299,a),flip(a)].">
      <j1 rule="hyper" parents="64 15370 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      K(x,y * (z \ ((u / (T(w,v5) \ 1)) \ T(v5,u / (T(w,v5) \ 1))))) = K(x,y * (z \ (T(v5,w) / (u / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(12390(a,2),15423(a,2,2,2,2))].">
      <j1 rule="para" parents="12390 15423"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,15254,a,b,15374,a(flip))].">
      <j1 rule="hyper" parents="36 15254 15374"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11248,a(flip),b,15401,a)].">
      <j1 rule="hyper" parents="64 11248 15401"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13570,a(flip),b,15426,a)].">
      <j1 rule="hyper" parents="64 13570 15426"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15415(a,1),15097(a,1))].">
      <j1 rule="para" parents="15415 15097"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,w)) = K(x,y * (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(15428,a,13564,a)].">
      <j1 rule="hyper" parents="15428 13564"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      K(x,y * T(z,u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u * w)) = v6
    ]]></literal>
    <justification jstring="[para(4646(a,1),15428(a,1,2,2,2))].">
      <j1 rule="para" parents="4646 15428"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      K(x,y * T(z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = v6
    ]]></literal>
    <justification jstring="[para(5933(a,1),15428(a,1,2,2,2))].">
      <j1 rule="para" parents="5933 15428"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w / v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (v5 \ w))) = v6
    ]]></literal>
    <justification jstring="[para(12774(a,1),15431(a,1,2,2,2))].">
      <j1 rule="para" parents="12774 15431"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      K(x,y / (z * (T(u,z) * K(w,v5)))) = K(x,y / ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(10114(a,1),14998(a,1,2,2))].">
      <j1 rule="para" parents="10114 14998"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) = K(x,y \ ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(10114(a,1),15000(a,1,2,2))].">
      <j1 rule="para" parents="10114 15000"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(10114(a,1),15003(a,1,2,1))].">
      <j1 rule="para" parents="10114 15003"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) * v5) = K(x,((K(u,w) * z) * y) * v5)
    ]]></literal>
    <justification jstring="[para(10114(a,1),15065(a,1,2,1))].">
      <j1 rule="para" parents="10114 15065"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(11628(a,1),15080(a,1,2,1))].">
      <j1 rule="para" parents="11628 15080"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      K(x,T(y,z * u) * z) = K(x,y * (u \ T(u * z,y)))
    ]]></literal>
    <justification jstring="[hyper(15402,a,14385,a),flip(a)].">
      <j1 rule="hyper" parents="15402 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,(x \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,11630,a(flip),b,15438,a),flip(a)].">
      <j1 rule="hyper" parents="319 11630 15438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),15439(a,2,2,1))].">
      <j1 rule="para" parents="9 15439"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15293,a(flip),b,15440,a),flip(a)].">
      <j1 rule="hyper" parents="64 15293 15440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(15430,a,15441,a)].">
      <j1 rule="hyper" parents="15430 15441"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13096,a,15437,a)].">
      <j1 rule="hyper" parents="13096 15437"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(8211(a,1),15443(a,2,2))].">
      <j1 rule="para" parents="8211 15443"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      K(x,((K(y,z) * u) / (y \ z)) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13518,a(flip),b,15072,a)].">
      <j1 rule="hyper" parents="64 13518 15072"/>
    </justification>
  </clause>

  <clause id="15446">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(10809(a,1),15445(a,1,2,1))].">
      <j1 rule="para" parents="10809 15445"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u)) = K(x,y * ((K(w,v5) * u) / z))
    ]]></literal>
    <justification jstring="[para(22(a,2),15076(a,1,2,2))].">
      <j1 rule="para" parents="22 15076"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * K(y,z)),w)) = K(x,K(y,z) * T(K(z,y) \ u,w))
    ]]></literal>
    <justification jstring="[para(5640(a,1),15082(a,1,2,1))].">
      <j1 rule="para" parents="5640 15082"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) * u) / z,w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6913,a(flip),b,15136,a),flip(a)].">
      <j1 rule="hyper" parents="64 6913 15136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(13349(a,1),15451(a,1,2,1))].">
      <j1 rule="para" parents="13349 15451"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(K(z,u) * (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15425,a(flip),b,15452,a),flip(a)].">
      <j1 rule="hyper" parents="64 15425 15452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15454">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14758,a(flip),b,15453,a),flip(a)].">
      <j1 rule="hyper" parents="319 14758 15453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14028,a(flip),b,15454,a),flip(a)].">
      <j1 rule="hyper" parents="64 14028 15454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(w,L(y,y,v7)))
    ]]></literal>
    <justification jstring="[hyper(15309,a,15278,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15309 15278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,6793,a(flip),b,15456,a),flip(a)].">
      <j1 rule="hyper" parents="319 6793 15456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15242,a,15457,a)].">
      <j1 rule="hyper" parents="15242 15457"/>
    </justification>
  </clause>

  <clause id="15460">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(14456,a,15283,a),flip(a)].">
      <j1 rule="hyper" parents="14456 15283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(5163(a,1),15460(a,1,2,2,1))].">
      <j1 rule="para" parents="5163 15460"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(7183,a,15461,a)].">
      <j1 rule="hyper" parents="7183 15461"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w / (v5 / T(v6,v7)))) = K(x,T(y,w / (v5 / v6)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7541,a(flip),b,15462,a),flip(a)].">
      <j1 rule="hyper" parents="319 7541 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(111(a,1),15462(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="111 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = K(1 / x,T(y,z / (u / w))) / x
    ]]></literal>
    <justification jstring="[para(15462(a,1),4211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15462 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),T(z,y) * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[para(14869(a,1),15284(a,1,2))].">
      <j1 rule="para" parents="14869 15284"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(13347(a,1),15305(a,1,2,2))].">
      <j1 rule="para" parents="13347 15305"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15400,a(flip),b,15467,a),flip(a)].">
      <j1 rule="hyper" parents="64 15400 15467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14783,a(flip),b,15468,a),flip(a)].">
      <j1 rule="hyper" parents="64 14783 15468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(12058(a,2),15469(a,1,2,2))].">
      <j1 rule="para" parents="12058 15469"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z * w),w)) = T(x,y / (w \ T(z * w,u)))
    ]]></literal>
    <justification jstring="[para(12187(a,1),15317(a,1,2,2,1))].">
      <j1 rule="para" parents="12187 15317"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(35,a,14401,a,b,15326,a(flip))].">
      <j1 rule="hyper" parents="35 14401 15326"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(13795,a,15472,a)].">
      <j1 rule="hyper" parents="13795 15472"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(231(a,1),15472(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 15472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(3266(a,1),15473(a,1,2,1))].">
      <j1 rule="para" parents="3266 15473"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      K(x / y,(y / x) * z) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14479,a(flip),b,15476,a)].">
      <j1 rule="hyper" parents="64 14479 15476"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ (y / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[para(12137(a,1),15476(a,1,2,1,2))].">
      <j1 rule="para" parents="12137 15476"/>
    </justification>
  </clause>

  <clause id="15479">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(y / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9097,a,b,15477,a)].">
      <j1 rule="hyper" parents="64 9097 15477"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      T(x,(y / (z / (z / u))) * w) = T(x,(y / T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(9318,a,15368,a),flip(a)].">
      <j1 rule="hyper" parents="9318 15368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / T(z / y,1)) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13197,a(flip),b,15480,a),flip(a)].">
      <j1 rule="hyper" parents="64 13197 15480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / (z / y)) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(208(a,1),15481(a,1,2,1,2))].">
      <j1 rule="para" parents="208 15481"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      T(x,((y / z) \ z) * u) = T(x,((z / y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11335,a(flip),b,15482,a)].">
      <j1 rule="hyper" parents="64 11335 15482"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),(T(z,v5) \ w) * y) = T(x,y * (T(z,v5) \ w))
    ]]></literal>
    <justification jstring="[para(14727(a,2),15422(a,1,1))].">
      <j1 rule="para" parents="14727 15422"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * K(y,z)),w)) = K(x,K(y,z) * T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(4356(a,1),15449(a,2,2,2,1))].">
      <j1 rule="para" parents="4356 15449"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      K(x,T((K(y,z) * u) * K(z,y),w)) = K(x,T(K(y,z) * (u * K(y,z)),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,15043,a,b,15485,a)].">
      <j1 rule="hyper" parents="319 15043 15485"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * K(y,z)),w)) = K(x,T(T(u,K(z,y)),w))
    ]]></literal>
    <justification jstring="[para(5966(a,1),15486(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5966 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * K(y,z)),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(15487(a,2),14153(a,1))].">
      <j1 rule="para" parents="15487 14153"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      K(x,y * (T(z * u,x) \ K(w,L(v5,u,z)))) = K(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[para(10133(a,1),15085(a,1,2,2,2))].">
      <j1 rule="para" parents="10133 15085"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(15233(a,1),15276(a,1))].">
      <j1 rule="para" parents="15233 15276"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(15336,a,15316,a),flip(a)].">
      <j1 rule="hyper" parents="15336 15316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,(K(y,z) / u) \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(3965(a,2),15491(a,1,2))].">
      <j1 rule="para" parents="3965 15491"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),w))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(15389,a,15301,a)].">
      <j1 rule="hyper" parents="15389 15301"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(3387(a,1),15493(a,1,2,2,2,1))].">
      <j1 rule="para" parents="3387 15493"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15366,a(flip),b,15494,a),flip(a)].">
      <j1 rule="hyper" parents="319 15366 15494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(110(a,1),15495(a,1,2,2,2))].">
      <j1 rule="para" parents="110 15495"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (z \ u)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(15421,a,14858,a)].">
      <j1 rule="hyper" parents="15421 14858"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (y \ u)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(15421,a,14857,a)].">
      <j1 rule="hyper" parents="15421 14857"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      K(x,T((y * (y \ z)) \ (u * (y \ z)),y)) = K(x,((z / y) * u) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12802,a(flip),b,15498,a)].">
      <j1 rule="hyper" parents="64 12802 15498"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,((y / u) * z) / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15499(a,1,2,1,1))].">
      <j1 rule="para" parents="10 15499"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,w) / v5) = K(x,(y * u) * (v5 \ K(y * u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11167,a(flip),b,15090,a),flip(a)].">
      <j1 rule="hyper" parents="64 11167 15090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,w) / v5) = K(x,T(y * u,w) / v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,15088,a(flip),b,15502,a),flip(a)].">
      <j1 rule="hyper" parents="319 15088 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,T(z * y,z) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11211,a(flip),b,15504,a)].">
      <j1 rule="hyper" parents="64 11211 15504"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[hyper(319,a,11135,a(flip),b,15505,a),flip(a)].">
      <j1 rule="hyper" parents="319 11135 15505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      K(x,(y * T(z,z * u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(3295(a,1),15507(a,1,2,1,2))].">
      <j1 rule="para" parents="3295 15507"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      K(x,(y * T(z,z \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(10(a,1),15508(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13906,a(flip),b,15098,a)].">
      <j1 rule="hyper" parents="64 13906 15098"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z * (u \ y)) \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(15510(a,2),7567(a,1))].">
      <j1 rule="para" parents="15510 7567"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[para(12057(a,1),15115(a,2,2,2))].">
      <j1 rule="para" parents="12057 15115"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(15011,a,15512,a)].">
      <j1 rule="hyper" parents="15011 15512"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / w) * (T(z,u) / w)) = K(x,(((z \ u) \ u) / w) * y)
    ]]></literal>
    <justification jstring="[hyper(11234,a,15513,a),flip(a)].">
      <j1 rule="hyper" parents="11234 15513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(9330,a,15514,a),flip(a)].">
      <j1 rule="hyper" parents="9330 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = v5 \ T(x * T(v5,K(w,u)),K(w,u))
    ]]></literal>
    <justification jstring="[para(15214(a,1),15237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15214 15237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,13423,a(flip),b,15517,a),flip(a)].">
      <j1 rule="hyper" parents="319 13423 15517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(15517(a,2),13493(a,1))].">
      <j1 rule="para" parents="15517 13493"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(14417,a,15518,a)].">
      <j1 rule="hyper" parents="14417 15518"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (K(w,v5) * y))) = T(x,u * T(K(w,v5) * y,z))
    ]]></literal>
    <justification jstring="[hyper(14228,a,15518,a),flip(a)].">
      <j1 rule="hyper" parents="14228 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(14171,a,15518,a)].">
      <j1 rule="hyper" parents="14171 15518"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(K(u,w) * y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(13490,a,15518,a),flip(a)].">
      <j1 rule="hyper" parents="13490 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u) * w) = T(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14330,a(flip),b,15518,a),flip(a)].">
      <j1 rule="hyper" parents="64 14330 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      T(x,K(T(y,z) \ u,w) * v5) = T(x,K(y \ u,w) * v5)
    ]]></literal>
    <justification jstring="[para(4292(a,1),15518(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4292 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = (K(v6 * K(v7,v8),v9) * x) \ (K(K(v7,v8) * v6,v9) * T(x,K(u,w) * v5))
    ]]></literal>
    <justification jstring="[para(15518(a,1),14465(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15518 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[para(4081(a,1),15521(a,1,2,2,2))].">
      <j1 rule="para" parents="4081 15521"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      x * T(x \ R(x,y,K(K(z,u) * w,v5)),K(w,v5) * y) = R(x,y,K(K(z,u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(131,a,15523,a(flip),b,12724,a(flip))].">
      <j1 rule="hyper" parents="131 15523 12724"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(u \ v5,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(14517,a,15526,a)].">
      <j1 rule="hyper" parents="14517 15526"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(v5 * u,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14941,a(flip),b,15531,a),flip(a)].">
      <j1 rule="hyper" parents="319 14941 15531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,y \ T(z,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14341,a(flip),b,15532,a),flip(a)].">
      <j1 rule="hyper" parents="319 14341 15532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[para(108(a,1),15533(a,1,2,2,2,1))].">
      <j1 rule="para" parents="108 15533"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      (x \ T(y * x,z \ T(u,w * v5))) * (T(y,x) \ 1) = K(x * y,z \ T(u,v5 \ w))
    ]]></literal>
    <justification jstring="[para(15534(a,1),13194(a,1,1,2))].">
      <j1 rule="para" parents="15534 13194"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(y \ K(w,u),z) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,13663,a(flip),b,15524,a),flip(a)].">
      <j1 rule="hyper" parents="319 13663 15524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(x \ T(y,x),z)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,9403,a(flip),b,15259,a),flip(a)].">
      <j1 rule="hyper" parents="319 9403 15259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(z,x \ y)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(15246(a,1),15538(a,1,2))].">
      <j1 rule="para" parents="15246 15538"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(x,z)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(7018(a,1),15539(a,1,2))].">
      <j1 rule="para" parents="7018 15539"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      T(T(x,T(y,z)),x \ y) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14816,a(flip),b,15540,a)].">
      <j1 rule="hyper" parents="64 14816 15540"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      T(T(x,x \ y),T(y,z)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(410,a,15542,a)].">
      <j1 rule="hyper" parents="410 15542"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K((x \ 1) * y,T(x,u))) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[hyper(319,a,6836,a(flip),b,14502,a),flip(a)].">
      <j1 rule="hyper" parents="319 6836 14502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(9288(a,1),15544(a,1,2))].">
      <j1 rule="para" parents="9288 15544"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(6537(a,1),15545(a,1,2))].">
      <j1 rule="para" parents="6537 15545"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6983,a,15546,a),flip(a)].">
      <j1 rule="hyper" parents="6983 15546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(z * u,w) * x) = K(y,x * T(T(u,z) * z,w))
    ]]></literal>
    <justification jstring="[para(14948(a,1),14571(a,1,2))].">
      <j1 rule="para" parents="14948 14571"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      K(x,y * T(T(z,u) * u,w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14402,a(flip),b,15548,a),flip(a)].">
      <j1 rule="hyper" parents="64 14402 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      K(x,y * T(z * ((z * u) / z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[para(231(a,1),15549(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="231 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      K(x,y * T(T(z * u,z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14682,a(flip),b,15550,a)].">
      <j1 rule="hyper" parents="64 14682 15550"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,T(z * u,w) * x) = K(y,x * T(T(u * z,u),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14402,a,b,15551,a)].">
      <j1 rule="hyper" parents="319 14402 15551"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      K(x,T(T(y * z,y),u) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(35,a,14570,a,b,15552,a)].">
      <j1 rule="hyper" parents="35 14570 15552"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15293,a(flip),b,15553,a),flip(a)].">
      <j1 rule="hyper" parents="64 15293 15553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      (x \ T(K(y,z),u)) \ K(y,T(z,w)) = (x \ K(y,z)) \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14081,a(flip),b,14746,a),flip(a)].">
      <j1 rule="hyper" parents="64 14081 14746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      (x \ K(y,T(z,u))) \ K(y,T(z,w)) = (x \ K(y,z)) \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(6099(a,2),15555(a,1,1,2))].">
      <j1 rule="para" parents="6099 15555"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) \ 1,y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[hyper(11267,a,14784,a)].">
      <j1 rule="hyper" parents="11267 14784"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,T(z \ (u * y),z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13658,a(flip),b,15557,a),flip(a)].">
      <j1 rule="hyper" parents="64 13658 15557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13474,a(flip),b,15558,a),flip(a)].">
      <j1 rule="hyper" parents="319 13474 15558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (u \ (y * z)),y)) = w
    ]]></literal>
    <justification jstring="[para(15559(a,1),12280(a,1))].">
      <j1 rule="para" parents="15559 12280"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      T(x,y / ((z \ T(z \ u,w)) \ (z \ u))) = T(x,y / (T(z \ u,w) \ u))
    ]]></literal>
    <justification jstring="[para(12407(a,1),14835(a,1,2,2,1))].">
      <j1 rule="para" parents="12407 14835"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      K(x,y) \ T(K(x,K(y,z)) * (u * K(x,y)),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(5640(a,1),14923(a,1,2,1))].">
      <j1 rule="para" parents="5640 14923"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      K(x * y,K(z \ u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,K(u * z,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(14944(a,1),13195(a,1))].">
      <j1 rule="para" parents="14944 13195"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(5403(a,1),14954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5403 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,9,a(flip),b,15564,a),flip(a)].">
      <j1 rule="hyper" parents="319 9 15564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5040,a,15565,a),flip(a)].">
      <j1 rule="hyper" parents="5040 15565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,T(u,z / x)) = w
    ]]></literal>
    <justification jstring="[para(15565(a,1),5040(a,1))].">
      <j1 rule="para" parents="15565 5040"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      K(x * K((y * z) \ x,z),T(u,((y * z) \ x) * z)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9301,a(flip),b,14965,a)].">
      <j1 rule="hyper" parents="64 9301 14965"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(K(z,w) * (u / z)) \ y) = T(x,y / (K(z,w) * (u / z)))
    ]]></literal>
    <justification jstring="[para(15224(a,1),14967(a,1,1))].">
      <j1 rule="para" parents="15224 14967"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      K(K(x,y),z) * (T(u \ y,K(x,u)) \ K(x,y)) = (u \ y) \ K(x,T(T(y,z),u \ y))
    ]]></literal>
    <justification jstring="[para(6099(a,2),14971(a,2,2))].">
      <j1 rule="para" parents="6099 14971"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(4935(a,2),15116(a,1,2))].">
      <j1 rule="para" parents="4935 15116"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = (K(x,y) \ z) \ (u * (z * K(y,x)))
    ]]></literal>
    <justification jstring="[para(6816(a,1),15228(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6816 15228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14925,a(flip),b,15574,a),flip(a)].">
      <j1 rule="hyper" parents="64 14925 15574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14972,a(flip),b,15575,a)].">
      <j1 rule="hyper" parents="64 14972 15575"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6791(a,1),15576(a,2,2))].">
      <j1 rule="para" parents="6791 15576"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,K(v5,v6) * x)) = (x \ K(y,z)) \ T(u,K(w,K(v7,v8) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,15243,a(flip),b,15275,a)].">
      <j1 rule="hyper" parents="64 15243 15275"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(T(K(z,y),x),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2758(a,1),15318(a,1,2,1))].">
      <j1 rule="para" parents="2758 15318"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(K(z,T(y,x)),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6099(a,2),15579(a,1,2,1))].">
      <j1 rule="para" parents="6099 15579"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / K(z,T(T(y,x),u)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6099(a,2),15580(a,1,2))].">
      <j1 rule="para" parents="6099 15580"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) * K(T(T(y,x),u),z) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5186,a,15581,a)].">
      <j1 rule="hyper" parents="5186 15581"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) * K(y,T(T(z,u),x)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6137(a,1),15582(a,1,2))].">
      <j1 rule="para" parents="6137 15582"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11948,a(flip),b,15583,a)].">
      <j1 rule="hyper" parents="64 11948 15583"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = K(y,K(z,u)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(6703(a,1),15584(a,2,1))].">
      <j1 rule="para" parents="6703 15584"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = (x \ 1) \ K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14104,a(flip),b,15585,a),flip(a)].">
      <j1 rule="hyper" parents="319 14104 15585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,z \ u)) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(15020,a,15343,a)].">
      <j1 rule="hyper" parents="15020 15343"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(w / (y * K(z,u))) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11291,a,15587,a),flip(a)].">
      <j1 rule="hyper" parents="11291 15587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,T(y * K(z,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(319,a,15342,a(flip),b,15588,a),flip(a)].">
      <j1 rule="hyper" parents="319 15342 15588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) = K(x,T(u * K(y,z),y) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15073,a(flip),b,15589,a)].">
      <j1 rule="hyper" parents="64 15073 15589"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(319,a,11295,a(flip),b,15382,a),flip(a)].">
      <j1 rule="hyper" parents="319 11295 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(13714,a,15591,a)].">
      <j1 rule="hyper" parents="13714 15591"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y * ((u \ z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(111(a,1),15592(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 15592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),z * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15154,a(flip),b,15466,a)].">
      <j1 rule="hyper" parents="64 15154 15466"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9336,a(flip),b,15594,a),flip(a)].">
      <j1 rule="hyper" parents="64 9336 15594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9336,a(flip),b,15596,a),flip(a)].">
      <j1 rule="hyper" parents="64 9336 15596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      x * T(x \ L(x,y,K(K(z,u) * w,v5)),K(w,v5) * y) = R(x,y,K(K(z,u) * w,v5))
    ]]></literal>
    <justification jstring="[para(13256(a,1),15529(a,1,2,1,2))].">
      <j1 rule="para" parents="13256 15529"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      K(x * y,z \ T(u,w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z \ T(u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(15535(a,1),13195(a,1))].">
      <j1 rule="para" parents="15535 13195"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      K(x,y) \ T(z * K(x,T(y,u)),w) = T(K(x,y) * z,w) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(14172(a,1),15562(a,1,2,1))].">
      <j1 rule="para" parents="14172 15562"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,x) * T(z * K(x,T(y,w)),u)
    ]]></literal>
    <justification jstring="[hyper(4384,a,15600,a),flip(a)].">
      <j1 rule="hyper" parents="4384 15600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),w) = K(x,y) * T(u * K(y,T(x,z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14203,a(flip),b,15601,a)].">
      <j1 rule="hyper" parents="64 14203 15601"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,((z * y) \ x) * y)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(8179(a,1),15569(a,1,1,2))].">
      <j1 rule="para" parents="8179 15569"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      K(K(x,y),z) * (T(u \ y,K(x,u)) \ K(x,y)) = (u \ y) \ K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(15164(a,1),15572(a,2,2))].">
      <j1 rule="para" parents="15164 15572"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(u \ x,K(y,u)) \ K(y,x)) = (u \ x) \ K(y,T(T(x,z),u))
    ]]></literal>
    <justification jstring="[para(6746(a,1),15604(a,1,1))].">
      <j1 rule="para" parents="6746 15604"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(u \ x,K(u,y)) \ K(y,x)) = (u \ x) \ K(y,T(T(x,z),u))
    ]]></literal>
    <justification jstring="[para(6791(a,1),15605(a,1,2,1))].">
      <j1 rule="para" parents="6791 15605"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      K(x,K(y,z)) * T((u \ x) \ K(y,x),K(u,y)) = (u \ x) \ K(y,T(T(x,z),u))
    ]]></literal>
    <justification jstring="[para(15310(a,2),15606(a,1,2))].">
      <j1 rule="para" parents="15310 15606"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      T((x \ y) \ K(z,y),K(x,z)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,14753,a(flip),b,15607,a),flip(a)].">
      <j1 rule="hyper" parents="35 14753 15607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      T((x \ y) \ K(z,y),K(x,z)) = (x \ y) \ K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12886,a,b,15608,a),flip(a)].">
      <j1 rule="hyper" parents="319 12886 15608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      T((x \ y) \ K(z,y),K(x,z)) != (x \ y) \ u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(15609(a,2),48(a,1))].">
      <j1 rule="para" parents="15609 48"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,K(v5,v6) * x)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(15233(a,1),15578(a,2,2))].">
      <j1 rule="para" parents="15233 15578"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(15235,a,15612,a)].">
      <j1 rule="hyper" parents="15235 15612"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      T((x \ K(y,z)) \ (u * (x \ K(y,z))),K(x,w)) = T(u,T(x,w) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14927,a(flip),b,15613,a),flip(a)].">
      <j1 rule="hyper" parents="319 14927 15613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) = T(x,T(y,w) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),15614(a,1,1))].">
      <j1 rule="para" parents="22 15614"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      T(x,T(y,z) \ K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(u,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(15615(a,1),15490(a,1))].">
      <j1 rule="para" parents="15615 15490"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      x * T(a(y,z,K(x,K(u,w) * v5)),K(v5,y) * z) = R(x,z,K(K(u,w) * v5,y))
    ]]></literal>
    <justification jstring="[para(13285(a,1),15598(a,1,2,1))].">
      <j1 rule="para" parents="13285 15598"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(6597(a,1),14306(a,1,2,2,1))].">
      <j1 rule="para" parents="6597 14306"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      K(x * ((x * y) \ (z * (x * y))),y) = K(z / (1 / x),L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(13229,a,14348,a)].">
      <j1 rule="hyper" parents="13229 14348"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      K(x / (1 / y),L(z,y,y \ 1)) = K(y * T(x,y * z),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15620(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 15620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      K(x * T(y,x * z),z) = K(y / (1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(12281,a,15621,a),flip(a)].">
      <j1 rule="hyper" parents="12281 15621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      K(x * T(y,x * z),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,12164,a(flip),b,15622,a),flip(a)].">
      <j1 rule="hyper" parents="319 12164 15622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14864,a(flip),b,15624,a),flip(a)].">
      <j1 rule="hyper" parents="64 14864 15624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(251(a,1),14394(a,2,2,2))].">
      <j1 rule="para" parents="251 14394"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (K(w,z) * y))) = K(x,u * T(K(w,z) * y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14505,a,13639,a),flip(a)].">
      <j1 rule="hyper" parents="14505 13639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,y * T(K(z,u) * w,u \ 1)) = K(x,y * T(K(z,u) * w,u))
    ]]></literal>
    <justification jstring="[hyper(14504,a,15627,a),flip(a)].">
      <j1 rule="hyper" parents="14504 15627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,z)) = K(x,y * T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12948,a(flip),b,15628,a),flip(a)].">
      <j1 rule="hyper" parents="64 12948 15628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12948,a(flip),b,15629,a),flip(a)].">
      <j1 rule="hyper" parents="64 12948 15629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,15630,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15630 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13564,a(flip),b,15630,a),flip(a)].">
      <j1 rule="hyper" parents="64 13564 15630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(5046(a,2),15632(a,1,2))].">
      <j1 rule="para" parents="5046 15632"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14538,a(flip),b,15633,a)].">
      <j1 rule="hyper" parents="64 14538 15633"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(2854(a,1),15634(a,1,2,1,2))].">
      <j1 rule="para" parents="2854 15634"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(14516,a,14690,a),flip(a)].">
      <j1 rule="hyper" parents="14516 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      T(x,T(K(y / z,u) * T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14887,a,b,15637,a)].">
      <j1 rule="hyper" parents="64 14887 15637"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(14751(a,2),15638(a,1,2,1))].">
      <j1 rule="para" parents="14751 15638"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * T(z / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14810,a(flip),b,15639,a),flip(a)].">
      <j1 rule="hyper" parents="64 14810 15639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * (w * (u / (z / y)))) = K(x,w * T((z / y) \ u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(12441(a,1),14363(a,1,2,1))].">
      <j1 rule="para" parents="12441 14363"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,T(K(y,z) * (K(z,y) / u),w) * K(y,z \ y)) = K(x,(K(z,y) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[para(4356(a,1),14383(a,1,2,1,1))].">
      <j1 rule="para" parents="4356 14383"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,T(y,u) * z)) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(14385(a,1),14396(a,1,2,2))].">
      <j1 rule="para" parents="14385 14396"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      T(x,K(y * z,u) * ((y * z) / T(y,w))) = T(x,T(y * (z * K(w,y)),u) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15528,a(flip),b,15643,a)].">
      <j1 rule="hyper" parents="64 15528 15643"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y * z,w) / T(y,u))
    ]]></literal>
    <justification jstring="[para(12057(a,1),15644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12057 15644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14379,a(flip),b,15646,a),flip(a)].">
      <j1 rule="hyper" parents="319 14379 15646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      T(x,y \ T((z * K(u,y)) * y,w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6905,a(flip),b,15647,a)].">
      <j1 rule="hyper" parents="64 6905 15647"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      T(x,y \ T(z * (y * K(u,y)),w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[para(7622(a,1),15648(a,1,2,2,1))].">
      <j1 rule="para" parents="7622 15648"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,K(u,w)) = T((x * y) / T(x,K(u,w)),z)
    ]]></literal>
    <justification jstring="[para(4287(a,1),14497(a,1,1))].">
      <j1 rule="para" parents="4287 14497"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      (x * T(x \ y,z)) / T(x,K(u,w)) = T(y / T(x,K(u,w)),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15650(a,2,1,1))].">
      <j1 rule="para" parents="10 15650"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      T(x,K(y,z)) * T(u / T(x,K(y,z)),w) = x * T(u / x,w)
    ]]></literal>
    <justification jstring="[para(15651(a,1),14476(a,1,2))].">
      <j1 rule="para" parents="15651 14476"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (x / T(y,K(z,u)))),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14685,a,b,15653,a)].">
      <j1 rule="hyper" parents="64 14685 15653"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x,T(y,z) * u) * a(w,v5,K(T(y,z) * u,x)) = K(x,L(((z \ y) * z) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(14868(a,1),14514(a,1,1))].">
      <j1 rule="para" parents="14868 14514"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      K(x,L(((y \ z) * y) * u,w,v5)) = K(x,L(T(z,y) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10155,a,15655,a),flip(a)].">
      <j1 rule="hyper" parents="10155 15655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13708,a(flip),b,14678,a)].">
      <j1 rule="hyper" parents="64 13708 14678"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / v5) = T(x,T(y * T(z,u),w) / v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,14677,a(flip),b,15657,a),flip(a)].">
      <j1 rule="hyper" parents="64 14677 15657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(u,z)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),14771(a,1,2,1,2))].">
      <j1 rule="para" parents="23 14771"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      K(x,y \ (z * u)) * a(w,v5,K(y \ (z * u),x)) = K(x,L(y \ T(u * z,z),v5,w))
    ]]></literal>
    <justification jstring="[para(13802(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="13802 14833"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ (u * z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15660(a,1),10155(a,1))].">
      <j1 rule="para" parents="15660 10155"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      K(x * (y * z),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[para(14962(a,1),14964(a,1,1))].">
      <j1 rule="para" parents="14962 14964"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(7000,a,15662,a),flip(a)].">
      <j1 rule="hyper" parents="7000 15662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,(y * (y \ z)) * R(T(u,z),y \ z,y)) = K(x,L(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(738(a,1),15663(a,2,2))].">
      <j1 rule="para" parents="738 15663"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,((y / z) * z) * R(T(u,y),z,y / z)) = K(x,L(u,z,z \ y) * y)
    ]]></literal>
    <justification jstring="[para(9550(a,1),15663(a,2,2))].">
      <j1 rule="para" parents="9550 15663"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15664(a,1,2,1))].">
      <j1 rule="para" parents="10 15664"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      K(x,R(y,z \ u,z) * u) = K(x,L(y,z \ u,z) * u)
    ]]></literal>
    <justification jstring="[para(243(a,1),15666(a,1,2))].">
      <j1 rule="para" parents="243 15666"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(8211(a,1),15668(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8211 15668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12997,a(flip),b,15669,a)].">
      <j1 rule="hyper" parents="64 12997 15669"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,y / u)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),15665(a,1,2,1))].">
      <j1 rule="para" parents="12 15665"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(8204(a,1),15671(a,1,2,2))].">
      <j1 rule="para" parents="8204 15671"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(731(a,1),15673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="731 15673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = a(y,z,K(x,K(z \ u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12584,a,b,15270,a),flip(a)].">
      <j1 rule="hyper" parents="319 12584 15270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = v5 \ T(x * T(v5,K(w,K(v6,v7) * y)),K(w,K(v8,v9) * y))
    ]]></literal>
    <justification jstring="[para(15243(a,1),15277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15243 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      K(x,K(y,z) * T(K(z,y) * (K(y,z) / u),w)) = K(x,(K(y,z) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14258,a(flip),b,15642,a)].">
      <j1 rule="hyper" parents="64 14258 15642"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      K(x,T((K(y,z) * (K(z,y) / u)) * K(y,z),w)) = K(x,(K(z,y) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15043,a,b,15677,a)].">
      <j1 rule="hyper" parents="64 15043 15677"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((K(z,y) / u) * K(y,z)),w)) = K(x,(K(z,y) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[para(5640(a,1),15678(a,1,2,1))].">
      <j1 rule="para" parents="5640 15678"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      K(x,(K(y,z) / u) * K(u \ 1,w)) = K(x,T(K(y,z) / u,w))
    ]]></literal>
    <justification jstring="[hyper(15488,a,15679,a),flip(a)].">
      <j1 rule="hyper" parents="15488 15679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K(x,(K(y,z) / u) * K(u \ 1,w)) = K(x,T(u \ K(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14138,a(flip),b,15680,a),flip(a)].">
      <j1 rule="hyper" parents="319 14138 15680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      K(x,K(y,z) * (K(u,w) / y)) = K(x,T(y \ K(u,w),z))
    ]]></literal>
    <justification jstring="[hyper(14267,a,15681,a)].">
      <j1 rule="hyper" parents="14267 15681"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ K(u,w))) = K(x,T(y \ K(u,w),z))
    ]]></literal>
    <justification jstring="[hyper(15056,a,15682,a)].">
      <j1 rule="hyper" parents="15056 15682"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      K(x,T(y \ K(z,u),w)) = K(x,T(y,w) \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13458,a(flip),b,15683,a),flip(a)].">
      <j1 rule="hyper" parents="64 13458 15683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(z,u)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(6791(a,1),15659(a,1,2))].">
      <j1 rule="para" parents="6791 15659"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[para(14096(a,1),15675(a,2,3))].">
      <j1 rule="para" parents="14096 15675"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,13423,a(flip),b,15676,a),flip(a)].">
      <j1 rule="hyper" parents="319 13423 15676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * K(v5,v6)) = T(x,u * T(u \ K(v6,v5),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14338,a(flip),b,15687,a),flip(a)].">
      <j1 rule="hyper" parents="64 14338 15687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      T(x,y * T(y \ K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w) * K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(15689(a,1),15519(a,1))].">
      <j1 rule="para" parents="15689 15519"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ (T(x,K(z,u)) * T(y,K(z,u))) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(14552(a,1),15685(a,1,2))].">
      <j1 rule="para" parents="14552 15685"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(u * K(y,z),x) * T(u,K(y,z))) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8573,a,15692,a)].">
      <j1 rule="hyper" parents="8573 15692"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      K(x,K(y,z)) * T(K(u * K(y,z),x) * u,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(15188(a,2),15693(a,1,2))].">
      <j1 rule="para" parents="15188 15693"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u * K(K(y,z) * u,x),K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(9295(a,1),15694(a,1,2,1))].">
      <j1 rule="para" parents="9295 15694"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,z) \ T(u * K(y,z),x)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(12045(a,1),15695(a,1,2))].">
      <j1 rule="para" parents="12045 15695"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * T(u * K(y,z),x)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(4356(a,1),15696(a,1,2))].">
      <j1 rule="para" parents="4356 15696"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(6617,a,15697,a)].">
      <j1 rule="hyper" parents="6617 15697"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      T(x,y) / T(x * K(z,x),y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,5989,a(flip),b,15698,a)].">
      <j1 rule="hyper" parents="128 5989 15698"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,15602,a(flip),b,15698,a)].">
      <j1 rule="hyper" parents="64 15602 15698"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      T(x,y) / T(x * K(z,T(x,u)),y) = K(x,T(T(z,u),y))
    ]]></literal>
    <justification jstring="[para(6102(a,1),15699(a,1,2,1,2))].">
      <j1 rule="para" parents="6102 15699"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ u,w)) = T(x,w) / T(x * K(T(z,y) \ u,x),w)
    ]]></literal>
    <justification jstring="[para(13522(a,1),15699(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13522 15699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4374,a,15700,a),flip(a)].">
      <j1 rule="hyper" parents="4374 15700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(206,a,15703,a,b,12499,a)].">
      <j1 rule="hyper" parents="206 15703 12499"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13097,a(flip),b,15704,a),flip(a)].">
      <j1 rule="hyper" parents="64 13097 15704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(5195,a,15706,a),flip(a)].">
      <j1 rule="hyper" parents="5195 15706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = L(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14078,a,b,15706,a)].">
      <j1 rule="hyper" parents="64 14078 15706"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,8663,a(flip),b,15706,a),flip(a)].">
      <j1 rule="hyper" parents="64 8663 15706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7746,a(flip),b,15706,a),flip(a)].">
      <j1 rule="hyper" parents="64 7746 15706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      L(x,K(y,z),u) * (K(y,z) * u) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,15706,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="130 15706 20"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(15706(a,1),7936(a,1,1))].">
      <j1 rule="para" parents="15706 7936"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15707(a,1,1,1))].">
      <j1 rule="para" parents="11 15707"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K(x,y) * L(K(y,x) * z,K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(15718(a,1),5223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15718 5223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K((x * K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(15718(a,2),14137(a,1,1))].">
      <j1 rule="para" parents="15718 14137"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ u,w)) = K(x,T(T(z,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,15699,a(flip),b,15702,a),flip(a)].">
      <j1 rule="hyper" parents="319 15699 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ K(u,w),v5)) = T(x,v5) / T(x * K(z \ K(u,w),T(x,y)),v5)
    ]]></literal>
    <justification jstring="[para(14797(a,1),15702(a,2,2,1,2))].">
      <j1 rule="para" parents="14797 15702"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ K(u,w),v5)) = K(x,T(T(z \ K(u,w),y),v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,15701,a(flip),b,15723,a),flip(a)].">
      <j1 rule="hyper" parents="319 15701 15723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      K(x,T(T(y \ K(z,u),w),v5)) = K(x,T(T(y,w) \ K(z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15722,a(flip),b,15724,a),flip(a)].">
      <j1 rule="hyper" parents="64 15722 15724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / (w * u))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15206,a(flip),b,15686,a)].">
      <j1 rule="hyper" parents="64 15206 15686"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(K(w,v5) * L(x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(13290(a,1),14057(a,1,1))].">
      <j1 rule="para" parents="13290 14057"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(y * T(x,K(y,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(11099(a,1),14643(a,1))].">
      <j1 rule="para" parents="11099 14643"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) = K(K(y * T(x,K(y,z)),x) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(14644,a,13554,a),flip(a)].">
      <j1 rule="hyper" parents="14644 13554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) = K(K(y * x,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(6001(a,1),15732(a,2,1,1))].">
      <j1 rule="para" parents="6001 15732"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = K(K(x * y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(15730,a,15734,a)].">
      <j1 rule="hyper" parents="15730 15734"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      K(K(x * y,y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11218,a(flip),b,15735,a),flip(a)].">
      <j1 rule="hyper" parents="64 11218 15735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14572,a,b,15737,a)].">
      <j1 rule="hyper" parents="64 14572 15737"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      K(K(x,y) \ (z / u),w) \ K((K(y \ 1,x) \ (z / u)) * w,w) = a(w,u \ (K(y \ 1,x) \ z),w)
    ]]></literal>
    <justification jstring="[para(15738(a,1),11437(a,1,1))].">
      <j1 rule="para" parents="15738 11437"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      T(x,R(y / y,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,(T(z,y * y) \ u) * (w \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12345,a(flip),b,14691,a),flip(a)].">
      <j1 rule="hyper" parents="319 12345 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      K(x,K(y,(L(z / u,u,1 / u) * w) * v5)) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),15376(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      K(x,K(y,(z * u) * R(L(w / v5,v5,1 / v5),z,u))) = K(x,K(y,(((1 / v5) * w) * z) * u))
    ]]></literal>
    <justification jstring="[hyper(14429,a,15741,a)].">
      <j1 rule="hyper" parents="14429 15741"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      K(x,K(y,(z * u) * L(R(w / v5,z,u),v5,1 / v5))) = K(x,K(y,(((1 / v5) * w) * z) * u))
    ]]></literal>
    <justification jstring="[para(29(a,1),15742(a,1,2,2,2))].">
      <j1 rule="para" parents="29 15742"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      T(x,(y \ z) * (K(y,T(y \ z,u)) * T(T(y \ z,u),u))) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(9015(a,1),14874(a,1,2))].">
      <j1 rule="para" parents="9015 14874"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      T(x,y / (z \ T(((z * K(u,w)) * v5) * z,K(w,u)))) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(14373(a,1),15126(a,1,2,2,2,1))].">
      <j1 rule="para" parents="14373 15126"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / w,v5))) * K(K(z,y),x) = a(v5,K(u,w) / (K(y,z) * w),K(K(z,y),x))
    ]]></literal>
    <justification jstring="[para(10137(a,1),15373(a,1,1))].">
      <j1 rule="para" parents="10137 15373"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      T(x,L(y * K(z,u \ w),K(u \ w,z),T(u,v5))) = T(x,(y * T(u,v5)) / (T(u,v5) * K(w / u,z)))
    ]]></literal>
    <justification jstring="[para(5174(a,1),14474(a,1,2,1))].">
      <j1 rule="para" parents="5174 14474"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((x \ y) \ 1,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(9353(a,1),14501(a,1,1))].">
      <j1 rule="para" parents="9353 14501"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(y \ x,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(4996(a,1),15749(a,1,2))].">
      <j1 rule="para" parents="4996 15749"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(14196(a,1),15750(a,1,2))].">
      <j1 rule="para" parents="14196 15750"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13204,a(flip),b,15751,a),flip(a)].">
      <j1 rule="hyper" parents="64 13204 15751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      a(x \ (x * y),z,x \ (x * y)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(15752(a,1),11834(a,1,1))].">
      <j1 rule="para" parents="15752 11834"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,(y * z) \ y)) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(11274(a,1),14855(a,1,2))].">
      <j1 rule="para" parents="11274 14855"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K((K(y \ 1,z) \ (x / y)) * u,u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(14297(a,1),15739(a,1,1))].">
      <j1 rule="para" parents="14297 15739"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(u * (K(y \ 1,z) \ (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(4281(a,1),15755(a,1,2))].">
      <j1 rule="para" parents="4281 15755"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(K(y \ 1,z) \ (u * (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(8792(a,2),15756(a,1,2))].">
      <j1 rule="para" parents="8792 15756"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(K(z,y) \ (u * (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(15738(a,1),15757(a,1,2))].">
      <j1 rule="para" parents="15738 15757"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y \ 1)) / (u * (z / (y * z)))) = K(x,L((z * y) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12988,a(flip),b,15754,a),flip(a)].">
      <j1 rule="hyper" parents="64 12988 15754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(x,((y * z) / z) / (u * (y / (z * y)))) = K(x,L((y * z) / u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15418,a(flip),b,15759,a)].">
      <j1 rule="hyper" parents="64 15418 15759"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(11(a,1),15760(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ (K(x,T(y,z)) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(6099(a,2),14477(a,1,2,1))].">
      <j1 rule="para" parents="6099 14477"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      K(x,y * T(T(z / u,T(w,u)) * v5,v5)) = K(x,y * ((K(u \ z,w) * v5) * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(15428,a,14545,a)].">
      <j1 rule="hyper" parents="15428 14545"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(x,y * ((K(z \ u,w) * v5) * (u / z))) = K(x,y * (v5 * T(u / z,T(w,z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,14542,a(flip),b,15763,a),flip(a)].">
      <j1 rule="hyper" parents="64 14542 15763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x,y * ((K(z \ u,w) * v5) * (u / z))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15110,a(flip),b,15764,a),flip(a)].">
      <j1 rule="hyper" parents="319 15110 15764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * (v5 * (u / z)))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(6246(a,1),15765(a,1,2,2))].">
      <j1 rule="para" parents="6246 15765"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,25,a,b,14656,a),flip(a)].">
      <j1 rule="hyper" parents="319 25 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(1858(a,1),14966(a,1,1,2))].">
      <j1 rule="para" parents="1858 14966"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(12240,a,15770,a),flip(a)].">
      <j1 rule="hyper" parents="12240 15770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(15771(a,1),12289(a,1))].">
      <j1 rule="para" parents="15771 12289"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u * K(y,T(z,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6146(a,1),15160(a,1,2))].">
      <j1 rule="para" parents="6146 15160"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,14465,a(flip),b,15527,a),flip(a)].">
      <j1 rule="hyper" parents="319 14465 15527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(15102,a,15775,a)].">
      <j1 rule="hyper" parents="15102 15775"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(14148,a,15775,a)].">
      <j1 rule="hyper" parents="14148 15775"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,13453,a,b,15775,a),flip(a)].">
      <j1 rule="hyper" parents="319 13453 15775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(4116(a,1),15775(a,1,2,1,1))].">
      <j1 rule="para" parents="4116 15775"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * v5) = v6
    ]]></literal>
    <justification jstring="[para(15775(a,2),13454(a,1))].">
      <j1 rule="para" parents="15775 13454"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y * K(v5,v6)) * u) = w
    ]]></literal>
    <justification jstring="[para(15775(a,1),15102(a,1))].">
      <j1 rule="para" parents="15775 15102"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * v5) = K(x,K(z,y) * (y * v5))
    ]]></literal>
    <justification jstring="[para(4081(a,1),15776(a,1,2))].">
      <j1 rule="para" parents="4081 15776"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 * K(z,y)) = v6
    ]]></literal>
    <justification jstring="[para(15776(a,2),14148(a,1))].">
      <j1 rule="para" parents="15776 14148"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(15778(a,2),13454(a,1))].">
      <j1 rule="para" parents="15778 13454"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(14349,a,15779,a)].">
      <j1 rule="hyper" parents="14349 15779"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * ((y / z) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((y / z) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(15779(a,1),14503(a,1))].">
      <j1 rule="para" parents="15779 14503"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * v5) = K(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,13456,a(flip),b,15783,a),flip(a)].">
      <j1 rule="hyper" parents="319 13456 15783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * v5) = T(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(129,a,15788,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 15788 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u) * w) = K(x,T(y / ((z \ u) * z),y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11195,a(flip),b,15788,a)].">
      <j1 rule="hyper" parents="64 11195 15788"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w) * v5) = T(x,T(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(5925(a,1),15789(a,1,2,1,2))].">
      <j1 rule="para" parents="5925 15789"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w) * v5) = T(x,T(y,w * K(v6,v7)) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,15789,a,b,15791,a),flip(a)].">
      <j1 rule="hyper" parents="319 15789 15791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z \ y,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(4116(a,1),15785(a,1,2,1,1))].">
      <j1 rule="para" parents="4116 15785"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u \ z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(4356(a,2),15793(a,1,2))].">
      <j1 rule="para" parents="4356 15793"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z / (1 / K(v5,v6)))) = T(x,(z / (1 / K(v5,v6))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14622,a(flip),b,15792,a),flip(a)].">
      <j1 rule="hyper" parents="64 14622 15792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u) * w) = K(x,(((z \ u) * z) \ y) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,11114,a(flip),b,15790,a),flip(a)].">
      <j1 rule="hyper" parents="319 11114 15790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z / K(v5,v6))) = T(x,(z / (1 / K(v6,v5))) * y)
    ]]></literal>
    <justification jstring="[para(4214(a,1),15795(a,1,2,2,2))].">
      <j1 rule="para" parents="4214 15795"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z * K(v5,v6))) = T(x,(z / (1 / K(v5,v6))) * y)
    ]]></literal>
    <justification jstring="[para(5174(a,1),15798(a,1,2,2))].">
      <j1 rule="para" parents="5174 15798"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ (K(y,T(x,z)) \ T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(6151(a,2),15762(a,1,2))].">
      <j1 rule="para" parents="6151 15762"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      (x \ (K(y,L(z,u,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[para(12750(a,1),15769(a,1,1,2,1))].">
      <j1 rule="para" parents="12750 15769"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      ((x \ y) * K(z,T(u,y))) \ (K(z,u) * ((y * x) / x)) = L(T(x,K(u,z) * (x \ y)),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(12765(a,1),15801(a,1,1))].">
      <j1 rule="para" parents="12765 15801"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,T(y,u))) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15802(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),K(z,y) * u) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(14641,a,15773,a)].">
      <j1 rule="hyper" parents="14641 15773"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      (x / T(K(y,z),u * K(z,y))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(14336,a,15804,a),flip(a)].">
      <j1 rule="hyper" parents="14336 15804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(15143(a,1),15805(a,1,1,2))].">
      <j1 rule="para" parents="15143 15805"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(6146(a,1),15807(a,1,1))].">
      <j1 rule="para" parents="6146 15807"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15803,a,b,15808,a)].">
      <j1 rule="hyper" parents="64 15803 15808"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = (x \ T(T(x,y),T(y,z))) \ T(T(x,y / x),T(y,z))
    ]]></literal>
    <justification jstring="[para(14494(a,1),15800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14494 15800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = (x \ T(T(x,y),T(y,z))) \ T(T(x,x \ y),T(y,z))
    ]]></literal>
    <justification jstring="[para(3274(a,1),15811(a,2,2,1))].">
      <j1 rule="para" parents="3274 15811"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = (x \ T(T(x,y),T(y,z))) \ T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(15543(a,1),15812(a,2,2))].">
      <j1 rule="para" parents="15543 15812"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(L(u,w,K(z,y)),w * K(z,y))) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(14140(a,2),14361(a,1,1))].">
      <j1 rule="para" parents="14140 14361"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      K(x,y * (z \ ((u / (T(w,v5) \ 1)) \ T(v5,u * T(w,v5))))) = K(x,y * (z \ (T(v5,w) / (u / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(12140(a,1),15424(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12140 15424"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      K(x,y * (z \ ((u / (T(w,v5) \ 1)) \ T(v5,u * w)))) = K(x,y * (z \ (T(v5,w) / (u / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(5819(a,1),15819(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5819 15819"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      K(x,y * (z \ ((T(u,w) \ 1) * K(w,w * u)))) = K(x,y * (z \ (T(w,u) / (w / (u \ 1)))))
    ]]></literal>
    <justification jstring="[para(12372(a,1),15820(a,1,2,2,2))].">
      <j1 rule="para" parents="12372 15820"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) \ K(w,w * u)))) = K(x,y * (z \ (T(w,u) / (w / (u \ 1)))))
    ]]></literal>
    <justification jstring="[para(11948(a,1),15821(a,1,2,2,2))].">
      <j1 rule="para" parents="11948 15821"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (T(y,K(z,u)) \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5856(a,1),15654(a,1,1,2))].">
      <j1 rule="para" parents="5856 15654"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(L(u,w,K(z,y)),K(y,z) \ w)) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(14140(a,2),15818(a,1,2,2))].">
      <j1 rule="para" parents="14140 15818"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),w * T(y,K(z,u))),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(14664,a,14724,a)].">
      <j1 rule="hyper" parents="14664 14724"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(14597(a,1),15825(a,1,1,2))].">
      <j1 rule="para" parents="14597 15825"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      T(T(x,K(y,z * (z * T(u,z)))),y * ((z * z) * (T(u,z \ 1) \ 1))) = T(x,((z * z) * (T(u,z \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(12975(a,1),14856(a,1,1,2))].">
      <j1 rule="para" parents="12975 14856"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      T(T(x,K(y,z * (u * z))),y * ((z * z) * (T(u,z \ 1) \ 1))) = T(x,((z * z) * (T(u,z \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(109(a,1),15829(a,1,1,2,2,2))].">
      <j1 rule="para" parents="109 15829"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * ((u * u) * (T(z,u \ 1) \ 1))) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(14737(a,1),15830(a,1,1))].">
      <j1 rule="para" parents="14737 15830"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      a(x,y,z \ (z * x)) * K(T(y,x),1 / ((z * x) \ z)) = K(y * (1 / ((z * x) \ z)),1 / ((z * x) \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),15753(a,1,1,1))].">
      <j1 rule="para" parents="9 15753"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),1 / ((y * z) \ y))
    ]]></literal>
    <justification jstring="[para(9(a,1),15833(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 15833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),y \ (y * z))
    ]]></literal>
    <justification jstring="[para(5089(a,1),15834(a,2,2))].">
      <j1 rule="para" parents="5089 15834"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15835(a,2,2,2))].">
      <j1 rule="para" parents="9 15835"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4159(a,1),15836(a,2,2))].">
      <j1 rule="para" parents="4159 15836"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,8332,a(flip),b,15837,a),flip(a)].">
      <j1 rule="hyper" parents="319 8332 15837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(5256,a,15838,a)].">
      <j1 rule="hyper" parents="5256 15838"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15839(a,1,2))].">
      <j1 rule="para" parents="9 15839"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3877,a(flip),b,15840,a)].">
      <j1 rule="hyper" parents="64 3877 15840"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(7821,a,15841,a)].">
      <j1 rule="hyper" parents="7821 15841"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15842(a,2,1))].">
      <j1 rule="para" parents="10 15842"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8121,a(flip),b,15843,a),flip(a)].">
      <j1 rule="hyper" parents="64 8121 15843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(11322,a,15844,a)].">
      <j1 rule="hyper" parents="11322 15844"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7882,a(flip),b,15845,a)].">
      <j1 rule="hyper" parents="64 7882 15845"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9200,a(flip),b,15847,a)].">
      <j1 rule="hyper" parents="64 9200 15847"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15847(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      T(x * K(y \ x,y),(y * z) \ z) \ T(x,T((y * z) \ z,T(y,u))) = K(y,x * ((y * z) \ z))
    ]]></literal>
    <justification jstring="[para(15849(a,1),14853(a,1,1,1,2))].">
      <j1 rule="para" parents="15849 14853"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6547,a,b,15850,a),flip(a)].">
      <j1 rule="hyper" parents="319 6547 15850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,15852,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="131 15852 89"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7805,a,b,15853,a)].">
      <j1 rule="hyper" parents="64 7805 15853"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2719,a(flip),b,15854,a)].">
      <j1 rule="hyper" parents="64 2719 15854"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      K(((1 / (x \ y)) * ((z * (((y \ x) \ u) * (y \ x))) / (1 / (x \ y)))) \ u,w) = K(1 / z,T(w,u / (1 / (x \ y))))
    ]]></literal>
    <justification jstring="[para(15854(a,1),15566(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="15854 15566"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = ((x \ (x * y)) \ z) * (x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5071,a,b,15855,a)].">
      <j1 rule="hyper" parents="64 5071 15855"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3072,a(flip),b,15855,a)].">
      <j1 rule="hyper" parents="64 3072 15855"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = (y \ z) * (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),15857(a,2,1,1))].">
      <j1 rule="para" parents="9 15857"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = (y \ z) * y
    ]]></literal>
    <justification jstring="[hyper(319,a,154,a(flip),b,15859,a),flip(a)].">
      <j1 rule="hyper" parents="319 154 15859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(x,y * ((z * x) \ z)) = (((x \ y) * x) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(15860(a,1),13987(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15860 13987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x,y * ((z * x) \ z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,13984,a(flip),b,15862,a),flip(a)].">
      <j1 rule="hyper" parents="319 13984 15862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9091,a(flip),b,15863,a),flip(a)].">
      <j1 rule="hyper" parents="64 9091 15863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      K(x / y,(x \ y) * z) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(13063,a,15865,a),flip(a)].">
      <j1 rule="hyper" parents="13063 15865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15479,a,b,15866,a)].">
      <j1 rule="hyper" parents="64 15479 15866"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (x / y)) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),15868(a,1,2,2))].">
      <j1 rule="para" parents="9 15868"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      K((x / y) \ 1,z * (x / y)) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(5051,a,15869,a)].">
      <j1 rule="hyper" parents="5051 15869"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(7685,a,15870,a)].">
      <j1 rule="hyper" parents="7685 15870"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z * (y \ x))) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(15872(a,1),7311(a,1,1))].">
      <j1 rule="para" parents="15872 7311"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,x * z)) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(14880(a,1),15874(a,1,2))].">
      <j1 rule="para" parents="14880 15874"/>
    </justification>
  </clause>

  <clause id="15876">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z)) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(6706(a,1),15875(a,1,2))].">
      <j1 rule="para" parents="6706 15875"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13399,a(flip),b,15876,a),flip(a)].">
      <j1 rule="hyper" parents="64 13399 15876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(15877(a,1),5030(a,2,2))].">
      <j1 rule="para" parents="15877 5030"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(319,a,11631,a(flip),b,15878,a),flip(a)].">
      <j1 rule="hyper" parents="319 11631 15878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      T((x \ y) * x,(x * z) \ z) \ T(y,T((x * z) \ z,T(x,u))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(305(a,1),15851(a,1,1,1))].">
      <j1 rule="para" parents="305 15851"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,T((x * z) \ z,T(x,u))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(6330(a,1),15880(a,1,1))].">
      <j1 rule="para" parents="6330 15880"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,T((x * z) \ z,x)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(108(a,1),15881(a,1,2,2,2))].">
      <j1 rule="para" parents="108 15881"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,T(z \ (x \ z),x)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(7684(a,1),15882(a,1,2))].">
      <j1 rule="para" parents="7684 15882"/>
    </justification>
  </clause>

  <clause id="15884">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,z \ (x \ z)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(2763(a,1),15883(a,1,2))].">
      <j1 rule="para" parents="2763 15883"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      K(x,T(x \ y,z \ (x \ z))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(9407,a,15884,a)].">
      <j1 rule="hyper" parents="9407 15884"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      K(x,T(x \ y,z \ z)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8044,a(flip),b,15885,a)].">
      <j1 rule="hyper" parents="64 8044 15885"/>
    </justification>
  </clause>

  <clause id="15887">
    <literal><![CDATA[
      K(x,y * ((x * z) \ z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(213(a,1),15886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="213 15886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9040,a,b,15887,a)].">
      <j1 rule="hyper" parents="64 9040 15887"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      K(x,y * (z / (x * z))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9036,a(flip),b,15888,a)].">
      <j1 rule="hyper" parents="64 9036 15888"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6411,a(flip),b,15891,a),flip(a)].">
      <j1 rule="hyper" parents="64 6411 15891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(131,a,15893,a(flip),b,4242,a)].">
      <j1 rule="hyper" parents="131 15893 4242"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9361,a,b,15895,a)].">
      <j1 rule="hyper" parents="64 9361 15895"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      K(((x \ y) * ((z * (((x \ y) \ u) * (x \ y))) / (x \ y))) \ u,w) = K(1 / z,T(w,u / (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[para(15896(a,1),15856(a,1,1,1))].">
      <j1 rule="para" parents="15896 15856"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15568,a,15897,a),flip(a)].">
      <j1 rule="hyper" parents="15568 15897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15147,a,b,15898,a),flip(a)].">
      <j1 rule="hyper" parents="319 15147 15898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15464,a,b,15899,a)].">
      <j1 rule="hyper" parents="64 15464 15899"/>
    </justification>
  </clause>

  <clause id="15901">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(14423,a,15900,a),flip(a)].">
      <j1 rule="hyper" parents="14423 15900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = K(1 / x,T(y,(w / u) * z)) / x
    ]]></literal>
    <justification jstring="[para(15901(a,1),15465(a,2,1))].">
      <j1 rule="para" parents="15901 15465"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4211,a(flip),b,15902,a),flip(a)].">
      <j1 rule="hyper" parents="319 4211 15902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),T(u,(w / v5) * v6)),1 / x) = T(L(x,y,z),T(u,v6 / (v5 / T(w,v7))))
    ]]></literal>
    <justification jstring="[para(15903(a,1),2662(a,1,1))].">
      <j1 rule="para" parents="15903 2662"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      T(L(x,y,z),T(u,w / (v5 / T(v6,v7)))) = T(L(x,y,z),T(u,(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,2662,a(flip),b,15904,a),flip(a)].">
      <j1 rule="hyper" parents="64 2662 15904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = (T(L(v5,v6,v7),T(x,(u / z) * y)) \ 1) * L((v5 \ 1) \ 1,v6,v7)
    ]]></literal>
    <justification jstring="[para(15905(a,1),11868(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15905 11868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = K(T(x,(u / z) * y),L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(319,a,11868,a(flip),b,15906,a),flip(a)].">
      <j1 rule="hyper" parents="319 11868 15906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = K(x,T(L(v5,v6,v7),(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a(flip),b,15907,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 15907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / (v5 / T(v6,v7)))) = K(x,T(L(y,z,u),(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(6244,a,15908,a)].">
      <j1 rule="hyper" parents="6244 15908"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / (v5 / v6))) = K(x,T(L(y,z,u),(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15462,a(flip),b,15909,a)].">
      <j1 rule="hyper" parents="64 15462 15909"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),(T(w,v5) / v6) * v7)) = K(x,T(y,v7 / (v6 / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15463,a(flip),b,15910,a),flip(a)].">
      <j1 rule="hyper" parents="64 15463 15910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7541,a(flip),b,15911,a)].">
      <j1 rule="hyper" parents="64 7541 15911"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(108(a,1),15912(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="108 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(15174,a,15913,a)].">
      <j1 rule="hyper" parents="15174 15913"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6713,a,b,15914,a)].">
      <j1 rule="hyper" parents="319 6713 15914"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(35,a,15179,a,b,15916,a)].">
      <j1 rule="hyper" parents="35 15179 15916"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(7177,a,15917,a)].">
      <j1 rule="hyper" parents="7177 15917"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15209,a(flip),b,15917,a),flip(a)].">
      <j1 rule="hyper" parents="64 15209 15917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15208,a(flip),b,15917,a),flip(a)].">
      <j1 rule="hyper" parents="64 15208 15917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      L(K(x,K(y,(z / u) * w)),v5,v6) = K(y,K(w / (z \ u),L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(15917(a,1),15262(a,1,1))].">
      <j1 rule="para" parents="15917 15262"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(14236,a,15920,a)].">
      <j1 rule="hyper" parents="14236 15920"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),15922(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      K(x,K(y / (z \ u),L(w,v5,v6))) = K(x,K((z / u) * y,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(10138,a,15921,a),flip(a)].">
      <j1 rule="hyper" parents="10138 15921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / (y * (y \ z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,15353,a(flip),b,15924,a),flip(a)].">
      <j1 rule="hyper" parents="64 15353 15924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      K(x,K(((y / z) / y) * u,L(w,v5,v6))) = K(x,K(u / z,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(81(a,1),15924(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="81 15924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      K(x,K(y * ((z / u) / z),L(w,v5,v6))) = K(x,K(y / u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(14352,a,15926,a)].">
      <j1 rule="hyper" parents="14352 15926"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),15925(a,2,2,2,2))].">
      <j1 rule="para" parents="10 15925"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(319,a,15217,a,b,15928,a),flip(a)].">
      <j1 rule="hyper" parents="319 15217 15928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(y * u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(15928(a,2),15280(a,1))].">
      <j1 rule="para" parents="15928 15280"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * ((v5 / u) / v5)) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15927,a(flip),b,15929,a)].">
      <j1 rule="hyper" parents="64 15927 15929"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(u * y) / z)) = v5
    ]]></literal>
    <justification jstring="[para(15929(a,2),15280(a,1))].">
      <j1 rule="para" parents="15929 15280"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(y * (1 / u)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(12169(a,1),15930(a,1,2))].">
      <j1 rule="para" parents="12169 15930"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      K(x,K((y / z) / (1 / u),L(w,z,y))) = K(x,K(w,(T(y,u) / (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(3059(a,2),15931(a,2,2,2,1))].">
      <j1 rule="para" parents="3059 15931"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(15933,a,15931,a),flip(a)].">
      <j1 rule="hyper" parents="15933 15931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(T(y,u) / (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(12164(a,1),15934(a,1,2))].">
      <j1 rule="para" parents="12164 15934"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = v5
    ]]></literal>
    <justification jstring="[para(15936(a,1),15930(a,1))].">
      <j1 rule="para" parents="15936 15930"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(15937,a,15918,a),flip(a)].">
      <j1 rule="hyper" parents="15937 15918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(15356,a,15938,a)].">
      <j1 rule="hyper" parents="15356 15938"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15386,a,b,15939,a)].">
      <j1 rule="hyper" parents="64 15386 15939"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15381,a(flip),b,15939,a),flip(a)].">
      <j1 rule="hyper" parents="64 15381 15939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(15387,a,15940,a)].">
      <j1 rule="hyper" parents="15387 15940"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(15271,a,15941,a)].">
      <j1 rule="hyper" parents="15271 15941"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15935,a,b,15941,a)].">
      <j1 rule="hyper" parents="64 15935 15941"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13036,a,b,15943,a)].">
      <j1 rule="hyper" parents="64 13036 15943"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      K(x,K(y,((1 / z) * u) / (((1 / z) * u) * w))) = K(x,K(y,(z / u) * (((1 / z) * u) / w)))
    ]]></literal>
    <justification jstring="[para(9102(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="9102 15943"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      K(x,K(y,((z / (z / ((u / z) \ 1))) / w) * v5)) = K(x,K(y,v5 / (((z / (z / u)) / z) * w)))
    ]]></literal>
    <justification jstring="[para(13245(a,1),15943(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13245 15943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15271,a,15944,a)].">
      <j1 rule="hyper" parents="15271 15944"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13183,a(flip),b,15945,a)].">
      <j1 rule="hyper" parents="64 13183 15945"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (((1 / z) * u) / (((1 / z) * u) * w)))) = K(x,K(y,1 / (w * ((1 / z) * u))))
    ]]></literal>
    <justification jstring="[para(14532(a,1),15946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14532 15946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      K(x,K(y,((z / (z / ((u / z) \ 1))) / w) * v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,15948,a(flip),b,15947,a),flip(a)].">
      <j1 rule="hyper" parents="319 15948 15947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15942,a(flip),b,15951,a)].">
      <j1 rule="hyper" parents="64 15942 15951"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15280,a,15953,a)].">
      <j1 rule="hyper" parents="15280 15953"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15323,a(flip),b,15953,a)].">
      <j1 rule="hyper" parents="64 15323 15953"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(7177,a,15956,a)].">
      <j1 rule="hyper" parents="7177 15956"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15726,a(flip),b,15957,a),flip(a)].">
      <j1 rule="hyper" parents="64 15726 15957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x,K(y,(z * u) * ((w / u) / (z * w)))) = a(x,w,K(y,K(z,u / w)))
    ]]></literal>
    <justification jstring="[hyper(14235,a,15958,a)].">
      <j1 rule="hyper" parents="14235 15958"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,(u / z) * z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12725,a,b,15958,a),flip(a)].">
      <j1 rule="hyper" parents="319 12725 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,((y / w) / (u * y)) * (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(15958(a,1),6744(a,1))].">
      <j1 rule="para" parents="15958 6744"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(x,u,K(y,K(z / u,w / u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),15959(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 15959"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,u,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),15960(a,2,2))].">
      <j1 rule="para" parents="12 15960"/>
    </justification>
  </clause>

  <clause id="15964">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (((1 / z) * u) / (((1 / z) * u) * w)))) = K(x,K(y,w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7034,a(flip),b,15950,a),flip(a)].">
      <j1 rule="hyper" parents="319 7034 15950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15922,a(flip),b,15964,a),flip(a)].">
      <j1 rule="hyper" parents="64 15922 15964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,15918,a(flip),b,15965,a),flip(a)].">
      <j1 rule="hyper" parents="319 15918 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(264(a,1),15967(a,1,2,2,2))].">
      <j1 rule="para" parents="264 15967"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,15265,a(flip),b,15968,a),flip(a)].">
      <j1 rule="hyper" parents="319 15265 15968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      K(x,K(y,R(z / u,w,v5) * (w * v5))) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15744,a(flip),b,15969,a),flip(a)].">
      <j1 rule="hyper" parents="64 15744 15969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(105(a,1),15971(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 15971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15974">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15216,a,b,15973,a)].">
      <j1 rule="hyper" parents="64 15216 15973"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * T(v5,v6))) = K(x,K(y,v5 * (w * ((1 / u) * z))))
    ]]></literal>
    <justification jstring="[hyper(15355,a,15974,a),flip(a)].">
      <j1 rule="hyper" parents="15355 15974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(14525,a,15974,a)].">
      <j1 rule="hyper" parents="14525 15974"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(15355,a,15975,a),flip(a)].">
      <j1 rule="hyper" parents="15355 15975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(15359,a,15977,a)].">
      <j1 rule="hyper" parents="15359 15977"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10427,a(flip),b,15976,a),flip(a)].">
      <j1 rule="hyper" parents="319 10427 15976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,15954,a(flip),b,15979,a),flip(a)].">
      <j1 rule="hyper" parents="319 15954 15979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(7177,a,15980,a)].">
      <j1 rule="hyper" parents="7177 15980"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = K(x,K(y,a(w,1 / z,u)))
    ]]></literal>
    <justification jstring="[para(11911(a,1),15981(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11911 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(x,1 / z,K(y,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12613,a,b,15982,a),flip(a)].">
      <j1 rule="hyper" parents="319 12613 15982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13614,a(flip),b,14773,a),flip(a)].">
      <j1 rule="hyper" parents="64 13614 14773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      K(x,T(1 / (y / z),y) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[para(66(a,1),15984(a,1,2,1))].">
      <j1 rule="para" parents="66 15984"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(R(w,K(z,u),v5),L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(14351,a,15354,a),flip(a)].">
      <j1 rule="hyper" parents="14351 15354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(L(y,K(z,u) * v5,v6),K(z,u),v5)))
    ]]></literal>
    <justification jstring="[para(12791(a,1),15986(a,2,2))].">
      <j1 rule="para" parents="12791 15986"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15458,a(flip),b,15988,a),flip(a)].">
      <j1 rule="hyper" parents="319 15458 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * v5))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15388,a,15989,a)].">
      <j1 rule="hyper" parents="15388 15989"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15269,a(flip),b,15990,a)].">
      <j1 rule="hyper" parents="64 15269 15990"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) * v5,v6))) = K(x,K(y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15253,a(flip),b,15992,a),flip(a)].">
      <j1 rule="hyper" parents="64 15253 15992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15995">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,K(x,y)),K(v6,v7) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(15993(a,1),10157(a,1))].">
      <j1 rule="para" parents="15993 10157"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / v5,v6))) = K(x,K(y,L(z,1 / v5,v6)))
    ]]></literal>
    <justification jstring="[para(11924(a,1),15993(a,1,2,2,2))].">
      <j1 rule="para" parents="11924 15993"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / v5,v6))) = K(x,K(z,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(319,a,10221,a(flip),b,15996,a),flip(a)].">
      <j1 rule="hyper" parents="319 10221 15996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(v5,K(w,L(u,z,x))) * K(K(w,u),v5)
    ]]></literal>
    <justification jstring="[para(15997(a,1),15747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15997 15747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      L(K(x,K(y,z)),K(u,w) * v5,v6) = a(x,v5,K(v6,K(y,z))) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15995,a,12697,a(flip))].">
      <j1 rule="hyper" parents="15995 12697"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,K(v5,v6))) = a(x,u,K(w,K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(12698,a,15999,a)].">
      <j1 rule="hyper" parents="12698 15999"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(3985(a,1),16000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3985 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4116(a,1),16000(a,1,2))].">
      <j1 rule="para" parents="4116 16000"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K((1 / y) / w,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10441,a(flip),b,16001,a),flip(a)].">
      <j1 rule="hyper" parents="64 10441 16001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K(z,K(u,(1 / y) / w)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),16003(a,2,3))].">
      <j1 rule="para" parents="6748 16003"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K(z,K(u,w * y)))
    ]]></literal>
    <justification jstring="[para(10439(a,1),16004(a,2,3))].">
      <j1 rule="para" parents="10439 16004"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(u,K(w,z))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),16005(a,1,3,2,2))].">
      <j1 rule="para" parents="10 16005"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(6748(a,1),16006(a,1,3))].">
      <j1 rule="para" parents="6748 16006"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),16007(a,2,3,2,2))].">
      <j1 rule="para" parents="10 16007"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6748(a,1),16008(a,2,3))].">
      <j1 rule="para" parents="6748 16008"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(81(a,1),16009(a,1,2,2))].">
      <j1 rule="para" parents="81 16009"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),16010(a,1,3))].">
      <j1 rule="para" parents="6748 16010"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),16011(a,2,3))].">
      <j1 rule="para" parents="6748 16011"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(12897,a,16012,a)].">
      <j1 rule="hyper" parents="12897 16012"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),16013(a,2,3))].">
      <j1 rule="para" parents="6758 16013"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(v5,K(w,L(u,z,x))) * K(v5,K(w,u))
    ]]></literal>
    <justification jstring="[para(6757(a,1),15998(a,2,2))].">
      <j1 rule="para" parents="6757 15998"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(K(w,L(u,z,x)) * K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,9811,a(flip),b,16015,a),flip(a)].">
      <j1 rule="hyper" parents="319 9811 16015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(a(x,z * u,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(8620(a,1),16017(a,2,1))].">
      <j1 rule="para" parents="8620 16017"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = a(u,z,K(v5,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13026,a(flip),b,16018,a),flip(a)].">
      <j1 rule="hyper" parents="319 13026 16018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(K(u,w),v5)) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[para(15372(a,1),16019(a,1,2))].">
      <j1 rule="para" parents="15372 16019"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(v5,K(u,w))) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12605,a,b,16020,a)].">
      <j1 rule="hyper" parents="64 12605 16020"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      a(x,K(y,z) / z,K(u,K(w,v5))) = a(v5,z,K(u,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(10212,a,16021,a)].">
      <j1 rule="hyper" parents="10212 16021"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(175(a,1),16022(a,1,2,1))].">
      <j1 rule="para" parents="175 16022"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(u,z,K(y,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15983,a,b,16023,a)].">
      <j1 rule="hyper" parents="64 15983 16023"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16014,a(flip),b,16023,a)].">
      <j1 rule="hyper" parents="64 16014 16023"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(y,z,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12898,a,b,16025,a),flip(a)].">
      <j1 rule="hyper" parents="319 12898 16025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[para(6748(a,1),16024(a,2,3))].">
      <j1 rule="para" parents="6748 16024"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (1 / (K(w,1 / z) / w))) * (((1 / z) * (1 / (1 / w))) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(12223(a,1),16027(a,1,2,2,2,1))].">
      <j1 rule="para" parents="12223 16027"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,u * K(z,y)),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(12087(a,1),15492(a,1,2,2,1,2))].">
      <j1 rule="para" parents="12087 15492"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(K(y,z) * (u \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(15314(a,1),16029(a,1,2,2,1))].">
      <j1 rule="para" parents="15314 16029"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (1 / (K(w,1 / z) / w))) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(13167(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="13167 16028"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * K(1 / z,w))) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(12093(a,1),16031(a,1,2))].">
      <j1 rule="para" parents="12093 16031"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      K(x,K(y,(((z / u) / w) * K(w,1 / z)) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(5309(a,1),16032(a,1,2,2,1))].">
      <j1 rule="para" parents="5309 16032"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,K(y,(((z / u) / w) * K(w,1 / z)) * ((w / z) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,15978,a(flip),b,16033,a)].">
      <j1 rule="hyper" parents="64 15978 16033"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,1 / (K(z,1 / u) / z))))
    ]]></literal>
    <justification jstring="[hyper(15267,a,16034,a)].">
      <j1 rule="hyper" parents="15267 16034"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z * K(1 / u,z))))
    ]]></literal>
    <justification jstring="[para(5197(a,1),16035(a,2,3,2))].">
      <j1 rule="para" parents="5197 16035"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15200(a,1),16036(a,2,3))].">
      <j1 rule="para" parents="15200 16036"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15962,a(flip),b,16037,a)].">
      <j1 rule="hyper" parents="64 15962 16037"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w / (y \ z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(78(a,1),16038(a,1,3,2,1))].">
      <j1 rule="para" parents="78 16038"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w * (y / z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(15923(a,1),16040(a,1,3))].">
      <j1 rule="para" parents="15923 16040"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w * (y / z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(6742(a,1),16041(a,1,3))].">
      <j1 rule="para" parents="6742 16041"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w / z))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(15413(a,1),16042(a,1,3))].">
      <j1 rule="para" parents="15413 16042"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(12649,a,16043,a),flip(a)].">
      <j1 rule="hyper" parents="12649 16043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),16044(a,1,3))].">
      <j1 rule="para" parents="6758 16044"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16002,a,b,16045,a)].">
      <j1 rule="hyper" parents="64 16002 16045"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16026,a(flip),b,16046,a),flip(a)].">
      <j1 rule="hyper" parents="64 16026 16046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6742(a,1),16047(a,2,3))].">
      <j1 rule="para" parents="6742 16047"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(15961,a,16048,a)].">
      <j1 rule="hyper" parents="15961 16048"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),16049(a,2,3))].">
      <j1 rule="para" parents="6748 16049"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15963,a(flip),b,16050,a)].">
      <j1 rule="hyper" parents="64 15963 16050"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(7035(a,1),16051(a,1,3))].">
      <j1 rule="para" parents="7035 16051"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(6758(a,1),16052(a,2,3))].">
      <j1 rule="para" parents="6758 16052"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16048,a(flip),b,16053,a),flip(a)].">
      <j1 rule="hyper" parents="64 16048 16053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(z,K(x,w)) = L(K(z,K(x,w)),u,y)
    ]]></literal>
    <justification jstring="[para(16054(a,1),12693(a,1,1))].">
      <j1 rule="para" parents="16054 12693"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) = L(K(z,K(x,w)),u,y)
    ]]></literal>
    <justification jstring="[para(6742(a,1),16055(a,1,2))].">
      <j1 rule="para" parents="6742 16055"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(13099,a,16056,a),flip(a)].">
      <j1 rule="hyper" parents="13099 16056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(10205,a,16057,a)].">
      <j1 rule="hyper" parents="10205 16057"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,15949,a(flip),b,16058,a),flip(a)].">
      <j1 rule="hyper" parents="319 15949 16058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,v5 \ ((v5 / (w * u)) * (w * (u * z)))))
    ]]></literal>
    <justification jstring="[para(718(a,1),16058(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="718 16058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) = K(x,K(y,1 / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(5359(a,1),16058(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5359 16058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(15932,a,16059,a)].">
      <j1 rule="hyper" parents="15932 16059"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(16061(a,2),7176(a,1))].">
      <j1 rule="para" parents="16061 7176"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,((v5 / (w * u)) * (w * (u * z))) / v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,14076,a,b,16060,a),flip(a)].">
      <j1 rule="hyper" parents="319 14076 16060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,((v5 / (w * u)) / v5) * (w * (u * z))))
    ]]></literal>
    <justification jstring="[hyper(319,a,16062,a(flip),b,16064,a),flip(a)].">
      <j1 rule="hyper" parents="319 16062 16064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,(w * (u * z)) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15919,a(flip),b,16065,a),flip(a)].">
      <j1 rule="hyper" parents="319 15919 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,T(L(z,u,w),w * u)))
    ]]></literal>
    <justification jstring="[para(6951(a,1),16066(a,2,2))].">
      <j1 rule="para" parents="6951 16066"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14066,a(flip),b,16069,a),flip(a)].">
      <j1 rule="hyper" parents="319 14066 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5,w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13183,a(flip),b,16070,a)].">
      <j1 rule="hyper" parents="64 13183 16070"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(16063,a,16073,a),flip(a)].">
      <j1 rule="hyper" parents="16063 16073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(7419(a,1),16074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7419 16074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,7034,a(flip),b,16076,a),flip(a)].">
      <j1 rule="hyper" parents="319 7034 16076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,w / z))
    ]]></literal>
    <justification jstring="[hyper(14431,a,16078,a)].">
      <j1 rule="hyper" parents="14431 16078"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10150,a,16078,a)].">
      <j1 rule="hyper" parents="10150 16078"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,16078,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16078 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,16078,a(flip),b,4012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 16078 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(z,u,w) / y) = K(x,y \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(16078(a,1),7302(a,1,1))].">
      <j1 rule="para" parents="16078 7302"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(16078(a,1),10186(a,1,2))].">
      <j1 rule="para" parents="16078 10186"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16078(a,1),14245(a,1,1))].">
      <j1 rule="para" parents="16078 14245"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      K(x * K(y,z),L(x,u,w)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11385,a,16082,a)].">
      <j1 rule="hyper" parents="11385 16082"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,16082,a,b,8619,a),flip(a)].">
      <j1 rule="hyper" parents="126 16082 8619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      x * ((x \ y) * K(z,K(u,w))) = y * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,16082,a(flip),b,3642,a),flip(a)].">
      <j1 rule="hyper" parents="131 16082 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(16082(a,1),12811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16082 12811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(16082(a,1),12867(a,1,1))].">
      <j1 rule="para" parents="16082 12867"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(x,y) * (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(16082(a,1),13107(a,1,1))].">
      <j1 rule="para" parents="16082 13107"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(12645,a,16095,a)].">
      <j1 rule="hyper" parents="12645 16095"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,12613,a(flip),b,16095,a)].">
      <j1 rule="hyper" parents="64 12613 16095"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,16102,a)].">
      <j1 rule="hyper" parents="53 16102"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      K(x,K(a(y,z,u),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(7047,a,16106,a)].">
      <j1 rule="hyper" parents="7047 16106"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,16111,a)].">
      <j1 rule="hyper" parents="57 16111"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15610,a,16117,a)].">
      <j1 rule="hyper" parents="15610 16117"/>
    </justification>
  </clause>

  <clause id="16120">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9262,a,16117,a),flip(a)].">
      <j1 rule="hyper" parents="9262 16117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[para(11589(a,2),16117(a,1,2))].">
      <j1 rule="para" parents="11589 16117"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      x \ T(y * x,K(a(z,u,w),v5)) = T(y,K(v5,a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(16117(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="16117 13423"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(y,z,K(u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(6413,a,16124,a),flip(a)].">
      <j1 rule="hyper" parents="6413 16124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2178,a,16124,a),flip(a)].">
      <j1 rule="hyper" parents="2178 16124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13268,a,b,16124,a)].">
      <j1 rule="hyper" parents="64 13268 16124"/>
    </justification>
  </clause>

  <clause id="16130">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12635,a(flip),b,16124,a)].">
      <j1 rule="hyper" parents="64 12635 16124"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(55,a,16124,a)].">
      <j1 rule="hyper" parents="55 16124"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16124(a,1),291(a,1,2))].">
      <j1 rule="para" parents="16124 291"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(11566(a,2),16124(a,1,2))].">
      <j1 rule="para" parents="11566 16124"/>
    </justification>
  </clause>

  <clause id="16134">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16124(a,1),12637(a,1,1))].">
      <j1 rule="para" parents="16124 12637"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      R(x,y,T(z,K(u,w))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13266,a,16129,a)].">
      <j1 rule="hyper" parents="13266 16129"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(589,a,16129,a),flip(a)].">
      <j1 rule="hyper" parents="589 16129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16139">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (K(x,K(y,z)) * (u * (w * v5))) = L(v5,w,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,484,a,b,16129,a)].">
      <j1 rule="hyper" parents="64 484 16129"/>
    </justification>
  </clause>

  <clause id="16140">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(206,a,16129,a(flip),b,8249,a(flip))].">
      <j1 rule="hyper" parents="206 16129 8249"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      (a(K(x,y),z,u) \ w) * a(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[hyper(130,a,13282,a(flip),b,16129,a(flip))].">
      <j1 rule="hyper" parents="130 13282 16129"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(16129(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="16129 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(16129(a,1),51(a,2))].">
      <j1 rule="para" parents="16129 51"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ (x * (K(y,K(z,u)) * (w * v5))) = L(v5,K(y,K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(16129(a,1),484(a,2,1))].">
      <j1 rule="para" parents="16129 484"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16129(a,1),483(a,1,2,2,1))].">
      <j1 rule="para" parents="16129 483"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(16129(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="16129 482"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13303,a,16110,a)].">
      <j1 rule="hyper" parents="13303 16110"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10130,a,16110,a)].">
      <j1 rule="hyper" parents="10130 16110"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(6455,a,16110,a)].">
      <j1 rule="hyper" parents="6455 16110"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10118,a(flip),b,16110,a),flip(a)].">
      <j1 rule="hyper" parents="64 10118 16110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5388,a(flip),b,16110,a),flip(a)].">
      <j1 rule="hyper" parents="64 5388 16110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      K(x,y) \ (z * K(u,w)) = (K(x,y) \ z) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,16110,a(flip),b,4773,a),flip(a)].">
      <j1 rule="hyper" parents="131 16110 4773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,16110,a(flip),b,8821,a(flip))].">
      <j1 rule="hyper" parents="131 16110 8821"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      L(K(x,y),z,L(K(u,w),v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4716(a,1),16110(a,1,3))].">
      <j1 rule="para" parents="4716 16110"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13571,a(flip),b,16119,a),flip(a)].">
      <j1 rule="hyper" parents="64 13571 16119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(16119(a,1),6938(a,1))].">
      <j1 rule="para" parents="16119 6938"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12635(a,1),16119(a,1,2))].">
      <j1 rule="para" parents="12635 16119"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      T(x / L(y,z,K(u,w)),y) = L(y,z,K(u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,16130,a),flip(a)].">
      <j1 rule="hyper" parents="393 16130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      ((x * L(x \ y,z,u)) \ y) \ y = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13420,a(flip),b,16130,a)].">
      <j1 rule="hyper" parents="64 13420 16130"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      T(x,(y * K(z,L(u,w,v5))) / (v5 * w)) = T(x,y / (v5 * (w * K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,13407,a(flip),b,16130,a),flip(a)].">
      <j1 rule="hyper" parents="64 13407 16130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      T(x,T((K(y,z) * u) \ w,v5)) = T(x,T(u \ (K(y,z) \ w),v5))
    ]]></literal>
    <justification jstring="[para(565(a,1),16130(a,1,2))].">
      <j1 rule="para" parents="565 16130"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4378(a,1),16130(a,1,2))].">
      <j1 rule="para" parents="4378 16130"/>
    </justification>
  </clause>

  <clause id="16170">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9526(a,1),16130(a,1,2))].">
      <j1 rule="para" parents="9526 16130"/>
    </justification>
  </clause>

  <clause id="16171">
    <literal><![CDATA[
      K(x,T(y,z) / L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,u,K(w,v5)) \ y) = v6
    ]]></literal>
    <justification jstring="[para(16130(a,1),11127(a,1,2,1))].">
      <j1 rule="para" parents="16130 11127"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(7179,a,16133,a)].">
      <j1 rule="hyper" parents="7179 16133"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(16147(a,1),12942(a,2,1))].">
      <j1 rule="para" parents="16147 12942"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9526(a,1),16148(a,1,2))].">
      <j1 rule="para" parents="9526 16148"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(11407(a,1),16148(a,1,2))].">
      <j1 rule="para" parents="11407 16148"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(13262(a,1),16148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13262 16148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,K(y,z) \ w)) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(16149(a,1),15824(a,1,2,2))].">
      <j1 rule="para" parents="16149 15824"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7226,a,16172,a)].">
      <j1 rule="hyper" parents="7226 16172"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      R(x,y,T(z,T(u,w))) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6386(a,1),16136(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6386 16136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w \ K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(11407(a,1),16142(a,1)),flip(b)].">
      <j1 rule="para" parents="11407 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,L(x,u,w))) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6798,a(flip),b,16088,a),flip(a)].">
      <j1 rule="hyper" parents="319 6798 16088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(w,K(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      w * K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16088(a,1),291(a,1,2))].">
      <j1 rule="para" parents="16088 291"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(504(a,1),16088(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="504 16088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      T(x / L(K(y,z),u,w),K(y,z)) = L(K(y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(393,a,16134,a),flip(a)].">
      <j1 rule="hyper" parents="393 16134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(12830,a,16162,a),flip(a)].">
      <j1 rule="hyper" parents="12830 16162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7171,a,16162,a),flip(a)].">
      <j1 rule="hyper" parents="7171 16162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      K(x * K(y,L(x,z,u)),w) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10144,a,b,16162,a)].">
      <j1 rule="hyper" parents="64 10144 16162"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ (w * z))) = K(x,T(y,u \ T(w,z)))
    ]]></literal>
    <justification jstring="[para(509(a,1),16162(a,1,2,2))].">
      <j1 rule="para" parents="509 16162"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(16162(a,1),9329(a,1))].">
      <j1 rule="para" parents="16162 9329"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(12829(a,1),16162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12829 16162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(9328,a,16181,a),flip(a)].">
      <j1 rule="hyper" parents="9328 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11600,a,b,16131,a)].">
      <j1 rule="hyper" parents="64 11600 16131"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (L(K(y,z),u,w) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,10118,a(flip),b,16155,a),flip(a)].">
      <j1 rule="hyper" parents="64 10118 16155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      K(x,y) \ (z * L(K(u,w),v5,v6)) = (K(x,y) \ z) * L(K(u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(16155(a,1),12867(a,1,1))].">
      <j1 rule="para" parents="16155 12867"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      K(x,y / a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,u,w) \ y) = v5
    ]]></literal>
    <justification jstring="[para(6858(a,1),16161(a,1))].">
      <j1 rule="para" parents="6858 16161"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(12635(a,1),16161(a,1,2))].">
      <j1 rule="para" parents="12635 16161"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(13261(a,2),16161(a,1,2))].">
      <j1 rule="para" parents="13261 16161"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      T(x,L(y * K(z,u * w),u \ T(w * u,z),w)) = T(x,(y * T(w,u)) / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13404,a(flip),b,16170,a),flip(a)].">
      <j1 rule="hyper" parents="64 13404 16170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) = T(x,L(y,K(u * z,w),T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12747,a(flip),b,16170,a),flip(a)].">
      <j1 rule="hyper" parents="64 12747 16170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),(w * u) \ w,z)) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,13409,a(flip),b,16176,a),flip(a)].">
      <j1 rule="hyper" parents="64 13409 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      K(x,L((y / T(z,u)) / w,w,z)) = K(x,y / (w * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12804,a(flip),b,16176,a),flip(a)].">
      <j1 rule="hyper" parents="64 12804 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10817,a(flip),b,16176,a),flip(a)].">
      <j1 rule="hyper" parents="64 10817 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) * (u \ 1))) = K(x,L(y,z,R(w,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(777(a,1),16176(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="777 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(16176(a,1),13402(a,1,1,1))].">
      <j1 rule="para" parents="16176 13402"/>
    </justification>
  </clause>

  <clause id="16217">
    <literal><![CDATA[
      R(T(x / y,y * T(z,u)),y,T(z,u)) = (y * T(z,T(u,w))) \ (x * T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(14651,a,16184,a),flip(a)].">
      <j1 rule="hyper" parents="14651 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a,b,16204,a),flip(a)].">
      <j1 rule="hyper" parents="319 12524 16204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a(flip),b,16204,a),flip(a)].">
      <j1 rule="hyper" parents="319 12524 16204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(111(a,1),16204(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="111 16204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(6109(a,1),16204(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6109 16204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[para(9269(a,1),16204(a,1,3))].">
      <j1 rule="para" parents="9269 16204"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(9288(a,1),16204(a,1,3))].">
      <j1 rule="para" parents="9288 16204"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      K(((K(x,T(y,z)) * u) * w) / a(x,u,K(w,y)),v5) = K((u * w) * K(y,x),v5)
    ]]></literal>
    <justification jstring="[para(16204(a,1),14658(a,1,1,2))].">
      <j1 rule="para" parents="16204 14658"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(5377(a,1),16209(a,1))].">
      <j1 rule="para" parents="5377 16209"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(8056(a,1),16209(a,1,2))].">
      <j1 rule="para" parents="8056 16209"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(8935(a,1),16209(a,1))].">
      <j1 rule="para" parents="8935 16209"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(11407(a,1),16209(a,1,2))].">
      <j1 rule="para" parents="11407 16209"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,16220,a(flip),b,11571,a),flip(a)].">
      <j1 rule="hyper" parents="131 16220 11571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(9288(a,1),16220(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9288 16220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16220(a,2),12644(a,1))].">
      <j1 rule="para" parents="16220 12644"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(12644,a,16221,a)].">
      <j1 rule="hyper" parents="12644 16221"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[para(9269(a,1),16221(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9269 16221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      K(x,L(y \ z,u,K(w,v5)) \ 1) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = v6
    ]]></literal>
    <justification jstring="[para(5100(a,2),16227(a,1))].">
      <j1 rule="para" parents="5100 16227"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      K((x * K(y,z)) / (u * K(y,z)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(12834(a,1),16229(a,1))].">
      <j1 rule="para" parents="12834 16229"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13018,a(flip),b,16235,a)].">
      <j1 rule="hyper" parents="64 13018 16235"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10911,a(flip),b,16235,a),flip(a)].">
      <j1 rule="hyper" parents="64 10911 16235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16089(a,2),4089(a,1))].">
      <j1 rule="para" parents="16089 4089"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      (x \ T(L(y,z,u),y * K(w,v5))) * K(y,K(w,v5)) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,16094,a(flip),b,12362,a)].">
      <j1 rule="hyper" parents="131 16094 12362"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(13307,a,16173,a)].">
      <j1 rule="hyper" parents="13307 16173"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      K(L(x,y,z) * K(u,x),w) = K(L(x,y,z),T(w,u))
    ]]></literal>
    <justification jstring="[para(13066(a,1),16196(a,1,1,2))].">
      <j1 rule="para" parents="13066 16196"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16243(a,1),13301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16243 13301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * a(y,z,u)) = T(x,T(a(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[para(4036(a,1),16120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4036 16120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * (a(w,v5,v6) * u))) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[para(16120(a,1),15455(a,1,2,1,2))].">
      <j1 rule="para" parents="16120 15455"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(w,z,K(u,y)) * x
    ]]></literal>
    <justification jstring="[hyper(319,a,12556,a(flip),b,16127,a),flip(a)].">
      <j1 rule="hyper" parents="319 12556 16127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(11596,a,16128,a),flip(a)].">
      <j1 rule="hyper" parents="11596 16128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * z) = w * T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11572,a(flip),b,16128,a),flip(a)].">
      <j1 rule="hyper" parents="319 11572 16128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(12525(a,1),16128(a,1,1))].">
      <j1 rule="para" parents="12525 16128"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(z,y,K(u,x)) = v5
    ]]></literal>
    <justification jstring="[para(16128(a,2),12891(a,1))].">
      <j1 rule="para" parents="16128 12891"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (w * a(u,z,K(y,x))) = w
    ]]></literal>
    <justification jstring="[hyper(12683,a,16141,a)].">
      <j1 rule="hyper" parents="12683 16141"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      a(K(x,y),z,u) \ w = w * a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(10554,a,16141,a),flip(a)].">
      <j1 rule="hyper" parents="10554 16141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(12982,a,16177,a),flip(a)].">
      <j1 rule="hyper" parents="12982 16177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ (z \ w))) = v5
    ]]></literal>
    <justification jstring="[para(302(a,1),16208(a,1,2,2))].">
      <j1 rule="para" parents="302 16208"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      a(x,y,K(y * z,u \ w)) * K(x,(y * (w / u)) / ((z \ 1) * (w / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(16222(a,1),12916(a,1,1))].">
      <j1 rule="para" parents="16222 12916"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(16222(a,1),13112(a,1,1))].">
      <j1 rule="para" parents="16222 13112"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,(u * w) \ v5)) = K(x,L(y,z,v5 / (T(u,x) * w)))
    ]]></literal>
    <justification jstring="[para(16222(a,1),12676(a,1,2))].">
      <j1 rule="para" parents="16222 12676"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(13771,a,16223,a)].">
      <j1 rule="hyper" parents="13771 16223"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      K(x,y / z) * a(x,u,K(z \ y,w)) = K(x,L(y / z,u,w \ 1))
    ]]></literal>
    <justification jstring="[para(16223(a,1),12600(a,1,2))].">
      <j1 rule="para" parents="16223 12600"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(16223(a,1),13058(a,1,2))].">
      <j1 rule="para" parents="16223 13058"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K(z / (u / T(w,z)),v5))
    ]]></literal>
    <justification jstring="[para(12410(a,1),16225(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12410 16225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12543,a(flip),b,16231,a),flip(a)].">
      <j1 rule="hyper" parents="319 12543 16231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16231(a,2),12565(a,1))].">
      <j1 rule="para" parents="16231 12565"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5295(a,1),16271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5295 16271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(11489(a,1),16273(a,1,2))].">
      <j1 rule="para" parents="11489 16273"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(z / y) * x))
    ]]></literal>
    <justification jstring="[para(13794(a,1),16236(a,2,3))].">
      <j1 rule="para" parents="13794 16236"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      a(x * (T(y,z) / z),u,K(w,v5)) = a(w,u,K(v5,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(15473(a,1),16236(a,2,3))].">
      <j1 rule="para" parents="15473 16236"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12533,a,b,16240,a)].">
      <j1 rule="hyper" parents="319 12533 16240"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(16240(a,1),12013(a,1,2))].">
      <j1 rule="para" parents="16240 12013"/>
    </justification>
  </clause>

  <clause id="16280">
    <literal><![CDATA[
      (x * K(y,z)) / a((1 / u) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(16240(a,1),13233(a,1,2))].">
      <j1 rule="para" parents="16240 13233"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ (z * w))) = v5
    ]]></literal>
    <justification jstring="[para(13081(a,1),16241(a,1,2))].">
      <j1 rule="para" parents="13081 16241"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = a(x,y,K(z,u)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,13381,a,b,16250,a)].">
      <j1 rule="hyper" parents="64 13381 16250"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(12154,a,16254,a),flip(a)].">
      <j1 rule="hyper" parents="12154 16254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12717,a(flip),b,16274,a),flip(a)].">
      <j1 rule="hyper" parents="319 12717 16274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(13295,a,16285,a)].">
      <j1 rule="hyper" parents="13295 16285"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a,b,16286,a),flip(a)].">
      <j1 rule="hyper" parents="319 13261 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      L(a(x,y,z),y * z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13390,a(flip),b,16287,a),flip(a)].">
      <j1 rule="hyper" parents="64 13390 16287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ (K(y,z) * u) = L((x * y) \ u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6286,a(flip),b,16287,a)].">
      <j1 rule="hyper" parents="64 6286 16287"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(16278(a,1),12647(a,1))].">
      <j1 rule="para" parents="16278 12647"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(10109(a,2),16228(a,1))].">
      <j1 rule="para" parents="10109 16228"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14076,a(flip),b,16080,a),flip(a)].">
      <j1 rule="hyper" parents="319 14076 16080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      L(K(K(x,y),z) * ((u * w) \ v5),K(z,K(x,y)),u * w) = (u * (w * K(z,K(x,y)))) \ v5
    ]]></literal>
    <justification jstring="[para(16091(a,1),4379(a,2,1))].">
      <j1 rule="para" parents="16091 4379"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(14089(a,2),16093(a,2,2))].">
      <j1 rule="para" parents="14089 16093"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(127,a,14100,a,b,16097,a)].">
      <j1 rule="hyper" parents="127 14100 16097"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(127,a,16091,a(flip),b,16097,a)].">
      <j1 rule="hyper" parents="127 16091 16097"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(127,a,14101,a(flip),b,16097,a),flip(a)].">
      <j1 rule="hyper" parents="127 14101 16097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(127,a,4922,a(flip),b,16097,a),flip(a)].">
      <j1 rule="hyper" parents="127 4922 16097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      x * (K(y,K(z,u)) * (x \ w)) = w * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14089(a,2),16097(a,1,2))].">
      <j1 rule="para" parents="14089 16097"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16093,a(flip),b,16098,a),flip(a)].">
      <j1 rule="hyper" parents="319 16093 16098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(14089(a,1),16098(a,1,1))].">
      <j1 rule="para" parents="14089 16098"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(10(a,1),16137(a,2,2))].">
      <j1 rule="para" parents="10 16137"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6783(a,2),16137(a,2,2))].">
      <j1 rule="para" parents="6783 16137"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(6783(a,2),16140(a,1,1))].">
      <j1 rule="para" parents="6783 16140"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) / v5 = K(z,K(u,w)) * ((x * y) / v5)
    ]]></literal>
    <justification jstring="[para(16093(a,1),16140(a,1,1))].">
      <j1 rule="para" parents="16093 16140"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(4356(a,2),16150(a,2,2,2))].">
      <j1 rule="para" parents="4356 16150"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      K(x,(y * z) \ (K(u,y) * w)) = K(x,(T(y,u) * z) \ w)
    ]]></literal>
    <justification jstring="[para(4308(a,1),16150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4308 16150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(14632,a,16151,a)].">
      <j1 rule="hyper" parents="14632 16151"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = R(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(16153(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="16153 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = T(K(u,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(4772(a,1),16163(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4772 16163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15064,a(flip),b,16178,a),flip(a)].">
      <j1 rule="hyper" parents="319 15064 16178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(6815,a,16189,a),flip(a)].">
      <j1 rule="hyper" parents="6815 16189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w \ (u \ z))) = v5
    ]]></literal>
    <justification jstring="[para(16189(a,1),7179(a,1))].">
      <j1 rule="para" parents="16189 7179"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(14221,a,16200,a),flip(a)].">
      <j1 rule="hyper" parents="14221 16200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12630,a(flip),b,16239,a),flip(a)].">
      <j1 rule="hyper" parents="319 12630 16239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      K(L(x,y,z) * K(u,x),w) = K(x,L(T(w,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,10133,a(flip),b,16245,a),flip(a)].">
      <j1 rule="hyper" parents="319 10133 16245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(11602,a,16252,a)].">
      <j1 rule="hyper" parents="11602 16252"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      K(x,y) / T(z \ 1,a(u,w,v5)) = K(x,y) * T(z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(206,a,16324,a,b,11926,a)].">
      <j1 rule="hyper" parents="206 16324 11926"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12759,a(flip),b,16262,a),flip(a)].">
      <j1 rule="hyper" parents="64 12759 16262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(13261(a,2),16283(a,2,1))].">
      <j1 rule="para" parents="13261 16283"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),16292(a,1,2,2,2))].">
      <j1 rule="para" parents="12 16292"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(6787,a,16295,a)].">
      <j1 rule="hyper" parents="6787 16295"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(127,a,153,a(flip),b,16295,a)].">
      <j1 rule="hyper" parents="127 153 16295"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      K(x,y * (z * (K(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * v6)) = v7
    ]]></literal>
    <justification jstring="[para(16295(a,1),15094(a,1,2,2))].">
      <j1 rule="para" parents="16295 15094"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,16301,a)].">
      <j1 rule="hyper" parents="134 16301"/>
    </justification>
  </clause>

  <clause id="16335">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(127,a,14453,a,b,16301,a)].">
      <j1 rule="hyper" parents="127 14453 16301"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(127,a,14100,a,b,16301,a)].">
      <j1 rule="hyper" parents="127 14100 16301"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (w \ 1)) = u \ (w \ K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(127,a,11948,a(flip),b,16301,a),flip(a)].">
      <j1 rule="hyper" parents="127 11948 16301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ ((K(z,K(u,w)) * x) * (y * v5)) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(16302(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16302 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,16295,a(flip),b,16303,a),flip(a)].">
      <j1 rule="hyper" parents="319 16295 16303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) * v5) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[para(16303(a,2),14978(a,1,2))].">
      <j1 rule="para" parents="16303 14978"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      K(x,(T(y,K(z,u)) \ w) * v5) = K(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[para(6418(a,1),16340(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6418 16340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      K(x,K(y,z / u) * w) = K(x,K(y,u \ z) * w)
    ]]></literal>
    <justification jstring="[para(7299(a,1),16340(a,1,2,1))].">
      <j1 rule="para" parents="7299 16340"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / w) = v5
    ]]></literal>
    <justification jstring="[para(16306(a,2),6787(a,1))].">
      <j1 rule="para" parents="16306 6787"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,w) \ v5) / K(y,z))) \ v6) = K(x,v5 \ (K(w,u) \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,14993,a,b,16308,a)].">
      <j1 rule="hyper" parents="64 14993 16308"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ (K(y,z) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4313(a,1),16308(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4313 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      K(x,(y / z) \ (K(((z \ 1) / (y / z)) \ 1,u) \ w)) = K(x,(T(y,u) / z) \ w)
    ]]></literal>
    <justification jstring="[para(4818(a,1),16308(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4818 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      K(x,y \ (K(y / x,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(16308(a,1),6456(a,1))].">
      <j1 rule="para" parents="16308 6456"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (K(L(z,u,w),y) \ v6))
    ]]></literal>
    <justification jstring="[para(10096(a,2),16308(a,1,2,1,1))].">
      <j1 rule="para" parents="10096 16308"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15004,a,16317,a)].">
      <j1 rule="hyper" parents="15004 16317"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(129,a,16317,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16317 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ K(w,y))) = K(x,T(T(y,w),z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15036,a(flip),b,16317,a),flip(a)].">
      <j1 rule="hyper" parents="64 15036 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,L(v5,z,y)))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10183,a(flip),b,16317,a),flip(a)].">
      <j1 rule="hyper" parents="64 10183 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z \ u,z))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,7437,a(flip),b,16317,a),flip(a)].">
      <j1 rule="hyper" parents="64 7437 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(5163(a,1),16317(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5163 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) = K(x,T(y,u) * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(5982(a,2),16317(a,1,2,1))].">
      <j1 rule="para" parents="5982 16317"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,T(z,v5)))) = K(x,(y / T(z,T(w,v5))) / u)
    ]]></literal>
    <justification jstring="[para(6148(a,1),16317(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6148 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(16317(a,2),15075(a,1))].">
      <j1 rule="para" parents="16317 15075"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(14221,a,16320,a)].">
      <j1 rule="hyper" parents="14221 16320"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      K(K(x,y) * L(y,z,u),w) = K(y,L(T(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(14145,a,16323,a)].">
      <j1 rule="hyper" parents="14145 16323"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      K(L(x,y,z) * K(u \ 1,x),w / (v5 / (u * v5))) = K(x,L((v5 / (u * v5)) \ w,y,z))
    ]]></literal>
    <justification jstring="[para(3425(a,1),16323(a,2,2,1))].">
      <j1 rule="para" parents="3425 16323"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15212,a(flip),b,16328,a),flip(a)].">
      <j1 rule="hyper" parents="319 15212 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * (w / x)) = u * (w / T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(14246(a,1),16329(a,2,2))].">
      <j1 rule="para" parents="14246 16329"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(14316(a,1),16331(a,2,2))].">
      <j1 rule="para" parents="14316 16331"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      T(x,y \ (z * K(u,K(w,v5)))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(16334(a,2),14589(a,1,2))].">
      <j1 rule="para" parents="16334 14589"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,K(w,v5)))) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(1187(a,1),16367(a,1,2,2))].">
      <j1 rule="para" parents="1187 16367"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      T(x,y \ (T(z,K(u,w)) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(6418(a,1),16367(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6418 16367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      T(x,y \ T(z * K(u,K(w,v5)),v6)) = T(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[para(14453(a,2),16367(a,1,2,2))].">
      <j1 rule="para" parents="14453 16367"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(8095,a,16339,a)].">
      <j1 rule="hyper" parents="8095 16339"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(488,a,16339,a)].">
      <j1 rule="hyper" parents="488 16339"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      (x / (K(y,K(z,u)) * w)) * K(y,K(z,u)) = x / w
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,16339,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 16339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(y,K(z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(127,a,74,a(flip),b,16339,a)].">
      <j1 rule="hyper" parents="127 74 16339"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      (x * (y * (K(z,K(u,w)) * v5))) \ ((x * (y * K(z,K(u,w)))) * v5) = a(x,y * K(z,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(16339(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16339 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ (((x * K(y,K(z,u))) * w) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(16339(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16339 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * ((v6 * (z * K(u,K(w,v5)))) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(16339(a,1),15108(a,1,2,2,1))].">
      <j1 rule="para" parents="16339 15108"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(16091(a,1),16339(a,1,1))].">
      <j1 rule="para" parents="16091 16339"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      ((x * y) * (K(z,K(u,w)) * v5)) / ((y * K(z,K(u,w))) * v5) = R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(16371(a,1),528(a,1,1,1,2))].">
      <j1 rule="para" parents="16371 528"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(16372(a,1),51(a,2))].">
      <j1 rule="para" parents="16372 51"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      K(x,(L(T(y,K(z,u)),w,v5) \ v6) * v7) = K(x,(L(y,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),16341(a,1,2,1,1))].">
      <j1 rule="para" parents="25 16341"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14928,a(flip),b,16342,a),flip(a)].">
      <j1 rule="hyper" parents="64 14928 16342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(129,a,16352,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16352 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (T(z,u) \ u)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15446,a(flip),b,16352,a),flip(a)].">
      <j1 rule="hyper" parents="64 15446 16352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      T(x,y * (T(y / z,u) \ K(z,w))) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14938,a(flip),b,16353,a),flip(a)].">
      <j1 rule="hyper" parents="64 14938 16353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      K(x * K(y,z),T(u,K(y,z) \ (w / x))) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(14285,a,16361,a),flip(a)].">
      <j1 rule="hyper" parents="14285 16361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,((z * u) \ w) \ x) = K(y,x / ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(16364(a,1),7295(a,1,1))].">
      <j1 rule="para" parents="16364 7295"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,(T(u * z,u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(16364(a,1),11173(a,1,1))].">
      <j1 rule="para" parents="16364 11173"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      T(x,y \ ((z * K(u,w)) \ (v5 * (K(u,w) * z)))) = T(x,y \ T(v5,z))
    ]]></literal>
    <justification jstring="[para(14159(a,1),16368(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14159 16368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (y \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(16369(a,1),15823(a,1,1,2))].">
      <j1 rule="para" parents="16369 15823"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(127,a,16373,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="127 16373 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = (x \ w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14243,a(flip),b,16374,a),flip(a)].">
      <j1 rule="hyper" parents="319 14243 16374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ u) = K(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(6774(a,1),16374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6774 16374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(14243(a,2),16374(a,1,1))].">
      <j1 rule="para" parents="14243 16374"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,z * (T(z / y,u) \ K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14933,a(flip),b,16383,a)].">
      <j1 rule="hyper" parents="64 14933 16383"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / T(v5,u * (w \ K(y,z)))) * v6) = K(x,(v5 \ ((K(y,z) * u) / w)) * v6)
    ]]></literal>
    <justification jstring="[para(16383(a,1),15476(a,1,2,1,2))].">
      <j1 rule="para" parents="16383 15476"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(10(a,1),16392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 16392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      x / (y * K(z,K(u,w))) = (x / y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(206,a,202,a(flip),b,16393,a)].">
      <j1 rule="hyper" parents="206 202 16393"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = (u \ w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14089(a,2),16393(a,1,1))].">
      <j1 rule="para" parents="14089 16393"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      K(K(x,T(y,z)) \ u,w) = K(K(x,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(16394(a,1),14580(a,1,1))].">
      <j1 rule="para" parents="16394 14580"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ w) = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16305,a(flip),b,16395,a),flip(a)].">
      <j1 rule="hyper" parents="64 16305 16395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(16395(a,2),14981(a,1,2))].">
      <j1 rule="para" parents="16395 14981"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(14176(a,1),16405(a,1,2,1))].">
      <j1 rule="para" parents="14176 16405"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)) * w,v5) \ v6) = K(x,T(y * w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(14498(a,1),16405(a,1,2,1))].">
      <j1 rule="para" parents="14498 16405"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(16304(a,1),16405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16304 16405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(4100(a,1),16408(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4100 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(14176(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="14176 16408"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,K(w,v5)))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(14316(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="14316 16408"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,y \ ((z / K(u,w)) \ (v5 * (K(u,w) \ z)))) = K(x,y \ T(v5,z / K(u,w)))
    ]]></literal>
    <justification jstring="[para(14467(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="14467 16408"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) = K(x,y \ (K(z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(16394(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="16394 16408"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      x / T(y * K(z,K(u,w)),v5) = (x / T(y,v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(14453(a,2),16401(a,1,2))].">
      <j1 rule="para" parents="14453 16401"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      K(x,(y * (K(z,u) \ w)) \ v5) = K(x,(y * (w * K(u,z))) \ v5)
    ]]></literal>
    <justification jstring="[para(5173(a,1),16406(a,1,2,1,2))].">
      <j1 rule="para" parents="5173 16406"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      K(x,y \ (L(T(z,K(u,w)),v5,v6) * v7)) = K(x,y \ (L(z,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(25(a,2),16409(a,1,2,2,1))].">
      <j1 rule="para" parents="25 16409"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(6386(a,1),16409(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6386 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      K(x,y \ (z * L(T(u,K(w,v5)),v6,v7))) = K(x,y \ (z * L(u,v6,v7)))
    ]]></literal>
    <justification jstring="[para(25(a,2),16410(a,1,2,2,2))].">
      <j1 rule="para" parents="25 16410"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(16185,a,11546,a(flip))].">
      <j1 rule="hyper" parents="16185 11546"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(w * u) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(11274(a,1),16230(a,1,2))].">
      <j1 rule="para" parents="11274 16230"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(x,z)) = L(T(x,a(u,w,z)),y,z)
    ]]></literal>
    <justification jstring="[hyper(16255,a,12956,a)].">
      <j1 rule="hyper" parents="16255 12956"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(16255,a,12586,a)].">
      <j1 rule="hyper" parents="16255 12586"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ K(z,y),u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(12631(a,1),16290(a,1))].">
      <j1 rule="para" parents="12631 16290"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w)) * v5) / L(y,u,w))) = K(x,(T(L(y,u,w),z) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(4309(a,1),16159(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4309 16159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,(((z \ L(y,u,w)) * z) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(9227(a,1),16159(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9227 16159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      K(x,(K(y,L(z,u,w) \ 1) * (L(z,u,w) \ v5)) * z) = K(x,z * ((K(y,L(z,u,w) \ 1) * v5) / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(9647(a,1),16159(a,1,2,1))].">
      <j1 rule="para" parents="9647 16159"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      T(x * K(L(y,z,u),w),K(w,y)) = L(K(w,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(10104(a,1),16192(a,1,1))].">
      <j1 rule="para" parents="10104 16192"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16361,a(flip),b,16198,a)].">
      <j1 rule="hyper" parents="64 16361 16198"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z \ 1)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * a(y,z,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(16201(a,2),13919(a,1))].">
      <j1 rule="para" parents="16201 13919"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) \ (K(y,L(z,u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(12848(a,1),16237(a,1))].">
      <j1 rule="para" parents="12848 16237"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(12650,a,16267,a)].">
      <j1 rule="hyper" parents="12650 16267"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(14289(a,1),16433(a,1,3))].">
      <j1 rule="para" parents="14289 16433"/>
    </justification>
  </clause>

  <clause id="16435">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(w \ u,y))
    ]]></literal>
    <justification jstring="[para(16434(a,1),12673(a,2,2))].">
      <j1 rule="para" parents="16434 12673"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(16299(a,1),15018(a,1,2,2))].">
      <j1 rule="para" parents="16299 15018"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      T((x \ (y * z)) / ((K(u,w) * z) / K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(5305,a,16300,a)].">
      <j1 rule="hyper" parents="5305 16300"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(16300(a,1),14977(a,1,2))].">
      <j1 rule="para" parents="16300 14977"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      T(T(x,K(y,z)) * (u / x),w) = x * (T(u,w) / T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14681,a(flip),b,16365,a)].">
      <j1 rule="hyper" parents="64 14681 16365"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,u \ z) * z = (K(y,x) \ u) * (u \ T(z,K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13396,a(flip),b,16366,a)].">
      <j1 rule="hyper" parents="64 13396 16366"/>
    </justification>
  </clause>

  <clause id="16441">
    <literal><![CDATA[
      K(x * (y \ T(z,K(u,w))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ z),v5) = v6
    ]]></literal>
    <justification jstring="[para(16366(a,1),14630(a,1,1))].">
      <j1 rule="para" parents="16366 14630"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      K(x,y \ (K(z / u,w) \ v5)) = K(x,y \ (K(u \ z,w) \ v5))
    ]]></literal>
    <justification jstring="[para(6109(a,1),16413(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6109 16413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16443">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(9229(a,1),16417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9229 16417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11290,a(flip),b,16419,a),flip(a)].">
      <j1 rule="hyper" parents="64 11290 16419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16185,a,16444,a)].">
      <j1 rule="hyper" parents="16185 16444"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,9539,a(flip),b,16445,a),flip(a)].">
      <j1 rule="hyper" parents="64 9539 16445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      L(x,T(y,z),(z \ T(y,z \ y)) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(12886(a,1),16446(a,1,3))].">
      <j1 rule="para" parents="12886 16446"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(13094,a,16421,a(flip))].">
      <j1 rule="hyper" parents="13094 16421"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = (w * K(L(x,z,u),y)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,16428,a(flip),b,4367,a)].">
      <j1 rule="hyper" parents="127 16428 4367"/>
    </justification>
  </clause>

  <clause id="16450">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,15140,a(flip),b,16429,a),flip(a)].">
      <j1 rule="hyper" parents="319 15140 16429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (w * z)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[hyper(15176,a,16450,a)].">
      <j1 rule="hyper" parents="15176 16450"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      K((x * K(y,z)) * (u \ K(z,y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(14667(a,1),16238(a,1))].">
      <j1 rule="para" parents="14667 16238"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(15234(a,2),16281(a,1))].">
      <j1 rule="para" parents="15234 16281"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ T(K(u,z) \ y,x) = v5
    ]]></literal>
    <justification jstring="[para(16315(a,2),762(a,1))].">
      <j1 rule="para" parents="16315 762"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * (v5 \ u)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * (v5 \ T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(12365(a,1),16438(a,1,2,2,2))].">
      <j1 rule="para" parents="12365 16438"/>
    </justification>
  </clause>

  <clause id="16458">
    <literal><![CDATA[
      K(x \ T(y \ T(z,K(u,w)),v5),v6) = K((x \ K(y \ z,v5)) * (y \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(16441,a,14609,a),flip(a)].">
      <j1 rule="hyper" parents="16441 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(16117(a,1),16126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16117 16126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,22,a,b,16459,a),flip(a)].">
      <j1 rule="hyper" parents="319 22 16459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(16459(a,2),335(a,1))].">
      <j1 rule="para" parents="16459 335"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      T(x,y * K(a(z,u,w),v5)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(14417,a,16460,a)].">
      <j1 rule="hyper" parents="14417 16460"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(11570(a,2),16460(a,1,2,1))].">
      <j1 rule="para" parents="11570 16460"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(16254(a,1),16460(a,1,2))].">
      <j1 rule="para" parents="16254 16460"/>
    </justification>
  </clause>

  <clause id="16466">
    <literal><![CDATA[
      T(x,y * (z * T(u,a(w,v5,v6)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5362(a,1),16463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5362 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[hyper(206,a,16464,a(flip),b,4030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="206 16464 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(12701(a,1),16464(a,1,2))].">
      <j1 rule="para" parents="12701 16464"/>
    </justification>
  </clause>

  <clause id="16469">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(12926(a,1),16464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12926 16464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      (a(x,y,K(z,u)) \ T(w,v5)) / (a(u,y,K(z,x)) * w) = K(w,v5 * a(u,y,K(z,x)))
    ]]></literal>
    <justification jstring="[para(16464(a,1),12663(a,1,1,2))].">
      <j1 rule="para" parents="16464 12663"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(12527(a,1),16465(a,1,2))].">
      <j1 rule="para" parents="12527 16465"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      T(x,y * L(z,u,K(w,v5))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(13289(a,1),16465(a,1,2))].">
      <j1 rule="para" parents="13289 16465"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,4007,a,b,16467,a),flip(a)].">
      <j1 rule="hyper" parents="319 4007 16467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(16467(a,2),4117(a,1))].">
      <j1 rule="para" parents="16467 4117"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * K(w,v5) = T(a(x,y,K(z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(131,a,16475,a(flip),b,4012,a(flip))].">
      <j1 rule="hyper" parents="131 16475 4012"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(12701(a,1),16475(a,1,1))].">
      <j1 rule="para" parents="12701 16475"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(16253(a,1),16475(a,1,1))].">
      <j1 rule="para" parents="16253 16475"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12643,a(flip),b,16479,a)].">
      <j1 rule="hyper" parents="64 12643 16479"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,13437,a,b,16469,a),flip(a)].">
      <j1 rule="hyper" parents="319 13437 16469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (z * (w * K(y,z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,14926,a(flip),b,16469,a),flip(a)].">
      <j1 rule="hyper" parents="64 14926 16469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      T(x,((y * K(z,L(u,w,v5))) * v6) / a(K(z,L(u,w,v5)),T(y,K(z,L(u,w,v5))),v6)) = T(x,K(z,u) * (T(y,K(z,L(u,w,v5))) * v6))
    ]]></literal>
    <justification jstring="[para(706(a,2),16469(a,1,2))].">
      <j1 rule="para" parents="706 16469"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w)) * v5) = T(x,K(y,z) * (y * v5))
    ]]></literal>
    <justification jstring="[para(4081(a,1),16469(a,1,2))].">
      <j1 rule="para" parents="4081 16469"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w) \ (K(z,L(u,v5,v6)) * w)) = T(x,(K(z,L(u,v5,v6)) * w) / y)
    ]]></literal>
    <justification jstring="[para(16469(a,1),11182(a,1,2,1))].">
      <j1 rule="para" parents="16469 11182"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      T(x,K(R(y,z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(12791(a,2),16469(a,1,2,1))].">
      <j1 rule="para" parents="12791 16469"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      T(x,y * K(L(z,u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(14417,a,16482,a)].">
      <j1 rule="hyper" parents="14417 16482"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(12796(a,1),16482(a,1,2))].">
      <j1 rule="para" parents="12796 16482"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(16482(a,2),13489(a,1))].">
      <j1 rule="para" parents="16482 13489"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      (T(x,K(y,z) * u) * K(z,L(T(y,x),w,v5))) / (K(z,L(y,w,v5)) * x) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(16482(a,1),14723(a,1,1,1))].">
      <j1 rule="para" parents="16482 14723"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      T(x,K((y / z) / u,w) * v5) = T(x,K(y / (u * z),w) * v5)
    ]]></literal>
    <justification jstring="[para(303(a,1),16487(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="303 16487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(14231,a,16488,a)].">
      <j1 rule="hyper" parents="14231 16488"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * y))) = T(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(5360(a,1),16488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5360 16488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(5377(a,1),16494(a,1,2,1))].">
      <j1 rule="para" parents="5377 16494"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,11397,a,b,16496,a),flip(a)].">
      <j1 rule="hyper" parents="319 11397 16496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(127,a,16497,a(flip),b,4019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 16497 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      T(x,y * (z * K(u,T(w,v5)))) = T(x,K(w,u) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(14641,a,16468,a),flip(a)].">
      <j1 rule="hyper" parents="14641 16468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(14305,a,16468,a)].">
      <j1 rule="hyper" parents="14305 16468"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * w)) = T(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(14231,a,16468,a)].">
      <j1 rule="hyper" parents="14231 16468"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w * v5)) = T(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14904,a(flip),b,16468,a)].">
      <j1 rule="hyper" parents="64 14904 16468"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14888,a(flip),b,16468,a),flip(a)].">
      <j1 rule="hyper" parents="64 14888 16468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / z) * w)) = T(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14620,a(flip),b,16473,a),flip(a)].">
      <j1 rule="hyper" parents="64 14620 16473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((z \ u) * w)) = T(x,((y * (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(9629(a,1),16473(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9629 16473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7352,a(flip),b,16480,a),flip(a)].">
      <j1 rule="hyper" parents="64 7352 16480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      T(x,K(y,z) * ((y \ u) * w)) = T(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4314(a,1),16489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4314 16489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * K(y,z)) * w)) = T(x,T(u,K(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(6801(a,1),16489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6801 16489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 * v6) = v7
    ]]></literal>
    <justification jstring="[para(16489(a,2),16461(a,1))].">
      <j1 rule="para" parents="16489 16461"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * z))) = T(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),16500(a,2,2,2))].">
      <j1 rule="para" parents="4922 16500"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * w)) = T(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14624,a,b,16501,a),flip(a)].">
      <j1 rule="hyper" parents="319 14624 16501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      x \ T(x,K(y,z) \ (u * w)) = K(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(127,a,16512,a,b,4019,a(flip))].">
      <j1 rule="hyper" parents="127 16512 4019"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * (K(z,y) \ w))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(4365(a,1),16512(a,2,2,2))].">
      <j1 rule="para" parents="4365 16512"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) \ (v5 * v6)) = T(x,v5 * (L(K(y,z),u,w) \ v6))
    ]]></literal>
    <justification jstring="[para(10096(a,2),16512(a,2,2,2,1))].">
      <j1 rule="para" parents="10096 16512"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w)) * v5) = T(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(4081(a,1),16485(a,2,2))].">
      <j1 rule="para" parents="4081 16485"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      T(x,T(R(y,z,u) * w,y) * v5) = T(x,(w * R(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,14873,a(flip),b,16516,a),flip(a)].">
      <j1 rule="hyper" parents="64 14873 16516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,16498,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 16498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(16498(a,2),4106(a,1))].">
      <j1 rule="para" parents="16498 4106"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ v5) = K(x,K(w,y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(14443,a,16518,a)].">
      <j1 rule="hyper" parents="14443 16518"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,(K(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(12864(a,1),16520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12864 16520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      K(x,K(y,z) \ ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4285(a,1),16522(a,2,2,1))].">
      <j1 rule="para" parents="4285 16522"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      T(x,y * T(K(z,u) * w,v5)) = T(x,y * (K(z,u) * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15522,a(flip),b,16495,a)].">
      <j1 rule="hyper" parents="64 15522 16495"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      T(x,K(T(y,z),u) * (w * (v5 * T(y,z)))) = T(x,w * (v5 * T(T(y,u),z)))
    ]]></literal>
    <justification jstring="[para(23(a,1),16495(a,2,2,2,2))].">
      <j1 rule="para" parents="23 16495"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (K(y,z) * w))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(5926(a,1),16499(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5926 16499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16527">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(6434(a,1),16499(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6434 16499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16322,a(flip),b,16507,a),flip(a)].">
      <j1 rule="hyper" parents="64 16322 16507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(1 / (z \ y)) * x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[para(2655(a,1),16528(a,1,1,2))].">
      <j1 rule="para" parents="2655 16528"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      T(x,(T(y,z) \ u) * (K(y,z) * w)) = T(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16526,a(flip),b,16508,a),flip(a)].">
      <j1 rule="hyper" parents="64 16526 16508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      T(x,K(T(y,z),T(u,z)) * (w * (v5 * T(u,z)))) = T(x,w * (v5 * (K(u,y) * T(u,z))))
    ]]></literal>
    <justification jstring="[para(6869(a,1),16511(a,2,2,2,2))].">
      <j1 rule="para" parents="6869 16511"/>
    </justification>
  </clause>

  <clause id="16532">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(4106,a,16513,a)].">
      <j1 rule="hyper" parents="4106 16513"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15007,a(flip),b,16532,a),flip(a)].">
      <j1 rule="hyper" parents="319 15007 16532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w * K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(16532(a,2),15050(a,1))].">
      <j1 rule="para" parents="16532 15050"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(14214,a,16533,a)].">
      <j1 rule="hyper" parents="14214 16533"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(13491,a,16533,a)].">
      <j1 rule="hyper" parents="13491 16533"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * (w / y))) = K(x,u * (w / T(y,z)))
    ]]></literal>
    <justification jstring="[para(5163(a,1),16533(a,2,2,2))].">
      <j1 rule="para" parents="5163 16533"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ (v5 * v6)) = K(x,v5 * (v6 * L(K(w,y),z,u)))
    ]]></literal>
    <justification jstring="[para(10096(a,2),16533(a,2,2,2,2))].">
      <j1 rule="para" parents="10096 16533"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(12477,a,16535,a),flip(a)].">
      <j1 rule="hyper" parents="12477 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      K(x,(y * z) * K(u * (w \ v5),v5 \ w)) = K(x,y * (z * K((v5 \ w) \ u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(15850(a,1),16535(a,1,2,2))].">
      <j1 rule="para" parents="15850 16535"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6))) = K(x,(y * z) * K(u,v6))
    ]]></literal>
    <justification jstring="[hyper(15784,a,16536,a),flip(a)].">
      <j1 rule="hyper" parents="15784 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(15102,a,16536,a)].">
      <j1 rule="hyper" parents="15102 16536"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14986,a,b,16536,a),flip(a)].">
      <j1 rule="hyper" parents="319 14986 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12296,a(flip),b,16536,a),flip(a)].">
      <j1 rule="hyper" parents="319 12296 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[para(11948(a,1),16536(a,2,2,2))].">
      <j1 rule="para" parents="11948 16536"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (T(z,y) / w)) = v5
    ]]></literal>
    <justification jstring="[para(16536(a,2),15054(a,1))].">
      <j1 rule="para" parents="16536 15054"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K(x,y * (K(y \ 1,z) * u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(12284,a,16543,a),flip(a)].">
      <j1 rule="hyper" parents="12284 16543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(16543(a,1),5844(a,1))].">
      <j1 rule="para" parents="16543 5844"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (v5 * v6)) = K(x,v5 * (K(z,L(y,u,w)) * v6))
    ]]></literal>
    <justification jstring="[para(10133(a,1),16543(a,1,2,1))].">
      <j1 rule="para" parents="10133 16543"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(4081(a,1),16548(a,1,2,2))].">
      <j1 rule="para" parents="4081 16548"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(13722(a,1),16548(a,1))].">
      <j1 rule="para" parents="13722 16548"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,y) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(14759(a,1),16519(a,1))].">
      <j1 rule="para" parents="14759 16519"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(14421,a,16523,a)].">
      <j1 rule="hyper" parents="14421 16523"/>
    </justification>
  </clause>

  <clause id="16554">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(13491,a,16523,a)].">
      <j1 rule="hyper" parents="13491 16523"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4356(a,1),16523(a,1,2))].">
      <j1 rule="para" parents="4356 16523"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (y * w))) = T(x,u * (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(13489,a,16527,a)].">
      <j1 rule="hyper" parents="13489 16527"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      T(x,(y \ z) * (K(y,u) * w)) = T(x,(T(y,u) \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13720,a(flip),b,16530,a),flip(a)].">
      <j1 rule="hyper" parents="64 13720 16530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(12298(a,1),16539(a,1,2,2))].">
      <j1 rule="para" parents="12298 16539"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(15056,a,16558,a)].">
      <j1 rule="hyper" parents="15056 16558"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,T(u \ z,y)))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[para(9405(a,1),16559(a,1,2,2,2))].">
      <j1 rule="para" parents="9405 16559"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13454,a,16544,a)].">
      <j1 rule="hyper" parents="13454 16544"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,z \ u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,w)) = v5
    ]]></literal>
    <justification jstring="[para(16545(a,1),15787(a,1))].">
      <j1 rule="para" parents="16545 15787"/>
    </justification>
  </clause>

  <clause id="16563">
    <literal><![CDATA[
      K(x,y * (K(y \ 1,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16547(a,2),15308(a,1))].">
      <j1 rule="para" parents="16547 15308"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16533,a(flip),b,16553,a)].">
      <j1 rule="hyper" parents="64 16533 16553"/>
    </justification>
  </clause>

  <clause id="16565">
    <literal><![CDATA[
      K(x,(T(y,z) \ (y * u)) * w) = K(x,K(y,z) \ (u * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),16553(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 16553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      T(x,(T(y,L(z \ u,w,u / z)) \ v5) * v6) = T(x,(y \ v5) * (K(y,z \ u) * v6))
    ]]></literal>
    <justification jstring="[para(7320(a,1),16557(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7320 16557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16544,a(flip),b,16561,a)].">
      <j1 rule="hyper" parents="64 16544 16561"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(12287,a,16567,a),flip(a)].">
      <j1 rule="hyper" parents="12287 16567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15086,a(flip),b,16567,a),flip(a)].">
      <j1 rule="hyper" parents="319 15086 16567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K((z \ 1) * u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(12301(a,2),16568(a,2,2,2))].">
      <j1 rule="para" parents="12301 16568"/>
    </justification>
  </clause>

  <clause id="16571">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(12484(a,1),16564(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12484 16564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(K(y,z) \ u,w)) = K(w * (T(y,z) \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(16565(a,1),14360(a,1,1))].">
      <j1 rule="para" parents="16565 14360"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(14140(a,1),16534(a,1))].">
      <j1 rule="para" parents="14140 16534"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),z,K(x \ y,u)) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13304,a,b,16165,a)].">
      <j1 rule="hyper" parents="64 13304 16165"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(4356(a,2),16168(a,1,2,1,1))].">
      <j1 rule="para" parents="4356 16168"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(9328,a,16194,a),flip(a)].">
      <j1 rule="hyper" parents="9328 16194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16159,a(flip),b,16577,a),flip(a)].">
      <j1 rule="hyper" parents="319 16159 16577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(12560,a,16269,a),flip(a)].">
      <j1 rule="hyper" parents="12560 16269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(16230,a,16579,a)].">
      <j1 rule="hyper" parents="16230 16579"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * (x \ T(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16297(a,2),14103(a,1))].">
      <j1 rule="para" parents="16297 14103"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(14089(a,2),16298(a,1,2,2))].">
      <j1 rule="para" parents="14089 16298"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * T(z,a(v5,u,w))
    ]]></literal>
    <justification jstring="[para(13261(a,2),16325(a,1,2))].">
      <j1 rule="para" parents="13261 16325"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) * v5 = (x * w) * (K(y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(14089(a,2),16378(a,1,1,2))].">
      <j1 rule="para" parents="14089 16378"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,T(T(y,K(v5,v6)) * (((y \ 1) \ z) / y),u) \ w)
    ]]></literal>
    <justification jstring="[para(6491(a,2),16407(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6491 16407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16414(a,2),14977(a,1,2))].">
      <j1 rule="para" parents="16414 14977"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,v5) = a(x,y,K(z,u)) * T(w,v5)
    ]]></literal>
    <justification jstring="[hyper(4976,a,16477,a),flip(a)].">
      <j1 rule="hyper" parents="4976 16477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,v5) = T(w,v5) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,16128,a(flip),b,16588,a),flip(a)].">
      <j1 rule="hyper" parents="319 16128 16588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      T(x,y * (z * (u * K(w,z)))) = T(x,y * (T(z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16527,a(flip),b,16483,a),flip(a)].">
      <j1 rule="hyper" parents="64 16527 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      T(x,y * ((1 / z) * (u * K(w,z \ 1)))) = T(x,y * (T(1 / z,w) * u))
    ]]></literal>
    <justification jstring="[para(3886(a,1),16594(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3886 16594"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      T(x,K(y / (z * u),w) * v5) = T(x,K(z \ (y / u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,14663,a(flip),b,16493,a),flip(a)].">
      <j1 rule="hyper" parents="64 14663 16493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      T(x,y * (z * K(u,w \ v5))) = T(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16468,a(flip),b,16502,a),flip(a)].">
      <j1 rule="hyper" parents="64 16468 16502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * K(y,z)) * w)) = T(x,u * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14596,a(flip),b,16509,a),flip(a)].">
      <j1 rule="hyper" parents="319 14596 16509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16526,a(flip),b,16598,a)].">
      <j1 rule="hyper" parents="64 16526 16598"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[para(5172(a,1),16598(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5172 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      T(x,T(y * (K(z,u) * w),K(v5,v6))) = T(x,(y * K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14136,a,b,16600,a)].">
      <j1 rule="hyper" parents="319 14136 16600"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14599,a(flip),b,16600,a),flip(a)].">
      <j1 rule="hyper" parents="319 14599 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      T(x,(y * z) * (K(u,L(w,y,z)) * v5)) = T(x,((K(u,w) * y) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,14621,a(flip),b,16600,a),flip(a)].">
      <j1 rule="hyper" parents="64 14621 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,T(u * T(z / u,w),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15640,a(flip),b,16601,a),flip(a)].">
      <j1 rule="hyper" parents="64 15640 16601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      T(x,(y * K(z,T(u,w))) * v5) = T(x,K(u,z) * (y * v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,16499,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="319 16499 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) * v5) = T(x,K(z,y) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[para(12947(a,1),16606(a,1,2,1))].">
      <j1 rule="para" parents="12947 16606"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      T(x,((K(y * z,y) * u) * T(y,z)) * w) = T(x,(u * R(y,z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14951,a,b,16517,a)].">
      <j1 rule="hyper" parents="64 14951 16517"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      T(x,(T(y,z * T(K(u,w) * u,v5)) * (z * T(u,w))) * K(u,v5)) = T(x,((z * T(u,w)) * K(u,v5)) * R(y,z * T(u,w),K(u,v5)))
    ]]></literal>
    <justification jstring="[para(16524(a,2),9660(a,1,2,1,1))].">
      <j1 rule="para" parents="16524 9660"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(11249(a,1),16542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11249 16542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(15162,a,16576,a),flip(a)].">
      <j1 rule="hyper" parents="15162 16576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(K(u,z) \ y) / w) = v5
    ]]></literal>
    <justification jstring="[para(16612(a,1),7263(a,1))].">
      <j1 rule="para" parents="16612 7263"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(13261(a,2),16583(a,2,2))].">
      <j1 rule="para" parents="13261 16583"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      T(x,K(y \ (z / y),u) * w) = T(x,K(u,y \ (y \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14045,a(flip),b,16596,a),flip(a)].">
      <j1 rule="hyper" parents="64 14045 16596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z * K(v5,v6 * v7))) = T(x,(z / (1 / K(v5,v6 \ v7))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15799,a(flip),b,16597,a),flip(a)].">
      <j1 rule="hyper" parents="64 15799 16597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(16602(a,1),14174(a,1))].">
      <j1 rule="para" parents="16602 14174"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u \ z,w) * u)) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(12415,a,16607,a),flip(a)].">
      <j1 rule="hyper" parents="12415 16607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      T(x,K(y * (z / y),u) * w) = T(x,K(u,y \ (y \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14902,a(flip),b,16616,a)].">
      <j1 rule="hyper" parents="64 14902 16616"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * w) = T(x,K(u,T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(9298(a,1),16620(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9298 16620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * w) = T(x,K(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14655,a(flip),b,16621,a),flip(a)].">
      <j1 rule="hyper" parents="319 14655 16621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / z) * (w * w))) = T(x,u / T((w * w) \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14929,a(flip),b,16622,a),flip(a)].">
      <j1 rule="hyper" parents="64 14929 16622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),16622(a,1,2,1,2,2))].">
      <j1 rule="para" parents="9 16622"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      T(x,K(y,z * u) * (w * (y * v5))) = T(x,w * (T(y,z \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16556,a(flip),b,16625,a),flip(a)].">
      <j1 rule="hyper" parents="64 16556 16625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(16188,a,13111,a)].">
      <j1 rule="hyper" parents="16188 13111"/>
    </justification>
  </clause>

  <clause id="16628">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(L(w,u,z),v5))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(16627(a,1),15292(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16627 15292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * (u / z))) = K(x,w * (u / T(z,K(v5,v6) * y)))
    ]]></literal>
    <justification jstring="[para(16627(a,1),15777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16627 15777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) * (u \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(w,u,u \ 1))) = v5
    ]]></literal>
    <justification jstring="[para(16215(a,2),13002(a,1))].">
      <j1 rule="para" parents="16215 13002"/>
    </justification>
  </clause>

  <clause id="16631">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(12662,a,16265,a)].">
      <j1 rule="hyper" parents="12662 16265"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(16291,a,14830,a)].">
      <j1 rule="hyper" parents="16291 14830"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(12325,a,16326,a)].">
      <j1 rule="hyper" parents="12325 16326"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x,L(((y \ L(y,z,u)) \ 1) \ w,y,y * (y \ L(y,z,u)))) = K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w))
    ]]></literal>
    <justification jstring="[para(8426(a,1),16326(a,2,2,2,1))].">
      <j1 rule="para" parents="8426 16326"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((z / (T(y,z) \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(109(a,1),16633(a,1,2,3))].">
      <j1 rule="para" parents="109 16633"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(7302(a,1),16333(a,1,2,2,2))].">
      <j1 rule="para" parents="7302 16333"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z * u) * v7)) = v8
    ]]></literal>
    <justification jstring="[para(16378(a,2),16333(a,1,2,2))].">
      <j1 rule="para" parents="16378 16333"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(16420,a,12987,a)].">
      <j1 rule="hyper" parents="16420 12987"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),u * z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11779,a(flip),b,16638,a),flip(a)].">
      <j1 rule="hyper" parents="64 11779 16638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),16638(a,1,2,3,1))].">
      <j1 rule="para" parents="10 16638"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(12338(a,1),16638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12338 16638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(16638(a,1),12738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16638 12738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16640(a,1),10128(a,1,2))].">
      <j1 rule="para" parents="16640 10128"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z * (z \ (z / u))) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[para(16640(a,1),12850(a,1,1))].">
      <j1 rule="para" parents="16640 12850"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(12546(a,1),16631(a,1,1))].">
      <j1 rule="para" parents="12546 16631"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,w)) / u) = K(x,y / (u / T(z,w)))
    ]]></literal>
    <justification jstring="[para(16220(a,1),16631(a,1,1))].">
      <j1 rule="para" parents="16220 16631"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13081,a(flip),b,16641,a),flip(a)].">
      <j1 rule="hyper" parents="64 13081 16641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),16648(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 16648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),((z / u) \ w) \ u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,T(((u / z) * w) \ u,x)) = v5
    ]]></literal>
    <justification jstring="[para(16649(a,2),13047(a,1))].">
      <j1 rule="para" parents="16649 13047"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13074,a(flip),b,16643,a),flip(a)].">
      <j1 rule="hyper" parents="64 13074 16643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      (((T(x,K(y,z)) / u) \ x) / x) * (x * K(y,z)) = (x / u) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,12232,a(flip),b,16651,a),flip(a)].">
      <j1 rule="hyper" parents="319 12232 16651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      (x / y) \ (x * K(z,u)) = (y / x) * (x * K(z,u))
    ]]></literal>
    <justification jstring="[para(81(a,1),16651(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="81 16651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16654">
    <literal><![CDATA[
      K(x,(T((y \ z) / z,x) * (z * K(u,w))) * v5) = K(x,(y \ (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(16651(a,1),5969(a,2,2,1))].">
      <j1 rule="para" parents="16651 5969"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u * K(w,v5))) = K(x,y * ((u * K(w,v5)) * ((z \ u) / u)))
    ]]></literal>
    <justification jstring="[para(16651(a,1),14542(a,1,2,2,1))].">
      <j1 rule="para" parents="16651 14542"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(16132,a,16646,a)].">
      <j1 rule="hyper" parents="16132 16646"/>
    </justification>
  </clause>

  <clause id="16657">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((T(y,z) \ z) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(10851(a,1),16646(a,1,1,3,1))].">
      <j1 rule="para" parents="10851 16646"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(12919,a,16656,a)].">
      <j1 rule="hyper" parents="12919 16656"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ (L(K(y,z),u,w) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),16205(a,2,2,2))].">
      <j1 rule="para" parents="10 16205"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      (x \ L(T(y,y * K(z,u)),w,v5)) * K(y,K(z,u)) = x \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),16242(a,1,1,2))].">
      <j1 rule="para" parents="25 16242"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,w,K(u \ y,z)) = K(x,L((y * z) / u,w,z \ 1))
    ]]></literal>
    <justification jstring="[para(10296(a,1),16268(a,1,2))].">
      <j1 rule="para" parents="10296 16268"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(12172(a,1),16318(a,1,1))].">
      <j1 rule="para" parents="12172 16318"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / z) * (v5 \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(15096,a,16359,a),flip(a)].">
      <j1 rule="hyper" parents="15096 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16670">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,16357,a(flip),b,16669,a),flip(a)].">
      <j1 rule="hyper" parents="319 16357 16669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16671">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,(z / T(u,w)) / T(y,T(u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(15331,a,16670,a)].">
      <j1 rule="hyper" parents="15331 16670"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (z \ u),u) * w)
    ]]></literal>
    <justification jstring="[para(14289(a,1),16382(a,2,2,1))].">
      <j1 rule="para" parents="14289 16382"/>
    </justification>
  </clause>

  <clause id="16673">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(15167,a,16387,a)].">
      <j1 rule="hyper" parents="15167 16387"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(14221,a,16673,a)].">
      <j1 rule="hyper" parents="14221 16673"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      T(x,y \ T(z * K(K(u,w),v5),v5 * K(u,w))) = T(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(8889(a,2),16390(a,1,2,2))].">
      <j1 rule="para" parents="8889 16390"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,K(v7,L(T(z,K(u,w)),v5,v6)))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(4790(a,2),16418(a,1,2))].">
      <j1 rule="para" parents="4790 16418"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12557,a(flip),b,16435,a),flip(a)].">
      <j1 rule="hyper" parents="319 12557 16435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,10826,a(flip),b,16447,a)].">
      <j1 rule="hyper" parents="64 10826 16447"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      T(x,K(y,z) * ((y \ u) * w)) = T(x,((z * (y / z)) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(13627,a,16505,a)].">
      <j1 rule="hyper" parents="13627 16505"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      T(x,((y * (z / y)) \ u) * w) = T(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16508,a(flip),b,16680,a),flip(a)].">
      <j1 rule="hyper" parents="64 16508 16680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(T(z,w) \ u) * y) = T(x,y * ((w * (z / w)) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15257,a(flip),b,16681,a),flip(a)].">
      <j1 rule="hyper" parents="64 15257 16681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ (v5 * v6)) = T(x,v5 * (L(K(y,z),u,w) \ v6))
    ]]></literal>
    <justification jstring="[para(10096(a,2),16515(a,1,2,1))].">
      <j1 rule="para" parents="10096 16515"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,w),v5,v6))) = K(x,K(u,w) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(16552,a,16538,a),flip(a)].">
      <j1 rule="hyper" parents="16552 16538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * (w * y))) = K(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(4109(a,1),16684(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4109 16684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * T(w,y))) = K(x,u * (y \ (w * T(y,z))))
    ]]></literal>
    <justification jstring="[para(6252(a,1),16684(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6252 16684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      K(x,x * (y * T(z,u))) \ T(x,y * T(z,u)) = R(x,K(z,u) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(16686(a,1),14946(a,1,1))].">
      <j1 rule="para" parents="16686 14946"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      K(x,K(y,z) \ (x * T(y \ u,y))) \ T(x,u / T(y,z)) = R(x,y \ ((y \ u) * T(y,z)),x)
    ]]></literal>
    <justification jstring="[para(16687(a,2),14523(a,1,1))].">
      <j1 rule="para" parents="16687 14523"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      T(x,y / T((z * z) \ u,w)) = T(x,(y / T(u,w)) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16504,a(flip),b,16624,a),flip(a)].">
      <j1 rule="hyper" parents="64 16504 16624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      T(x,y / T((z * z) \ u,w)) = T(x,y * (T(u,w) \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12345,a(flip),b,16691,a),flip(a)].">
      <j1 rule="hyper" parents="319 12345 16691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      T(x,y * T(z \ (u * u),w)) = T(x,y * (T(z,w) \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14779,a(flip),b,16692,a)].">
      <j1 rule="hyper" parents="64 14779 16692"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) = T(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16556,a(flip),b,16626,a),flip(a)].">
      <j1 rule="hyper" parents="64 16556 16626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      T(x,y * (T(z,u * u) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(213(a,1),16694(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="213 16694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      T(x,y * (((z * z) \ u) * w)) = T(x,y * (u * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[para(700(a,1),16695(a,1,2,2))].">
      <j1 rule="para" parents="700 16695"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) * ((u * u) \ w))) = T(x,y * ((1 / T(u,z)) * w))
    ]]></literal>
    <justification jstring="[para(5224(a,1),16696(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5224 16696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      (x \ L(T(y,K(z,u)),w,v5)) * K(y,K(z,u)) = x \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(11374(a,1),16666(a,1,1,2,1))].">
      <j1 rule="para" parents="11374 16666"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(x,u,w) = x \ L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(14249,a,16699,a),flip(a)].">
      <j1 rule="hyper" parents="14249 16699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(6815,a,16668,a),flip(a)].">
      <j1 rule="hyper" parents="6815 16668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      T(x,T(T(y * z,u) \ (y * y),w)) = T(x,T((z * K(y * z,u)) \ y,w))
    ]]></literal>
    <justification jstring="[para(12043(a,1),16701(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12043 16701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,15786,a(flip),b,16672,a),flip(a)].">
      <j1 rule="hyper" parents="319 15786 16672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * (u / (y / z)))) = K(x,w * T((y / z) \ u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15641,a(flip),b,16703,a),flip(a)].">
      <j1 rule="hyper" parents="64 15641 16703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      T(x,y \ T(z * K(u,K(w,v5)),v5 * K(u,w))) = T(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(6705(a,1),16676(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6705 16676"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      T(x,y * (L(K(z,u),w,v5) \ v6)) = T(x,K(z,u) \ (y * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,16497,a(flip),b,16683,a),flip(a)].">
      <j1 rule="hyper" parents="64 16497 16683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      T(x,y \ T(z,u * K(w,v5))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16370,a(flip),b,16705,a)].">
      <j1 rule="hyper" parents="64 16370 16705"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) \ T(v5,y)) = T(x,v5 / T(y * K(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14648,a(flip),b,16709,a),flip(a)].">
      <j1 rule="hyper" parents="64 14648 16709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4356(a,2),16101(a,1,2))].">
      <j1 rule="para" parents="4356 16101"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      T(x,y * ((z * u) \ K(w,L(v5,u,z)))) = T(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16353,a(flip),b,16166,a)].">
      <j1 rule="hyper" parents="64 16353 16166"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(16510,a,16247,a),flip(a)].">
      <j1 rule="hyper" parents="16510 16247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16717">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u * a(w,v5,v6)) \ z) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,T(a(w,v5,v6),v8) * u)) = v7
    ]]></literal>
    <justification jstring="[para(16716(a,1),14183(a,1,2,1))].">
      <j1 rule="para" parents="16716 14183"/>
    </justification>
  </clause>

  <clause id="16718">
    <literal><![CDATA[
      K(x,y \ (K(x \ y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(16442(a,1),16347(a,1))].">
      <j1 rule="para" parents="16442 16347"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      (K(x,y) \ z) * (z \ T(u,K(x,y))) = (u / z) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9631,a(flip),b,16440,a),flip(a)].">
      <j1 rule="hyper" parents="64 9631 16440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,((z / y) * (y * K(w,u))) \ v5,x)
    ]]></literal>
    <justification jstring="[para(16719(a,1),11424(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16719 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      T(x * L(x \ y,z,z \ 1),y) = x * L(x \ y,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(9568,a,16575,a),flip(a)].">
      <j1 rule="hyper" parents="9568 16575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      T(x * L(x \ y,z,z \ 1),y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ y,z,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(16575(a,1),9568(a,1))].">
      <j1 rule="para" parents="16575 9568"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      (x * K(y,z)) * L(u,x,K(y,z)) = K(z,T(y,x)) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16394,a(flip),b,16712,a),flip(a)].">
      <j1 rule="hyper" parents="64 16394 16712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ (u * (w / u)),x) = a(x,w * K(z,y),x)
    ]]></literal>
    <justification jstring="[para(16723(a,1),13324(a,1,2))].">
      <j1 rule="para" parents="16723 13324"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(12561,a,16266,a),flip(a)].">
      <j1 rule="hyper" parents="12561 16266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16230,a,16725,a)].">
      <j1 rule="hyper" parents="16230 16725"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(16726(a,1),12907(a,1,1))].">
      <j1 rule="para" parents="16726 12907"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(16580(a,1),16727(a,1,1))].">
      <j1 rule="para" parents="16580 16727"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(16728(a,1),12797(a,1))].">
      <j1 rule="para" parents="16728 12797"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,T(x,z)) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(16729,a,15288,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16729 15288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K((u / T(w,z)) \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,16223,a(flip),b,16270,a),flip(a)].">
      <j1 rule="hyper" parents="319 16223 16270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,T(w,v5)) \ v6) / K(y,z))) \ v7) = K(x,v6 \ (K(w,T(u,v5)) \ v7))
    ]]></literal>
    <justification jstring="[para(6102(a,1),16344(a,1,2,1,2,1,1))].">
      <j1 rule="para" parents="6102 16344"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,T(T(y \ z,u) \ z,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,16386,a(flip),b,16397,a),flip(a)].">
      <j1 rule="hyper" parents="319 16386 16397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      K(x \ T(y \ T(z,K(u,w)),v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y \ z,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(16458(a,2),12243(a,1))].">
      <j1 rule="para" parents="16458 12243"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      K(x \ T(y \ (T(y,K(z,u)) * w),w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(16734,a,15827,a)].">
      <j1 rule="hyper" parents="16734 15827"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * T(z,v5)))) = T(x,u * (w * T(T(z,y),v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14660,a(flip),b,16525,a)].">
      <j1 rule="hyper" parents="64 14660 16525"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * K(w,z \ 1)))) = T(x,y * (T(1 / z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3778,a(flip),b,16595,a)].">
      <j1 rule="hyper" parents="64 3778 16595"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13590,a(flip),b,16619,a)].">
      <j1 rule="hyper" parents="64 13590 16619"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      ((x * K(K(y,z),u)) / u) * (u * K(y,z)) = (u / x) \ (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(12364(a,1),16652(a,1,1,1))].">
      <j1 rule="para" parents="12364 16652"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      (x / T(y,K(z,u))) * (y * K(z,u)) = (y / x) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(5146(a,1),16740(a,1,1))].">
      <j1 rule="para" parents="5146 16740"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      (x / y) \ (K(z,u) * x) = (y / x) * (K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(8903,a,16741,a),flip(a)].">
      <j1 rule="hyper" parents="8903 16741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      ((x \ y) / y) * (K(z,u) * y) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(78(a,1),16742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 16742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,4303,a(flip),b,16743,a)].">
      <j1 rule="hyper" parents="128 4303 16743"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,12419,a(flip),b,16744,a)].">
      <j1 rule="hyper" parents="64 12419 16744"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      L(K(x,y) * (((x \ z) / z) \ u),K(y,x),(x \ z) / z) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[para(16745(a,1),4379(a,2,1))].">
      <j1 rule="para" parents="16745 4379"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15068,a(flip),b,16671,a),flip(a)].">
      <j1 rule="hyper" parents="319 15068 16671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(u,z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(16682(a,1),15256(a,1))].">
      <j1 rule="para" parents="16682 15256"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) * ((u * u) \ w))) = T(x,y * ((T(u,z) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,3778,a(flip),b,16697,a),flip(a)].">
      <j1 rule="hyper" parents="319 3778 16697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z * y),u))
    ]]></literal>
    <justification jstring="[para(12127(a,1),16702(a,2,2,1))].">
      <j1 rule="para" parents="12127 16702"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,y * z),u))
    ]]></literal>
    <justification jstring="[para(3327(a,1),16750(a,2,2,1,2))].">
      <j1 rule="para" parents="3327 16750"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11403,a(flip),b,16751,a),flip(a)].">
      <j1 rule="hyper" parents="319 11403 16751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11336,a(flip),b,16752,a),flip(a)].">
      <j1 rule="hyper" parents="319 11336 16752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(11402,a,16753,a)].">
      <j1 rule="hyper" parents="11402 16753"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      T(K(x,T(y,T(z / u,w)) * v5),v5 \ T(v5 * T(y,T(z / u,w)),x)) = (v5 \ T(v5 * T(y,T(z / u,w)),x)) \ T(y,T((u * z) \ (z * z),w))
    ]]></literal>
    <justification jstring="[hyper(417,a,16754,a,b,12141,a)].">
      <j1 rule="hyper" parents="417 16754 12141"/>
    </justification>
  </clause>

  <clause id="16756">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K(T(w,u) / (z / u),v5))
    ]]></literal>
    <justification jstring="[para(14331(a,1),16731(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14331 16731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K((z / u) \ T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,16223,a(flip),b,16756,a),flip(a)].">
      <j1 rule="hyper" parents="319 16223 16756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      T(x,y * (T(1 / z,u) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16594,a(flip),b,16738,a),flip(a)].">
      <j1 rule="hyper" parents="64 16594 16738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16759">
    <literal><![CDATA[
      T(x,y * T(T(z,T(u,y)) / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16605,a(flip),b,16739,a),flip(a)].">
      <j1 rule="hyper" parents="64 16605 16739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z * z) \ w))) = T(x,y * ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13715,a(flip),b,16749,a)].">
      <j1 rule="hyper" parents="64 13715 16749"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * ((K(u,T(x,w)) * y) * z),v5) = K((y * z) * K(x,u),v5)
    ]]></literal>
    <justification jstring="[para(16250(a,1),16226(a,1,1))].">
      <j1 rule="para" parents="16250 16226"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = L(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,15706,a(flip),b,16312,a),flip(a)].">
      <j1 rule="hyper" parents="319 15706 16312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(w,L(v5,u,z)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(10133(a,1),16628(a,1,2,2,2))].">
      <j1 rule="para" parents="10133 16628"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,y * z)))) = K(x,y * (z / T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(10283(a,1),16629(a,1,2))].">
      <j1 rule="para" parents="10283 16629"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(15335,a,16765,a),flip(a)].">
      <j1 rule="hyper" parents="15335 16765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / T(v5,w))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11212,a(flip),b,16766,a),flip(a)].">
      <j1 rule="hyper" parents="64 11212 16766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(4789,a,16642,a)].">
      <j1 rule="hyper" parents="4789 16642"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(331,a,16644,a)].">
      <j1 rule="hyper" parents="331 16644"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      (K(x,y) * z) \ ((K(x,y) * z) / u) = z \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(127,a,13076,a(flip),b,16770,a(flip))].">
      <j1 rule="hyper" parents="127 13076 16770"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (K(z,u) * x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(9241,a,16773,a)].">
      <j1 rule="hyper" parents="9241 16773"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (x * K(z,u))) = x / y
    ]]></literal>
    <justification jstring="[para(5933(a,1),16774(a,1,2,3,2))].">
      <j1 rule="para" parents="5933 16774"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      x * L((y \ (x * K(z,u))) \ 1,y \ (x * K(z,u)),y) = x / (y \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[para(9537(a,1),16775(a,1,2))].">
      <j1 rule="para" parents="9537 16775"/>
    </justification>
  </clause>

  <clause id="16777">
    <literal><![CDATA[
      R(x,K(y,z) \ (u * y),x) = R(x,u * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4461,a(flip),b,16688,a),flip(a)].">
      <j1 rule="hyper" parents="64 4461 16688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16778">
    <literal><![CDATA[
      R(x,y * (y \ (K(y,z) \ u)),x) = R(x,(y \ u) * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11513,a(flip),b,16777,a)].">
      <j1 rule="hyper" parents="64 11513 16777"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      R(x,y * (y \ (K(y,z) \ u)),x) = R(x,y \ (T(y,z) * u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11512,a,b,16778,a),flip(a)].">
      <j1 rule="hyper" parents="319 11512 16778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      R(x,y \ (T(y,z) * u),x) = R(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),16779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 16779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      a(x,y \ (T(y,z) * u),x) = R(x,K(y,z) \ u,x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,16780,a(flip),b,8319,a),flip(a)].">
      <j1 rule="hyper" parents="128 16780 8319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      a(x,y \ (T(y,z) * u),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8316,a(flip),b,16781,a),flip(a)].">
      <j1 rule="hyper" parents="319 8316 16781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      a(x,K(y,z) \ u,x) = a(x,K(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[para(4427(a,1),16783(a,1,2))].">
      <j1 rule="para" parents="4427 16783"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      a(x,K(y,z) \ (y * u),x) = a(x,T(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(4308(a,1),16784(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4308 16784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      a(x,K(y \ (y / z),u) \ ((y \ (y / z)) * w),x) = a(x,T(T(y \ (y / z),u),z \ 1) * w,x)
    ]]></literal>
    <justification jstring="[para(5053(a,2),16785(a,2,2,1))].">
      <j1 rule="para" parents="5053 16785"/>
    </justification>
  </clause>

  <clause id="16787">
    <literal><![CDATA[
      K((K(x,T(y,z)) * u) * w,v5) = K((u * w) * K(y,x),v5)
    ]]></literal>
    <justification jstring="[hyper(16476,a,16762,a)].">
      <j1 rule="hyper" parents="16476 16762"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K((z * u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[para(108(a,1),16787(a,1,1,1,1,2))].">
      <j1 rule="para" parents="108 16787"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (u * K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,16478,a(flip),b,16789,a),flip(a)].">
      <j1 rule="hyper" parents="319 16478 16789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      K((x \ K(y,z)) \ u,w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(12265,a,16790,a)].">
      <j1 rule="hyper" parents="12265 16790"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) = K(y * (K(u,z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(9296,a,16790,a),flip(a)].">
      <j1 rule="hyper" parents="9296 16790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K((x \ K(y,y * z)) * (u * K(y,y * z)),w) = K(T(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11320,a(flip),b,16792,a),flip(a)].">
      <j1 rule="hyper" parents="64 11320 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = K(x * (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(15151,a,16793,a)].">
      <j1 rule="hyper" parents="15151 16793"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      K(x * (K(y,z) * (u \ K(y,z))),w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[hyper(16454,a,16795,a),flip(a)].">
      <j1 rule="hyper" parents="16454 16795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K((K(u,w) * (y \ K(u,w))) * x,z)
    ]]></literal>
    <justification jstring="[hyper(14345,a,16796,a),flip(a)].">
      <j1 rule="hyper" parents="14345 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K((K(x,y) * (z \ K(x,y))) * u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(6352,a,16797,a),flip(a)].">
      <j1 rule="hyper" parents="6352 16797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      K((x \ K(y,z)) * (u * K(z,y)),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16790,a(flip),b,16798,a)].">
      <j1 rule="hyper" parents="64 16790 16798"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(10190(a,1),16764(a,1,2,2))].">
      <j1 rule="para" parents="10190 16764"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (u * z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(12733(a,1),16216(a,1,1,1))].">
      <j1 rule="para" parents="12733 16216"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      ((K(x,y) * z) * T(u,z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(12795(a,1),16801(a,1,1))].">
      <j1 rule="para" parents="12795 16801"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,8464,a(flip),b,16803,a)].">
      <j1 rule="hyper" parents="64 8464 16803"/>
    </justification>
  </clause>

  <clause id="16806">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(538(a,1),16804(a,2,2))].">
      <j1 rule="para" parents="538 16804"/>
    </justification>
  </clause>

  <clause id="16807">
    <literal><![CDATA[
      x \ R(K(y,z) * (K(z,y) * x),u,u \ 1) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(16804(a,2),13373(a,1,2))].">
      <j1 rule="para" parents="16804 13373"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      (K(x,y) * (z * (u \ 1))) / (u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (z / u)) * u = w
    ]]></literal>
    <justification jstring="[para(16806(a,1),563(a,1,1))].">
      <j1 rule="para" parents="16806 563"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4363(a,1),16807(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4363 16807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16810">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,768,a(flip),b,16809,a),flip(a)].">
      <j1 rule="hyper" parents="319 768 16809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11042,a(flip),b,16810,a)].">
      <j1 rule="hyper" parents="64 11042 16810"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1107(a,2),16810(a,1,1))].">
      <j1 rule="para" parents="1107 16810"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      a(x \ T(y,z),u,u \ 1) = a(x \ y,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4522(a,1),16810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4522 16810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,16812,a(flip),b,768,a)].">
      <j1 rule="hyper" parents="131 16812 768"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(111(a,1),16813(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 16813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(16814(a,1),3644(a,2,2))].">
      <j1 rule="para" parents="16814 3644"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      (R(x,y,y \ 1) * z) / R(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,243,a(flip),b,16816,a)].">
      <j1 rule="hyper" parents="128 243 16816"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,13236,a(flip),b,16817,a)].">
      <j1 rule="hyper" parents="64 13236 16817"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      (L(x \ T(y,z),u,u \ 1) * K(z,y)) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(12359(a,1),16818(a,2,1))].">
      <j1 rule="para" parents="12359 16818"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12562,a(flip),b,16282,a),flip(a)].">
      <j1 rule="hyper" parents="319 12562 16282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16821">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) * K(L(x,y,z) \ u,x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(5186,a,16820,a)].">
      <j1 rule="hyper" parents="5186 16820"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),T(x,u)) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(6180,a,16821,a)].">
      <j1 rule="hyper" parents="6180 16821"/>
    </justification>
  </clause>

  <clause id="16823">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(7779(a,1),16822(a,1,2))].">
      <j1 rule="para" parents="7779 16822"/>
    </justification>
  </clause>

  <clause id="16824">
    <literal><![CDATA[
      T(x * L(y,z,u),a(u,z,y)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),16823(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 16823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(16824(a,1),16119(a,1,2))].">
      <j1 rule="para" parents="16824 16119"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(11312,a,16825,a)].">
      <j1 rule="hyper" parents="11312 16825"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y / (z \ K(y,z)))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(8492(a,1),16826(a,1,2,1,1))].">
      <j1 rule="para" parents="8492 16826"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) \ (v5 * (K(w,u) \ z)))) = K(x,y \ T(v5,z / K(w,u)))
    ]]></literal>
    <justification jstring="[para(5174(a,1),16412(a,1,2,2,1))].">
      <j1 rule="para" parents="5174 16412"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      T((x \ (y * z)) / T(z,K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(6818(a,1),16437(a,1,1,2))].">
      <j1 rule="para" parents="6818 16437"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[hyper(14163,a,16830,a)].">
      <j1 rule="hyper" parents="14163 16830"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(15096,a,16560,a)].">
      <j1 rule="hyper" parents="15096 16560"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,T(y,w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,14868,a(flip),b,16611,a),flip(a)].">
      <j1 rule="hyper" parents="319 14868 16611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(12229(a,1),16833(a,1,2,2,2))].">
      <j1 rule="para" parents="12229 16833"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16656,a(flip),b,16667,a),flip(a)].">
      <j1 rule="hyper" parents="64 16656 16667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      K(x,L((y * z) * (u \ T(w,w \ u)),y,z \ 1)) = K(x,y / (T((u \ w) \ 1,w) / z))
    ]]></literal>
    <justification jstring="[hyper(12458,a,16835,a)].">
      <j1 rule="hyper" parents="12458 16835"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(12349,a,16835,a)].">
      <j1 rule="hyper" parents="12349 16835"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15761,a(flip),b,16835,a)].">
      <j1 rule="hyper" parents="64 15761 16835"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),16838(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10 16838"/>
    </justification>
  </clause>

  <clause id="16840">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) = K(x,y * T((u / w) \ z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16546,a,16704,a)].">
      <j1 rule="hyper" parents="16546 16704"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(16840(a,2),15011(a,1))].">
      <j1 rule="para" parents="16840 15011"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      K(x \ T(K(y,K(z,u)) * w,w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(4288(a,1),16735(a,1,1,2,1))].">
      <j1 rule="para" parents="4288 16735"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      K(K(x,K(y,z)) * (u \ T(w,w * x)),v5) = K(u \ T(w,K(z,y) * x),v5)
    ]]></literal>
    <justification jstring="[para(16336(a,1),16844(a,1,1))].">
      <j1 rule="para" parents="16336 16844"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      K(K(x,K(y,z)) * (u \ T(w,x)),v5) = K(u \ T(w,K(z,y) * x),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11541,a(flip),b,16845,a)].">
      <j1 rule="hyper" parents="64 11541 16845"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(14587,a,16846,a),flip(a)].">
      <j1 rule="hyper" parents="14587 16846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(14714,a,16847,a),flip(a)].">
      <j1 rule="hyper" parents="14714 16847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),v5) = v6
    ]]></literal>
    <justification jstring="[para(16848(a,1),5418(a,1))].">
      <j1 rule="para" parents="16848 5418"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      K(x \ K(y,K(z,u) * w),v5) = K(x \ K(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(16850,a,14713,a),flip(a)].">
      <j1 rule="hyper" parents="16850 14713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K(x,y \ K(z,K(u,w) * v5)) = (v6 * K(y \ K(z,v5),x)) \ v6
    ]]></literal>
    <justification jstring="[para(16851(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16851 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      K(x,y \ K(z,K(u,w) * v5)) = K(x,y \ K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,16852,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      K(x,y \ K(z * K(u,w),v5)) = K(x,y \ K(v5,z))
    ]]></literal>
    <justification jstring="[hyper(15338,a,16853,a)].">
      <j1 rule="hyper" parents="15338 16853"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      K(x,y \ (z \ T(u * z,K(w,v5)))) = K(x,y \ T(u,z / K(v5,w)))
    ]]></literal>
    <justification jstring="[para(15577(a,1),16829(a,1,2,2))].">
      <j1 rule="para" parents="15577 16829"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16411,a(flip),b,16855,a),flip(a)].">
      <j1 rule="hyper" parents="64 16411 16855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),16856(a,2,2,2))].">
      <j1 rule="para" parents="22 16856"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      K(x,y \ T(z,u * K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),16858(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5192(a,1),16858(a,1,2,2,2))].">
      <j1 rule="para" parents="5192 16858"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(15049,a,16859,a)].">
      <j1 rule="hyper" parents="15049 16859"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      K(x,y \ T(z,T(u,w) * v5)) = K(x,y \ T(z,u * v5))
    ]]></literal>
    <justification jstring="[para(4636(a,1),16859(a,1,2,2,2))].">
      <j1 rule="para" parents="4636 16859"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ T(y,z)) = K(x,((z * K(u,w)) * y) \ y)
    ]]></literal>
    <justification jstring="[para(5136(a,1),16859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5136 16859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,K(w,v5) * v6)) \ T(u,v6)) = K(x,z * (y \ T(u,K(w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(517(a,1),16861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="517 16861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(15049,a,16862,a)].">
      <j1 rule="hyper" parents="15049 16862"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,(y * K(z,u)) \ K(w,y))
    ]]></literal>
    <justification jstring="[hyper(5323,a,16863,a),flip(a)].">
      <j1 rule="hyper" parents="5323 16863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      (x * T(y,T(z,u))) \ (w * T(y,T(z,u))) = (x * T(y,z)) \ (w * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(884,a,16217,a),flip(a)].">
      <j1 rule="hyper" parents="884 16217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      (x * T(y,T(z,u))) \ (z * T(y,T(z,u))) = (x * T(y,z)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),16867(a,2,2))].">
      <j1 rule="para" parents="109 16867"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w)) * v5) / L(y,u,w))) = K(x,(L(T(y,z),u,w) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),16425(a,2,2,1,1))].">
      <j1 rule="para" parents="25 16425"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * T(w,v5)) / (a(x,y,K(z,u)) * w) = K(w,v5 * a(x,y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(12556(a,1),16470(a,1,1))].">
      <j1 rule="para" parents="12556 16470"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(12240,a,16529,a)].">
      <j1 rule="hyper" parents="12240 16529"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,3880,a(flip),b,16872,a)].">
      <j1 rule="hyper" parents="64 3880 16872"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(319,a,11934,a(flip),b,16873,a),flip(a)].">
      <j1 rule="hyper" parents="319 11934 16873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(15772,a,16874,a)].">
      <j1 rule="hyper" parents="15772 16874"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      L(K(x,y) * (((x \ z) / z) \ u),K(y,x),z \ (z / x)) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,11277,a(flip),b,16746,a)].">
      <j1 rule="hyper" parents="64 11277 16746"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      x / (y \ (x * K(z,u))) = x * ((x * K(z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(371(a,1),16776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="371 16776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * ((x * K(z,u)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(16653(a,1),16878(a,1,2))].">
      <j1 rule="para" parents="16653 16878"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      K(x,T(y,a(z,u,K(w,v5)))) = K(x,y * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(7091,a,16870,a)].">
      <j1 rule="hyper" parents="7091 16870"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16161,a,16880,a),flip(a)].">
      <j1 rule="hyper" parents="16161 16880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(16880(a,1),16161(a,1))].">
      <j1 rule="para" parents="16880 16161"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10398(a,1),16881(a,1,2))].">
      <j1 rule="para" parents="10398 16881"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(12527(a,1),16881(a,1,2))].">
      <j1 rule="para" parents="12527 16881"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13289(a,1),16881(a,1,2))].">
      <j1 rule="para" parents="13289 16881"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13292(a,1),16881(a,1,2))].">
      <j1 rule="para" parents="13292 16881"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(16128(a,2),16881(a,1,2))].">
      <j1 rule="para" parents="16128 16881"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(14518,a,16888,a)].">
      <j1 rule="hyper" parents="14518 16888"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) \ v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),16888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 16888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(12926(a,1),16888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12926 16888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x,a(K(y,z),u,w) \ v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(11920(a,2),16890(a,1,2,1))].">
      <j1 rule="para" parents="11920 16890"/>
    </justification>
  </clause>

  <clause id="16895">
    <literal><![CDATA[
      K(x,y) \ T(x,(a(K(z,u),w,v5) \ y) * x) = L(x,a(K(z,u),w,v5) \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(16893(a,1),10230(a,1,1))].">
      <j1 rule="para" parents="16893 10230"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,v6)) = K(x,y * T(w \ (K(z,u) \ v5),v6))
    ]]></literal>
    <justification jstring="[para(565(a,1),16886(a,1,2,2))].">
      <j1 rule="para" parents="565 16886"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(z,u) \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(567(a,1),16886(a,1,2,2))].">
      <j1 rule="para" parents="567 16886"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) \ ((w * v5) * K(z,u)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(12192(a,1),16886(a,1,2,2))].">
      <j1 rule="para" parents="12192 16886"/>
    </justification>
  </clause>

  <clause id="16899">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) \ v5)) = K(x,y \ (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(4378(a,1),16887(a,1,2,2))].">
      <j1 rule="para" parents="4378 16887"/>
    </justification>
  </clause>

  <clause id="16900">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(13280(a,1),16887(a,1,2,2))].">
      <j1 rule="para" parents="13280 16887"/>
    </justification>
  </clause>

  <clause id="16901">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(13542,a,16889,a)].">
      <j1 rule="hyper" parents="13542 16889"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13261(a,2),16889(a,1,2,2))].">
      <j1 rule="para" parents="13261 16889"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,T(v5,y) / y)
    ]]></literal>
    <justification jstring="[hyper(16171,a,16903,a)].">
      <j1 rule="hyper" parents="16171 16903"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(829(a,1),16903(a,1,2,2))].">
      <j1 rule="para" parents="829 16903"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(4378(a,1),16903(a,1,2,2))].">
      <j1 rule="para" parents="4378 16903"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(12527(a,1),16882(a,1,2))].">
      <j1 rule="para" parents="12527 16882"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      K(x,y * (T(z,y) * a(u,w,K(v5,v6)))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(109(a,1),16884(a,2,2))].">
      <j1 rule="para" parents="109 16884"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w,v5))) = K(x,y * (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(85(a,1),16884(a,1,2,2))].">
      <j1 rule="para" parents="85 16884"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (u / a(w,v5,K(v6,v7))),a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(755(a,2),16884(a,1,2,2))].">
      <j1 rule="para" parents="755 16884"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      K(x,y * (T(z,a(u,w,v5)) \ v6)) = K(x,y * (z \ v6))
    ]]></literal>
    <justification jstring="[para(16252(a,1),16884(a,1,2,2))].">
      <j1 rule="para" parents="16252 16884"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      K(x,y * (K(z,L(u,w,v5)) * v6)) = K(x,K(u,z) * (y * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,16549,a(flip),b,16892,a)].">
      <j1 rule="hyper" parents="64 16549 16892"/>
    </justification>
  </clause>

  <clause id="16913">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15626,a(flip),b,16892,a),flip(a)].">
      <j1 rule="hyper" parents="64 15626 16892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16914">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(10141(a,1),16892(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10141 16892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16915">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14999,a(flip),b,16900,a),flip(a)].">
      <j1 rule="hyper" parents="319 14999 16900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16916">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,11070,a(flip),b,16904,a),flip(a)].">
      <j1 rule="hyper" parents="319 11070 16904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16917">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(13280(a,1),16916(a,1,2,1))].">
      <j1 rule="para" parents="13280 16916"/>
    </justification>
  </clause>

  <clause id="16918">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(13264(a,1),16916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13264 16916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(11225,a,16917,a),flip(a)].">
      <j1 rule="hyper" parents="11225 16917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,13453,a,b,16885,a),flip(a)].">
      <j1 rule="hyper" parents="319 13453 16885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,16555,a(flip),b,16885,a),flip(a)].">
      <j1 rule="hyper" parents="319 16555 16885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(12057(a,1),16885(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12057 16885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(16885(a,2),13454(a,1))].">
      <j1 rule="para" parents="16885 13454"/>
    </justification>
  </clause>

  <clause id="16924">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15019,a,16918,a)].">
      <j1 rule="hyper" parents="15019 16918"/>
    </justification>
  </clause>

  <clause id="16925">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14115,a,b,16918,a),flip(a)].">
      <j1 rule="hyper" parents="319 14115 16918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,L(v5,u,z))) = K(x,y \ (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(10115(a,1),16918(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10115 16918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(1 / (z / y)) \ L(y / z,u,w))
    ]]></literal>
    <justification jstring="[para(598(a,1),16919(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="598 16919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(12264,a,16920,a)].">
      <j1 rule="hyper" parents="12264 16920"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,K(y \ z,y) * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13694,a,b,16920,a)].">
      <j1 rule="hyper" parents="64 13694 16920"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14992,a(flip),b,16920,a)].">
      <j1 rule="hyper" parents="64 14992 16920"/>
    </justification>
  </clause>

  <clause id="16932">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(12057(a,1),16920(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12057 16920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(12498(a,1),16920(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12498 16920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(u,w) * (z * x)) = K(y,x * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(16920(a,1),15219(a,1,2))].">
      <j1 rule="para" parents="16920 15219"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14115,a,b,16924,a),flip(a)].">
      <j1 rule="hyper" parents="319 14115 16924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ v5) * K(y,L(z,u,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(16924(a,1),16431(a,1))].">
      <j1 rule="para" parents="16924 16431"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,w / T(y,z)) \ (w / y))) = K(x,((w / y) * K(y,z)) / u)
    ]]></literal>
    <justification jstring="[hyper(13612,a,16925,a),flip(a)].">
      <j1 rule="hyper" parents="13612 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,16925,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16925 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,K(z * x,y) * ((y \ (x * z)) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9315,a(flip),b,16925,a)].">
      <j1 rule="hyper" parents="64 9315 16925"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(4922(a,1),16925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(5241(a,1),16925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5241 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(8163(a,1),16925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8163 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(8188(a,1),16925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8188 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(129,a,16929,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16929 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      K(x,K(y,T(z,x)) * (((y * z) / u) * w)) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13116,a(flip),b,16929,a),flip(a)].">
      <j1 rule="hyper" parents="64 13116 16929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K(x \ K(y,K(z,u) * (w * y)),v5) = K(x \ K(w \ K(z,u),y),v5)
    ]]></literal>
    <justification jstring="[para(16929(a,1),13777(a,1,1,2))].">
      <j1 rule="para" parents="16929 13777"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(12241,a,16931,a)].">
      <j1 rule="hyper" parents="12241 16931"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * (T(u * z,x) * v5)) = K(x,(u * (z * K(w,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,10181,a(flip),b,16931,a),flip(a)].">
      <j1 rule="hyper" parents="64 10181 16931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / y) * w)) = K(x,(u / T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(5163(a,1),16931(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5163 16931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(12363(a,1),16931(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12363 16931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(13347(a,1),16931(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13347 16931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * (v5 * v6))) = a(x,y,K(z,v6 * (v5 * K(w,u))))
    ]]></literal>
    <justification jstring="[para(16931(a,1),16224(a,1,3))].">
      <j1 rule="para" parents="16931 16224"/>
    </justification>
  </clause>

  <clause id="16953">
    <literal><![CDATA[
      K(x,K(y \ z,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(14945,a,16935,a),flip(a)].">
      <j1 rule="hyper" parents="14945 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,z \ 1) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13647,a,16935,a),flip(a)].">
      <j1 rule="hyper" parents="13647 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,y \ z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13469,a,16935,a),flip(a)].">
      <j1 rule="hyper" parents="13469 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13446,a,16935,a),flip(a)].">
      <j1 rule="hyper" parents="13446 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y \ z,y) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(11239,a,16935,a),flip(a)].">
      <j1 rule="hyper" parents="11239 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(129,a,16935,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16935 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) \ w)) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16309,a(flip),b,16935,a),flip(a)].">
      <j1 rule="hyper" parents="64 16309 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(4081(a,1),16935(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4081 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(4437(a,1),16935(a,1,2,2))].">
      <j1 rule="para" parents="4437 16935"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (u / z))) = K(x,w \ (u / T(z,y)))
    ]]></literal>
    <justification jstring="[para(7202(a,1),16935(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7202 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16963">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(9188(a,1),16935(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9188 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,K(u,w) * (y \ z))) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[para(16938(a,1),14996(a,1,2,2))].">
      <j1 rule="para" parents="16938 14996"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      T(x,K(y,z \ u) * ((u \ z) * w)) = T(x,T((u \ z) \ 1,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13478,a(flip),b,16944,a),flip(a)].">
      <j1 rule="hyper" parents="64 13478 16944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(129,a,16947,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 16947 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z)))) = K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16030,a(flip),b,16947,a)].">
      <j1 rule="hyper" parents="64 16030 16947"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,13437,a,b,16958,a),flip(a)].">
      <j1 rule="hyper" parents="319 13437 16958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16169,a,b,16958,a)].">
      <j1 rule="hyper" parents="64 16169 16958"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ u)) = T(x,T(T(y \ u,w) \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16733,a(flip),b,16958,a),flip(a)].">
      <j1 rule="hyper" parents="64 16733 16958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(16958(a,1),4390(a,1,1))].">
      <j1 rule="para" parents="16958 4390"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      K(x,L(T(1 / y,K(z,u) * (y * z)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(16967(a,1),12313(a,1,2,1,1))].">
      <j1 rule="para" parents="16967 12313"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (y \ w))) = T(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(4314(a,1),16969(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4314 16969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16976">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(16969(a,2),13489(a,1))].">
      <j1 rule="para" parents="16969 13489"/>
    </justification>
  </clause>

  <clause id="16978">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),K(w,z) * ((u / z) \ y)) = T(x,y / (K(z,w) * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15570,a(flip),b,16971,a),flip(a)].">
      <j1 rule="hyper" parents="64 15570 16971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14602,a(flip),b,16971,a)].">
      <j1 rule="hyper" parents="64 14602 16971"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(12057(a,1),16971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12057 16971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y / T(K(z,u) * w,K(u,z) * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(16971(a,1),14645(a,2,2,2))].">
      <j1 rule="para" parents="16971 14645"/>
    </justification>
  </clause>

  <clause id="16982">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,13437,a,b,16979,a),flip(a)].">
      <j1 rule="hyper" parents="319 13437 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,11397,a,b,16979,a),flip(a)].">
      <j1 rule="hyper" parents="319 11397 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(y \ z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13852,a,b,16979,a)].">
      <j1 rule="hyper" parents="64 13852 16979"/>
    </justification>
  </clause>

  <clause id="16986">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(12774(a,1),16979(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12774 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16987">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(4922(a,1),16982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4922 16982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / z) \ w)) = T(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5163(a,1),16982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5163 16982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / (y * z)) \ w)) = T(x,(u / (z * y)) \ w)
    ]]></literal>
    <justification jstring="[para(8891(a,1),16982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8891 16982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(12363(a,1),16982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12363 16982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      T(x,K(y,z) \ ((K(y,z) \ u) \ w)) = T(x,T(u,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11171,a(flip),b,16983,a),flip(a)].">
      <j1 rule="hyper" parents="64 11171 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x,y * T(a(z,u,K(w,v5)) * v6,y)) = K(x,v6 * y)
    ]]></literal>
    <justification jstring="[para(16589(a,2),16908(a,1,2,2))].">
      <j1 rule="para" parents="16589 16908"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      K(x,y * (L(z,u,K(w,v5)) \ v6)) = K(x,y * (z \ v6))
    ]]></literal>
    <justification jstring="[para(13261(a,2),16911(a,1,2,2,1))].">
      <j1 rule="para" parents="13261 16911"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(109(a,1),16992(a,1,2))].">
      <j1 rule="para" parents="109 16992"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(16128(a,1),16994(a,1,2,1))].">
      <j1 rule="para" parents="16128 16994"/>
    </justification>
  </clause>

  <clause id="16996">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(13292(a,1),16995(a,1,2,1))].">
      <j1 rule="para" parents="13292 16995"/>
    </justification>
  </clause>

  <clause id="16997">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(16327(a,1),16995(a,1,2,1))].">
      <j1 rule="para" parents="16327 16995"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ v8)) = K(x,y * (z \ v8))
    ]]></literal>
    <justification jstring="[para(11447(a,1),16993(a,1,2,2,1,3))].">
      <j1 rule="para" parents="11447 16993"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ (v5 * K(K(z,u) * w,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(4194(a,1),16996(a,1,2,1,2))].">
      <j1 rule="para" parents="4194 16996"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(y,z) \ w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(565(a,1),16997(a,1,2,1,1))].">
      <j1 rule="para" parents="565 16997"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,((z / (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4512(a,2),16921(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4512 16921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16920,a,b,16922,a)].">
      <j1 rule="hyper" parents="64 16920 16922"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(15780,a,16932,a)].">
      <j1 rule="hyper" parents="15780 16932"/>
    </justification>
  </clause>

  <clause id="17004">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) * u) = w
    ]]></literal>
    <justification jstring="[para(16932(a,1),5844(a,1))].">
      <j1 rule="para" parents="16932 5844"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(13030(a,1),16932(a,1,2))].">
      <j1 rule="para" parents="13030 16932"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) / u) * w) = v5
    ]]></literal>
    <justification jstring="[para(23(a,1),17004(a,1,2,1,1))].">
      <j1 rule="para" parents="23 17004"/>
    </justification>
  </clause>

  <clause id="17007">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(13454,a,16940,a)].">
      <j1 rule="hyper" parents="13454 16940"/>
    </justification>
  </clause>

  <clause id="17008">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(13454,a,16950,a)].">
      <j1 rule="hyper" parents="13454 16950"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,u)) * w) = K(x,K(u,z) * (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11243,a(flip),b,16950,a),flip(a)].">
      <j1 rule="hyper" parents="64 11243 16950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17010">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(16950(a,1),5844(a,1))].">
      <j1 rule="para" parents="16950 5844"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * u) \ w)) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(13454,a,16959,a)].">
      <j1 rule="hyper" parents="13454 16959"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(13454,a,16960,a)].">
      <j1 rule="hyper" parents="13454 16960"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13457,a,b,16960,a)].">
      <j1 rule="hyper" parents="64 13457 16960"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4356(a,2),16960(a,1,2))].">
      <j1 rule="para" parents="4356 16960"/>
    </justification>
  </clause>

  <clause id="17015">
    <literal><![CDATA[
      T(x,T(y,z) \ (y \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(13490,a,16975,a)].">
      <j1 rule="hyper" parents="13490 16975"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) = T(x,y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(4292(a,1),16975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4292 16975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(4314(a,1),16975(a,1,2))].">
      <j1 rule="para" parents="4314 16975"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(16975(a,1),15130(a,1,2))].">
      <j1 rule="para" parents="16975 15130"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      T(T(x,T(y,z) * u),y \ (y \ w)) = T(T(x,T(y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14920,a(flip),b,17016,a),flip(a)].">
      <j1 rule="hyper" parents="64 14920 17016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ ((z * z) * u))) = T(x,T(y,z) \ ((1 / z) \ u))
    ]]></literal>
    <justification jstring="[para(452(a,1),17017(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="452 17017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      T(x * K(y,x),K(y,T(z,u) \ (u \ w))) = x * K(y,T(x,z \ (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[para(17017(a,1),7077(a,2,2,2))].">
      <j1 rule="para" parents="17017 7077"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13468,a(flip),b,16980,a),flip(a)].">
      <j1 rule="hyper" parents="64 13468 16980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      T(x,((y \ z) / y) \ u) = T(x,(y \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(111(a,1),17022(a,1,2,1,1))].">
      <j1 rule="para" parents="111 17022"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) = T(x,(y * z) \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(14661,a,16987,a),flip(a)].">
      <j1 rule="hyper" parents="14661 16987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17026">
    <literal><![CDATA[
      T(x,(K(y,z) * T(u,w)) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,15536,a(flip),b,16987,a),flip(a)].">
      <j1 rule="hyper" parents="64 15536 16987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(12220(a,1),17002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12220 17002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      K(x,(T(y,z) / (u \ 1)) * w) = K(x,(y / (u \ K(y,z))) * w)
    ]]></literal>
    <justification jstring="[para(12413(a,1),17002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12413 17002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(17012(a,2),8408(a,1))].">
      <j1 rule="para" parents="17012 8408"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (T(y,w) * v5))) = K(x,u \ (T(T(y,w),z) * v5))
    ]]></literal>
    <justification jstring="[hyper(15047,a,17014,a)].">
      <j1 rule="hyper" parents="15047 17014"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      K(x,((y * z) / u) \ (T(y,w) * z)) = K(x,K(w,y) \ u)
    ]]></literal>
    <justification jstring="[para(81(a,1),17014(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="81 17014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,K(z,y) * u) / v5) * v6) = K(x,((w / (K(y,z) * u)) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(13437(a,1),17027(a,1,2,1,1))].">
      <j1 rule="para" parents="13437 17027"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      K(x,y * (z * K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(15051,a,16912,a)].">
      <j1 rule="hyper" parents="15051 16912"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(12829(a,1),16915(a,1,2,2))].">
      <j1 rule="para" parents="12829 16915"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(14992(a,1),16923(a,1))].">
      <j1 rule="para" parents="14992 16923"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(16169(a,2),16976(a,1))].">
      <j1 rule="para" parents="16169 16976"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15674,a(flip),b,17005,a),flip(a)].">
      <j1 rule="hyper" parents="64 15674 17005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      K(x,(T(y,((z \ 1) \ u) / u) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(8472(a,2),17038(a,1,2,2))].">
      <j1 rule="para" parents="8472 17038"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12296,a(flip),b,17033,a)].">
      <j1 rule="hyper" parents="64 12296 17033"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(4314(a,1),16899(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4314 16899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      K(x,y * (z * (u * K(y,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w) * (z * u)) = v5
    ]]></literal>
    <justification jstring="[para(16909(a,1),14218(a,1))].">
      <j1 rule="para" parents="16909 14218"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      K(x,K(y \ (z * (u \ 1)),w) * v5) = K(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13651,a(flip),b,16914,a),flip(a)].">
      <j1 rule="hyper" parents="64 13651 16914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w / y))) = K(x,u \ (w / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15040,a,16962,a)].">
      <j1 rule="hyper" parents="15040 16962"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(15782,a,16963,a)].">
      <j1 rule="hyper" parents="15782 16963"/>
    </justification>
  </clause>

  <clause id="17047">
    <literal><![CDATA[
      T(x,K(y * y,z) * ((y * y) * ((u / z) \ w))) = T(x,(u / (z * (y * y))) \ w)
    ]]></literal>
    <justification jstring="[para(690(a,1),16989(a,1,2,2))].">
      <j1 rule="para" parents="690 16989"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      T(x,K(y,z) \ ((K(y,z) \ u) \ w)) = T(x,u \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14592,a(flip),b,16991,a),flip(a)].">
      <j1 rule="hyper" parents="319 14592 16991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      T(x,K(y,z) \ K(K(y,z) \ u,w)) = T(x,u \ T(K(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(4012(a,2),17048(a,1,2,2))].">
      <j1 rule="para" parents="4012 17048"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,13871,a(flip),b,17001,a),flip(a)].">
      <j1 rule="hyper" parents="319 13871 17001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(110(a,1),17051(a,1,2,1,1))].">
      <j1 rule="para" parents="110 17051"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,T(y,z)) * w) = K(x,K(z,y) * (T(y * u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(12206,a,17009,a)].">
      <j1 rule="hyper" parents="12206 17009"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      T(T(x,T(y \ z,u) * T(z / y,u)),(y \ z) \ ((y \ z) \ w)) = T(T(x,K(y,T(y \ z,u))),w)
    ]]></literal>
    <justification jstring="[para(4151(a,1),17019(a,2,1,2))].">
      <j1 rule="para" parents="4151 17019"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11187,a(flip),b,17025,a),flip(a)].">
      <j1 rule="hyper" parents="64 11187 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17037,a,17026,a),flip(a)].">
      <j1 rule="hyper" parents="17037 17026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(15048,a,17035,a)].">
      <j1 rule="hyper" parents="15048 17035"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) \ v5) = T(x,K(u,z) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14741,a,b,17056,a)].">
      <j1 rule="hyper" parents="64 14741 17056"/>
    </justification>
  </clause>

  <clause id="17059">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ v5)) = T(x,T(T(y,z) \ u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13664,a(flip),b,17056,a),flip(a)].">
      <j1 rule="hyper" parents="64 13664 17056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u,w) \ T(v5,u))) = T(x,v5 / T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16711,a(flip),b,17058,a),flip(a)].">
      <j1 rule="hyper" parents="64 16711 17058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      K(x,(y * ((T(y,x) / (z \ 1)) / T(y,x))) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(6383(a,1),17006(a,1))].">
      <j1 rule="para" parents="6383 17006"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16544,a(flip),b,17040,a),flip(a)].">
      <j1 rule="hyper" parents="319 16544 17040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16355,a(flip),b,17062,a),flip(a)].">
      <j1 rule="hyper" parents="64 16355 17062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      K(x,y * (T(z * u,x) \ K(w,v5))) = K(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,15489,a(flip),b,17062,a),flip(a)].">
      <j1 rule="hyper" parents="64 15489 17062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(17042,a,16800,a)].">
      <j1 rule="hyper" parents="17042 16800"/>
    </justification>
  </clause>

  <clause id="17066">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15444,a(flip),b,17065,a),flip(a)].">
      <j1 rule="hyper" parents="64 15444 17065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) * K(x,K(u,w)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(14419,a,16934,a)].">
      <j1 rule="hyper" parents="14419 16934"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(4676(a,1),16941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4676 16941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(13492,a,16942,a),flip(a)].">
      <j1 rule="hyper" parents="13492 16942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17007,a(flip),b,17069,a),flip(a)].">
      <j1 rule="hyper" parents="319 17007 17069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),17070(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13809,a(flip),b,17071,a),flip(a)].">
      <j1 rule="hyper" parents="64 13809 17071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(11269,a,16943,a),flip(a)].">
      <j1 rule="hyper" parents="11269 16943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16940,a(flip),b,17073,a),flip(a)].">
      <j1 rule="hyper" parents="319 16940 17073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),17074(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 17074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,14712,a(flip),b,16946,a),flip(a)].">
      <j1 rule="hyper" parents="64 14712 16946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(16850,a,17076,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16850 17076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5 \ w)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14576,a(flip),b,17077,a),flip(a)].">
      <j1 rule="hyper" parents="64 14576 17077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      K(x,y \ K(z \ K(u,w),v5)) = (v6 * K(y \ K(v5,z),x)) \ v6
    ]]></literal>
    <justification jstring="[para(17077(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17077 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      K(T(x,y \ K(z,u \ z)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(14574,a,17078,a),flip(a)].">
      <j1 rule="hyper" parents="14574 17078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17083">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[para(81(a,1),17081(a,1,1,1,2,2,2))].">
      <j1 rule="para" parents="81 17081"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14950,a(flip),b,17083,a),flip(a)].">
      <j1 rule="hyper" parents="64 14950 17083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(12180(a,1),17083(a,1,1,1))].">
      <j1 rule="para" parents="12180 17083"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(17085(a,1),5176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17085 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      K(x,y \ K(z \ K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(v5,z)) = v6
    ]]></literal>
    <justification jstring="[para(17080(a,2),5187(a,1))].">
      <j1 rule="para" parents="17080 5187"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2176(a,1),17084(a,1,1,1))].">
      <j1 rule="para" parents="2176 17084"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(L(z,u,u \ 1) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(17089(a,1),11856(a,1,2,2))].">
      <j1 rule="para" parents="17089 11856"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(11269,a,16951,a)].">
      <j1 rule="hyper" parents="11269 16951"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17008,a(flip),b,17091,a),flip(a)].">
      <j1 rule="hyper" parents="64 17008 17091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ T(z,u)) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(13797,a,17092,a),flip(a)].">
      <j1 rule="hyper" parents="13797 17092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(z,y) * w) \ w)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16352,a(flip),b,16956,a),flip(a)].">
      <j1 rule="hyper" parents="319 16352 16956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      T(x,(y \ z) * (K(u,z \ y) * w)) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(9682(a,1),16966(a,1,2))].">
      <j1 rule="para" parents="9682 16966"/>
    </justification>
  </clause>

  <clause id="17096">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16990,a(flip),b,16986,a)].">
      <j1 rule="hyper" parents="64 16990 16986"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      K(x,(T(y,K(z,u) * w) / v5) * v6) = K(x,(T(y,w) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,16922,a(flip),b,17003,a),flip(a)].">
      <j1 rule="hyper" parents="64 16922 17003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      T(x,T(y,z) \ ((1 / z) \ u)) = T(x,y \ ((K(z,y) / z) \ u))
    ]]></literal>
    <justification jstring="[para(4975(a,1),17020(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4975 17020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17099">
    <literal><![CDATA[
      T(x,T(y,z) \ ((1 / z) \ u)) = T(x,y \ ((z \ K(z,y)) \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13091,a(flip),b,17098,a),flip(a)].">
      <j1 rule="hyper" parents="319 13091 17098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17100">
    <literal><![CDATA[
      T(x,K(y \ (z * (u \ 1)),w) * v5) = T(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(129,a,17043,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17043 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(T(y,w) \ z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16972,a(flip),b,17059,a)].">
      <j1 rule="hyper" parents="64 16972 17059"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,K(w,u) * (y / T(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14815,a(flip),b,17060,a),flip(a)].">
      <j1 rule="hyper" parents="64 14815 17060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      T(x,K(y,z) * (u / T(w,v5))) = T(x,u * T(w \ K(y,z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14786,a(flip),b,17102,a),flip(a)].">
      <j1 rule="hyper" parents="64 14786 17102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      T(x,K(y \ z,u) * (w / T(y,z))) = T(x,w / (T(y \ z,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11189,a(flip),b,17102,a),flip(a)].">
      <j1 rule="hyper" parents="64 11189 17102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) * (v5 \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(17063(a,1),6468(a,1))].">
      <j1 rule="para" parents="17063 6468"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,v5)))) = K(x,y * ((z * u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(16551,a,17064,a),flip(a)].">
      <j1 rule="hyper" parents="16551 17064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      K(x,y / ((z * u) * K(w,v5))) = K(x,y / (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(319,a,15064,a,b,17107,a)].">
      <j1 rule="hyper" parents="319 15064 17107"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16569,a(flip),b,17107,a),flip(a)].">
      <j1 rule="hyper" parents="319 16569 17107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      K(x,y * ((z * T(u,z)) \ K(w,v5))) = K(x,y / ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15433,a(flip),b,17107,a),flip(a)].">
      <j1 rule="hyper" parents="64 15433 17107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17112">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(4055(a,1),17110(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4055 17110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(4097(a,1),17110(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4097 17110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      K(x,y / (z * (T(u,z) * K(w,v5)))) = K(x,y / ((u * z) * K(w,v5)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17109(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 17109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13807,a(flip),b,17072,a),flip(a)].">
      <j1 rule="hyper" parents="64 13807 17072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17116">
    <literal><![CDATA[
      K(x,y \ ((z * (u / z)) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(12(a,1),17115(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 17115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      R(T(K(x,y \ z),y * u),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13148,a(flip),b,17116,a)].">
      <j1 rule="hyper" parents="64 13148 17116"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      R(K(x,T(y \ z,y * u)),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(6099(a,2),17117(a,1,1))].">
      <j1 rule="para" parents="6099 17117"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * u),y,u)) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(12814,a,17118,a)].">
      <j1 rule="hyper" parents="12814 17118"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (T(z,y) * (z \ u))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15497,a(flip),b,17119,a),flip(a)].">
      <j1 rule="hyper" parents="64 15497 17119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,5176,a(flip),b,17086,a),flip(a)].">
      <j1 rule="hyper" parents="319 5176 17086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(5712(a,1),17121(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5712 17121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14889,a,b,17122,a)].">
      <j1 rule="hyper" parents="64 14889 17122"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),(y \ z) * y)) = K(x,T((y \ z) \ u,y \ z) / y)
    ]]></literal>
    <justification jstring="[para(4673(a,1),17123(a,1,2,1))].">
      <j1 rule="para" parents="4673 17123"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(13796,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="13796 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(3103(a,2),17126(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3103 17126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,w * (u \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(13454,a,17094,a)].">
      <j1 rule="hyper" parents="13454 17094"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      T(x,(y \ z) * (u * K(w,z \ y))) = T(x,T((y \ z) \ 1,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14599,a(flip),b,17095,a)].">
      <j1 rule="hyper" parents="64 14599 17095"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(14417,a,17100,a)].">
      <j1 rule="hyper" parents="14417 17100"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (T(z \ y,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(14942,a,17104,a)].">
      <j1 rule="hyper" parents="14942 17104"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) * v5)) = K(x,y * ((w * v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17111(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 17111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      K(x,y / (((z \ K(u,w)) \ 1) * v5)) = K(x,y * ((z * v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12083,a,b,17132,a)].">
      <j1 rule="hyper" parents="64 12083 17132"/>
    </justification>
  </clause>

  <clause id="17134">
    <literal><![CDATA[
      K(x,y / (z * (T(u,z) * K(w,v5)))) = K(x,y / (u * (z * K(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(319,a,17109,a(flip),b,17114,a),flip(a)].">
      <j1 rule="hyper" parents="319 17109 17114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (K(z,y) * u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(4037(a,1),17120(a,1,2,2))].">
      <j1 rule="para" parents="4037 17120"/>
    </justification>
  </clause>

  <clause id="17136">
    <literal><![CDATA[
      K(x,(T(y,z) * (z \ u)) \ u) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16309,a(flip),b,17135,a)].">
      <j1 rule="hyper" parents="64 16309 17135"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = T(x,w * (u \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(129,a,17128,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17128 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * z,u)) = T(x,T((u \ z) \ 1,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16503,a(flip),b,17129,a)].">
      <j1 rule="hyper" parents="64 16503 17129"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(14232,a,17138,a)].">
      <j1 rule="hyper" parents="14232 17138"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(6347,a,17139,a),flip(a)].">
      <j1 rule="hyper" parents="6347 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13657,a(flip),b,17140,a),flip(a)].">
      <j1 rule="hyper" parents="64 13657 17140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,9311,a(flip),b,17141,a),flip(a)].">
      <j1 rule="hyper" parents="319 9311 17141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17143">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17101,a,b,17142,a)].">
      <j1 rule="hyper" parents="64 17101 17142"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14808,a(flip),b,17142,a),flip(a)].">
      <j1 rule="hyper" parents="64 14808 17142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17145">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,T(w,z))) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,16759,a(flip),b,17143,a),flip(a)].">
      <j1 rule="hyper" parents="319 16759 17143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17146">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14809,a(flip),b,17144,a),flip(a)].">
      <j1 rule="hyper" parents="64 14809 17144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(u * z,u \ 1)))
    ]]></literal>
    <justification jstring="[para(12302(a,1),17133(a,1,2,2,1,1))].">
      <j1 rule="para" parents="12302 17133"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      K(x,y \ ((T(z,y) * K(u,w)) \ y)) = K(x,y / (z * (y * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,7561,a(flip),b,17134,a)].">
      <j1 rule="hyper" parents="64 7561 17134"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(14230,a,17145,a)].">
      <j1 rule="hyper" parents="14230 17145"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = T(x,y * T(T(z,w) / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17143,a(flip),b,17149,a),flip(a)].">
      <j1 rule="hyper" parents="64 17143 17149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      K(x,(y * T(z,y)) * (u \ K(w,v5))) = K(x,((K(w,v5) * z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(17106,a,15435,a)].">
      <j1 rule="hyper" parents="17106 15435"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) / v5) = K(x,(u * w) * (v5 \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17153(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 17153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,v6)) = K(x,y * T(w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(4356(a,1),16896(a,2,2,2,1,2))].">
      <j1 rule="para" parents="4356 16896"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(13599,a,16905,a)].">
      <j1 rule="hyper" parents="13599 16905"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(13492,a,16913,a)].">
      <j1 rule="hyper" parents="13492 16913"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * L(y / z,w,v5)) = K(x,(y \ u) * L(z \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16554,a(flip),b,17157,a)].">
      <j1 rule="hyper" parents="64 16554 17157"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      K(x,K((y * z) / y,y) * (u * L(K(z,y) * (y / z),w,v5))) = K(x,u * L(((y * z) / y) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(6097(a,1),17157(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6097 17157"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,K(z,y) * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,11166,a(flip),b,16930,a),flip(a)].">
      <j1 rule="hyper" parents="319 11166 16930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,16949,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="319 16949 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      K(x,(y / ((z \ u) * z)) * w) = K(x,(y / T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15029,a(flip),b,17162,a)].">
      <j1 rule="hyper" parents="64 15029 17162"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      K(x,(y / T(z,u)) * (K(w,y / T(z,u)) * v5)) = K(x,T(y / ((u \ z) * u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(15307,a,17163,a),flip(a)].">
      <j1 rule="hyper" parents="15307 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(15040,a,16945,a)].">
      <j1 rule="hyper" parents="15040 16945"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16933,a(flip),b,17165,a),flip(a)].">
      <j1 rule="hyper" parents="64 16933 17165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17168">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12190,a,17167,a),flip(a)].">
      <j1 rule="hyper" parents="12190 17167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17169">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17127,a,b,17168,a)].">
      <j1 rule="hyper" parents="64 17127 17168"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z * u,z) * w)) = K(x,(u * T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14870,a(flip),b,17053,a),flip(a)].">
      <j1 rule="hyper" parents="64 14870 17053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),17170(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 17170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15066,a,b,17171,a)].">
      <j1 rule="hyper" parents="64 15066 17171"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13711,a(flip),b,17171,a)].">
      <j1 rule="hyper" parents="64 13711 17171"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15363,a,b,17172,a)].">
      <j1 rule="hyper" parents="64 15363 17172"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      K(x,y * T(z \ (K(u,w) * v5),z)) = K(x,y * (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15429,a(flip),b,17155,a),flip(a)].">
      <j1 rule="hyper" parents="64 15429 17155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13564,a(flip),b,17175,a)].">
      <j1 rule="hyper" parents="64 13564 17175"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u)) = K(x,y * (u / (K(v5,w) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15448,a,b,17176,a)].">
      <j1 rule="hyper" parents="64 15448 17176"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13796,a,17159,a)].">
      <j1 rule="hyper" parents="13796 17159"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (T(w * u,x) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(10133(a,1),16948(a,1,2,1))].">
      <j1 rule="para" parents="10133 16948"/>
    </justification>
  </clause>

  <clause id="17180">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(16550,a,17179,a)].">
      <j1 rule="hyper" parents="16550 17179"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,K(w,u) * ((y * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16892,a(flip),b,17180,a),flip(a)].">
      <j1 rule="hyper" parents="64 16892 17180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,K(y,z) * ((T((u \ w) / w,x) * w) * v5)) = K(x,(u \ (w * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16654,a(flip),b,17181,a),flip(a)].">
      <j1 rule="hyper" parents="64 16654 17181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(w,u)) * v5)) = K(x,((K(z,y) * w) * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,15436,a(flip),b,17181,a),flip(a)].">
      <j1 rule="hyper" parents="64 15436 17181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(109(a,1),17184(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 17184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17186">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,K(z,u) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15067,a,b,17185,a)].">
      <j1 rule="hyper" parents="64 15067 17185"/>
    </justification>
  </clause>

  <clause id="17187">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[para(5174(a,1),17186(a,1,2,1,1))].">
      <j1 rule="para" parents="5174 17186"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(u,z) * v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(4356(a,1),16897(a,2,2,2,1,2))].">
      <j1 rule="para" parents="4356 16897"/>
    </justification>
  </clause>

  <clause id="17189">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(z / y) * L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,12026,a(flip),b,16928,a),flip(a)].">
      <j1 rule="hyper" parents="319 12026 16928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = K(x,(z / y) * L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(14436,a,17189,a)].">
      <j1 rule="hyper" parents="14436 17189"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = K(x,(y \ z) * L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,17178,a(flip),b,17190,a),flip(a)].">
      <j1 rule="hyper" parents="319 17178 17190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ (z / T(u,w))) = K(x,((z / u) * K(u,w)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17044,a(flip),b,16937,a)].">
      <j1 rule="hyper" parents="64 17044 16937"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) / w) = K(x,(y / T(z,u)) / w)
    ]]></literal>
    <justification jstring="[hyper(11225,a,17192,a),flip(a)].">
      <j1 rule="hyper" parents="11225 17192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17194">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13515,a(flip),b,17193,a),flip(a)].">
      <j1 rule="hyper" parents="64 13515 17193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) = K(x,T(y * K(u,z),u) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13513,a(flip),b,17194,a)].">
      <j1 rule="hyper" parents="64 13513 17194"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z) / w) = K(x,T(y,z) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16358,a(flip),b,17195,a),flip(a)].">
      <j1 rule="hyper" parents="64 16358 17195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) = K(x,T(u,y) * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15590,a,b,17196,a)].">
      <j1 rule="hyper" parents="64 15590 17196"/>
    </justification>
  </clause>

  <clause id="17198">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13670,a,16953,a)].">
      <j1 rule="hyper" parents="13670 16953"/>
    </justification>
  </clause>

  <clause id="17199">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17128,a(flip),b,17198,a),flip(a)].">
      <j1 rule="hyper" parents="64 17128 17198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16352,a(flip),b,17199,a)].">
      <j1 rule="hyper" parents="64 16352 17199"/>
    </justification>
  </clause>

  <clause id="17201">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,z \ 1) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13643,a,16954,a)].">
      <j1 rule="hyper" parents="13643 16954"/>
    </justification>
  </clause>

  <clause id="17202">
    <literal><![CDATA[
      K(x,(K(y,z \ 1) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17128,a(flip),b,17201,a),flip(a)].">
      <j1 rule="hyper" parents="64 17128 17201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ 1))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16352,a(flip),b,17202,a)].">
      <j1 rule="hyper" parents="64 16352 17202"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ 1))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16567,a,b,17203,a),flip(a)].">
      <j1 rule="hyper" parents="319 16567 17203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17205">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,y \ z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13492,a,16955,a)].">
      <j1 rule="hyper" parents="13492 16955"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      K(x,(K(y,y \ z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17128,a(flip),b,17205,a),flip(a)].">
      <j1 rule="hyper" parents="64 17128 17205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16352,a(flip),b,17206,a)].">
      <j1 rule="hyper" parents="64 16352 17206"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16562,a,17207,a)].">
      <j1 rule="hyper" parents="16562 17207"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16832,a(flip),b,17207,a),flip(a)].">
      <j1 rule="hyper" parents="64 16832 17207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(4173(a,1),17207(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4173 17207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15087,a(flip),b,17208,a),flip(a)].">
      <j1 rule="hyper" parents="319 15087 17208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14774,a(flip),b,17211,a),flip(a)].">
      <j1 rule="hyper" parents="64 14774 17211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17213">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13614,a(flip),b,17212,a),flip(a)].">
      <j1 rule="hyper" parents="319 13614 17212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      T(x,y / (z / T(u,z))) = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,17213,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17213 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7374,a,b,17213,a)].">
      <j1 rule="hyper" parents="64 7374 17213"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      T(x,y / ((z \ u) / z)) = T(x,y / (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(3300(a,1),17214(a,1,2,2))].">
      <j1 rule="para" parents="3300 17214"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (z / u))) = T(x,((u \ z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14891,a(flip),b,17216,a),flip(a)].">
      <j1 rule="hyper" parents="64 14891 17216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (z / u))) = T(x,(u \ (z / u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,17023,a(flip),b,17217,a),flip(a)].">
      <j1 rule="hyper" parents="319 17023 17217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17219">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = w
    ]]></literal>
    <justification jstring="[para(17209(a,1),12290(a,1))].">
      <j1 rule="para" parents="17209 12290"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(z \ y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(11269,a,16957,a)].">
      <j1 rule="hyper" parents="11269 16957"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17128,a(flip),b,17220,a),flip(a)].">
      <j1 rule="hyper" parents="64 17128 17220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17222">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16352,a(flip),b,17221,a)].">
      <j1 rule="hyper" parents="64 16352 17221"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(6538(a,1),17221(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6538 17221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16356,a(flip),b,17222,a),flip(a)].">
      <j1 rule="hyper" parents="64 16356 17222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15084,a(flip),b,17222,a),flip(a)].">
      <j1 rule="hyper" parents="64 15084 17222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11339,a(flip),b,17223,a),flip(a)].">
      <j1 rule="hyper" parents="319 11339 17223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4693,a(flip),b,17226,a),flip(a)].">
      <j1 rule="hyper" parents="319 4693 17226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(6468,a,17224,a)].">
      <j1 rule="hyper" parents="6468 17224"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16384,a(flip),b,17228,a)].">
      <j1 rule="hyper" parents="64 16384 17228"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      K(x,(y / (y / z)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(78(a,1),17229(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(T(z,u) / (z / (y * z))) / w)
    ]]></literal>
    <justification jstring="[para(12391(a,1),17230(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12391 17230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16551,a,17225,a)].">
      <j1 rule="hyper" parents="16551 17225"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15089,a(flip),b,17232,a)].">
      <j1 rule="hyper" parents="64 15089 17232"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,T(y * z,z) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17197,a(flip),b,17231,a),flip(a)].">
      <j1 rule="hyper" parents="319 17197 17231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(z * y) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15554,a(flip),b,17234,a),flip(a)].">
      <j1 rule="hyper" parents="319 15554 17234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(14825,a,17235,a),flip(a)].">
      <j1 rule="hyper" parents="14825 17235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17227,a(flip),b,17236,a),flip(a)].">
      <j1 rule="hyper" parents="64 17227 17236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(4435(a,1),17237(a,1,2,1))].">
      <j1 rule="para" parents="4435 17237"/>
    </justification>
  </clause>

  <clause id="17239">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,((z \ 1) * y) / ((u \ 1) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13238,a(flip),b,17238,a)].">
      <j1 rule="hyper" parents="64 13238 17238"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(u / T(z,w)) \ y) = T(x,y / (K(z,w) * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16988,a(flip),b,16978,a)].">
      <j1 rule="hyper" parents="64 16988 16978"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      T(x,y / (K(z,u) * (w / z))) = T(x,y / (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15258,a(flip),b,17240,a),flip(a)].">
      <j1 rule="hyper" parents="64 15258 17240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      T(x,y * ((z / u) \ K(w,u))) = T(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12137,a(flip),b,17241,a)].">
      <j1 rule="hyper" parents="64 12137 17241"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14676,a(flip),b,17242,a),flip(a)].">
      <j1 rule="hyper" parents="64 14676 17242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y / T(z * K(w,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13608,a(flip),b,17243,a)].">
      <j1 rule="hyper" parents="64 13608 17243"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y * T(K(u,w) / z,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14776,a(flip),b,17244,a),flip(a)].">
      <j1 rule="hyper" parents="319 14776 17244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17246">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u * T(K(w,y) / z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14371,a,b,17245,a)].">
      <j1 rule="hyper" parents="64 14371 17245"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u * T(z \ K(w,y),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,14788,a(flip),b,17246,a),flip(a)].">
      <j1 rule="hyper" parents="319 14788 17246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),z \ w)) = T(x,y * T(z \ K(u,w),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14969,a,b,17247,a)].">
      <j1 rule="hyper" parents="64 14969 17247"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      T(x,y / ((z \ T(u,w)) \ u)) = T(x,y * T(z \ K(w,u),u))
    ]]></literal>
    <justification jstring="[para(14705(a,1),17248(a,1,2,2))].">
      <j1 rule="para" parents="14705 17248"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z \ w),z \ w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15561,a(flip),b,17249,a),flip(a)].">
      <j1 rule="hyper" parents="64 15561 17249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      T(x,T(y * y,z) * ((u / z) \ w)) = T(x,(u / (z * (y * y))) \ w)
    ]]></literal>
    <justification jstring="[para(4081(a,1),17047(a,1,2))].">
      <j1 rule="para" parents="4081 17047"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(15165,a,17125,a),flip(a)].">
      <j1 rule="hyper" parents="15165 17125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = w
    ]]></literal>
    <justification jstring="[para(17252(a,2),13144(a,1))].">
      <j1 rule="para" parents="17252 13144"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(u \ (w \ u),x)) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(443(a,1),17183(a,1,2,2,1))].">
      <j1 rule="para" parents="443 17183"/>
    </justification>
  </clause>

  <clause id="17255">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(5104,a,16877,a)].">
      <j1 rule="hyper" parents="5104 16877"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(17255(a,1),13691(a,1,2))].">
      <j1 rule="para" parents="17255 13691"/>
    </justification>
  </clause>

  <clause id="17258">
    <literal><![CDATA[
      K(x,y) \ T(x,x * (a(K(z,u),w,v5) \ y)) = L(x,a(K(z,u),w,v5) \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3327(a,1),16895(a,1,2))].">
      <j1 rule="para" parents="3327 16895"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * (T(v5,K(y,z) * v6) \ v6)) = T(x,(K(y,L(z,u,w)) * v6) / v5)
    ]]></literal>
    <justification jstring="[hyper(16976,a,16486,a)].">
      <j1 rule="hyper" parents="16976 16486"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * T(z,v5)))) = T(x,u * (w * (K(z,y) * T(z,v5))))
    ]]></literal>
    <justification jstring="[para(6851(a,1),16531(a,1,2,1))].">
      <j1 rule="para" parents="6851 16531"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      T(x,y * (z * (K(u,w) * T(u,v5)))) = T(x,y * (z * T(T(u,w),v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16736,a(flip),b,17260,a),flip(a)].">
      <j1 rule="hyper" parents="64 16736 17260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(14529,a,16540,a),flip(a)].">
      <j1 rule="hyper" parents="14529 16540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ y,u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,14262,a(flip),b,17263,a),flip(a)].">
      <j1 rule="hyper" parents="319 14262 17263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17265">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(12438(a,1),17264(a,1,2,2,2))].">
      <j1 rule="para" parents="12438 17264"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(z \ u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(5395(a,1),16570(a,1,2,2,2))].">
      <j1 rule="para" parents="5395 16570"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      K(x,y / ((z \ K(z \ u,u)) * u)) = K(x,y * (((z \ 1) * u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17200,a(flip),b,17266,a),flip(a)].">
      <j1 rule="hyper" parents="64 17200 17266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17268">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(12301(a,1),17267(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12301 17267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14550,a(flip),b,17268,a),flip(a)].">
      <j1 rule="hyper" parents="319 14550 17268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16569,a(flip),b,17269,a)].">
      <j1 rule="hyper" parents="64 16569 17269"/>
    </justification>
  </clause>

  <clause id="17271">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17112,a(flip),b,17270,a),flip(a)].">
      <j1 rule="hyper" parents="64 17112 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(w,K(y,z) \ (u * x)) \ K(u,K(w,x))
    ]]></literal>
    <justification jstring="[para(15244(a,1),16572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15244 16572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(w,K(y,z) \ (u * x)) \ K(w,K(u,x))
    ]]></literal>
    <justification jstring="[para(6742(a,1),17272(a,2,2))].">
      <j1 rule="para" parents="6742 17272"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      T(x,(y / (1 / K(z,u \ w))) * v5) = T(x,(y * K(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(9318,a,16617,a),flip(a)].">
      <j1 rule="hyper" parents="9318 16617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      T(x,(y / (1 / K(z,u \ w))) * v5) = T(x,y * (K(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,16600,a(flip),b,17275,a),flip(a)].">
      <j1 rule="hyper" parents="319 16600 17275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      T(x,(y / K(z \ u,w)) * v5) = T(x,y * (K(w,z * u) * v5))
    ]]></literal>
    <justification jstring="[para(4214(a,1),17276(a,1,2,1,2))].">
      <j1 rule="para" parents="4214 17276"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      T(x,(y * K(z,u \ w)) * v5) = T(x,y * (K(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[para(5174(a,1),17277(a,1,2,1))].">
      <j1 rule="para" parents="5174 17277"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      T(x,y * (K(z,u \ w) * v5)) = T(x,y * (K(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16618,a,17278,a)].">
      <j1 rule="hyper" parents="16618 17278"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      T(x,(T(y,L(z \ u,w,u / z)) \ v5) * v6) = T(x,(y \ v5) * (K(y,z * u) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,16566,a,b,17279,a)].">
      <j1 rule="hyper" parents="64 16566 17279"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      T(x,(T(y,L(z \ u,w,u / z)) \ v5) * v6) = T(x,(T(y,z * u) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(319,a,16557,a(flip),b,17280,a),flip(a)].">
      <j1 rule="hyper" parents="319 16557 17280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      T(x,(T(y,z \ u) \ w) * v5) = T(x,(T(y,z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(477(a,1),17281(a,1,2,1,1,2))].">
      <j1 rule="para" parents="477 17281"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),(T(z,v5 * v6) \ w) * y) = T(x,y * (T(z,v5 \ v6) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15484,a(flip),b,17282,a),flip(a)].">
      <j1 rule="hyper" parents="64 15484 17282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      T(x,(T(y,z * z) \ u) * w) = T(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(213(a,1),17282(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="213 17282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17285">
    <literal><![CDATA[
      T(x,R(y / y,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,(z \ u) * (w \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15740,a,b,17284,a)].">
      <j1 rule="hyper" parents="64 15740 17284"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      T(x,R(1,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,(z \ u) * (w \ (y * y)))
    ]]></literal>
    <justification jstring="[para(75(a,1),17285(a,1,2,1,1))].">
      <j1 rule="para" parents="75 17285"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      T(x,1 \ ((y \ ((z * z) * u)) / w)) = T(x,(y \ u) * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[para(362(a,1),17287(a,1,2,1))].">
      <j1 rule="para" parents="362 17287"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      T(x,(y \ ((z * z) * u)) / w) = T(x,(y \ u) * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[para(66(a,1),17289(a,1,2))].">
      <j1 rule="para" parents="66 17289"/>
    </justification>
  </clause>

  <clause id="17292">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * ((K(w,T(v5,v6)) \ v7) * K(z,T(y,u)))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(6146(a,1),16732(a,1,2,1,2))].">
      <j1 rule="para" parents="6146 16732"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,11221,a(flip),b,16984,a),flip(a)].">
      <j1 rule="hyper" parents="319 11221 16984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14592,a(flip),b,17293,a)].">
      <j1 rule="hyper" parents="64 14592 17293"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,16980,a(flip),b,17294,a),flip(a)].">
      <j1 rule="hyper" parents="319 16980 17294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(z,y) * w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(4356(a,1),17000(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="4356 17000"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w) * v5) = K(x,T(y / T(u,z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(15304,a,17164,a),flip(a)].">
      <j1 rule="hyper" parents="15304 17164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z) * w) = K(x,(((u \ z) * u) \ y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15797,a(flip),b,17298,a),flip(a)].">
      <j1 rule="hyper" parents="64 15797 17298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      K(x,(((y \ z) * y) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15031,a(flip),b,17299,a),flip(a)].">
      <j1 rule="hyper" parents="64 15031 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      T(x,(K(y,L(z,u,w)) * v5) / v6) = T(x,K(y,z) * (T(v6,K(y,z) * v5) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16490,a,17259,a),flip(a)].">
      <j1 rule="hyper" parents="16490 17259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      T(x,(K(y,L(z,u,w)) * v5) / v6) = T(x,v5 * (v6 \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17137,a(flip),b,17301,a),flip(a)].">
      <j1 rule="hyper" parents="319 17137 17301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      T(x,y * (z \ K(u,L(w,v5,v6)))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16383,a(flip),b,17303,a)].">
      <j1 rule="hyper" parents="64 16383 17303"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      T(x,y / (z * (u * K(w,v5)))) = T(x,y * ((z * u) \ K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16715,a(flip),b,17304,a)].">
      <j1 rule="hyper" parents="64 16715 17304"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) \ v5)) = T(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(9319,a,17283,a),flip(a)].">
      <j1 rule="hyper" parents="9319 17283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      T(x,(y \ 1) * (T(z,u * w) \ v5)) = T(x,y \ (T(z,u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(12244,a,17307,a),flip(a)].">
      <j1 rule="hyper" parents="12244 17307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      T(x,y * (T(z,u * u) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(213(a,1),17307(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="213 17307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,y * z) \ w))
    ]]></literal>
    <justification jstring="[para(4434(a,2),17307(a,1,2))].">
      <j1 rule="para" parents="4434 17307"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,(z * z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(961(a,1),17309(a,1,2))].">
      <j1 rule="para" parents="961 17309"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12967,a(flip),b,17311,a),flip(a)].">
      <j1 rule="hyper" parents="319 12967 17311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      T(x,(y / T(z,u * (u * y))) * (u * u)) = T(x,u * (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14792,a,b,17312,a)].">
      <j1 rule="hyper" parents="64 14792 17312"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      T(x,y * (y * (z \ T(u,y \ (y \ z))))) = T(x,u / ((y * y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12173,a(flip),b,17312,a),flip(a)].">
      <j1 rule="hyper" parents="64 12173 17312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      T(x,(y \ ((z * z) * u)) / T(w,z * (z * (y \ u)))) = T(x,w \ (y \ ((z * z) * u)))
    ]]></literal>
    <justification jstring="[para(17312(a,1),11064(a,1,2,2))].">
      <j1 rule="para" parents="17312 11064"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) \ v5)) = T(x,y \ (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(12244,a,17308,a),flip(a)].">
      <j1 rule="hyper" parents="12244 17308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,z * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14673,a,b,17310,a),flip(a)].">
      <j1 rule="hyper" parents="319 14673 17310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17318">
    <literal><![CDATA[
      T(x,y * (T(z,u * (u * y)) \ (u * u))) = T(x,u * (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12345,a(flip),b,17313,a)].">
      <j1 rule="hyper" parents="64 12345 17313"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      T(x,y * (y * (z \ T(u,y \ (y \ z))))) = T(x,(u / z) * (y * y))
    ]]></literal>
    <justification jstring="[para(688(a,1),17314(a,2,2))].">
      <j1 rule="para" parents="688 17314"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      T(x,y / (z / (u * u))) = T(x,(y / z) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14791,a(flip),b,17319,a)].">
      <j1 rule="hyper" parents="64 14791 17319"/>
    </justification>
  </clause>

  <clause id="17321">
    <literal><![CDATA[
      T(x,y / (z / (u * u))) = T(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12345,a(flip),b,17320,a),flip(a)].">
      <j1 rule="hyper" parents="319 12345 17320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17322">
    <literal><![CDATA[
      T(x,(y * (z * z)) / u) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12445,a,b,17321,a)].">
      <j1 rule="hyper" parents="64 12445 17321"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      T(x,y * ((z * z) * (u \ 1))) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12135,a,b,17321,a)].">
      <j1 rule="hyper" parents="64 12135 17321"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,(y * (u * u)) / (u * (z / u)))
    ]]></literal>
    <justification jstring="[para(9226(a,2),17322(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9226 17322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17325">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (T(z,u \ 1) \ (u * u))) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15831,a(flip),b,17323,a),flip(a)].">
      <j1 rule="hyper" parents="64 15831 17323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,(y * (u * u)) / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13621,a(flip),b,17324,a),flip(a)].">
      <j1 rule="hyper" parents="319 13621 17324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,y * (T(z,u) \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17322,a(flip),b,17326,a),flip(a)].">
      <j1 rule="hyper" parents="319 17322 17326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,y * T(z \ (u * u),u))
    ]]></literal>
    <justification jstring="[hyper(319,a,16693,a,b,17327,a),flip(a)].">
      <j1 rule="hyper" parents="319 16693 17327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) \ (z * z))) = T(x,y * T(u \ (z * z),z))
    ]]></literal>
    <justification jstring="[para(9226(a,1),17328(a,1,2,2))].">
      <j1 rule="para" parents="9226 17328"/>
    </justification>
  </clause>

  <clause id="17330">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,w * (w * (y \ z))) \ (w * w))) = T(x,u \ (y \ ((w * w) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17290,a(flip),b,17315,a)].">
      <j1 rule="hyper" parents="64 17290 17315"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      T(x,y \ (z \ ((u * u) * w))) = T(x,u * (u * (y \ (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,17318,a(flip),b,17330,a),flip(a)].">
      <j1 rule="hyper" parents="64 17318 17330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (u * (K(x,K(y,z)) * (w * v5))) = L(v5,K(x,K(y,z)) * w,u)
    ]]></literal>
    <justification jstring="[para(16329(a,2),16144(a,1,1))].">
      <j1 rule="para" parents="16329 16144"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * (u / y)) / (((u \ z) \ 1) * (u / y))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(12440(a,1),16264(a,1,1))].">
      <j1 rule="para" parents="12440 16264"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      L(K(x,K(y,z)) * ((u * w) \ v5),K(x,K(y,z)),u * w) = (u * (w * K(x,K(y,z)))) \ v5
    ]]></literal>
    <justification jstring="[para(6757(a,1),16293(a,1,1,1))].">
      <j1 rule="para" parents="6757 16293"/>
    </justification>
  </clause>

  <clause id="17335">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * ((y * v5) * K(z,K(u,w)))) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(16302(a,1),16338(a,1,2))].">
      <j1 rule="para" parents="16302 16338"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(12768,a,16639,a)].">
      <j1 rule="hyper" parents="12768 16639"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u),z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13922,a,17336,a)].">
      <j1 rule="hyper" parents="13922 17336"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15661,a,17338,a),flip(a)].">
      <j1 rule="hyper" parents="15661 17338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17340">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(12128(a,1),17339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12128 17339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      K(x,L((y * z) * (u / w),y,z \ 1)) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(14897,a,16836,a)].">
      <j1 rule="hyper" parents="14897 16836"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16837,a(flip),b,17341,a),flip(a)].">
      <j1 rule="hyper" parents="64 16837 17341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      T(K(x,(y * z) / ((u / w) \ 1)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(429,a,16658,a,b,17342,a)].">
      <j1 rule="hyper" parents="429 16658 17342"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(x,K(x,y) * (T(T(y,x) / (z \ 1),y) * u)) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(17061,a,17173,a),flip(a)].">
      <j1 rule="hyper" parents="17061 17173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      K(x,T(T(y,x) / (z \ 1),y) * u) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(5844,a,17344,a)].">
      <j1 rule="hyper" parents="5844 17344"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      K(x,((y \ 1) \ T(z,x)) * u) = K(x,(T(z,y) / (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15030,a(flip),b,17345,a)].">
      <j1 rule="hyper" parents="64 15030 17345"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(17010,a,17347,a),flip(a)].">
      <j1 rule="hyper" parents="17010 17347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17028,a(flip),b,17348,a)].">
      <j1 rule="hyper" parents="64 17028 17348"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (K(x,K(y,z)) \ (u * (w * v5))) = L(v5,K(x,K(y,z)) * w,u)
    ]]></literal>
    <justification jstring="[para(16329(a,2),17332(a,1,2))].">
      <j1 rule="para" parents="16329 17332"/>
    </justification>
  </clause>

  <clause id="17351">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ v5 = K(z,K(u,w)) * ((x * y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(16380,a,17334,a),flip(a)].">
      <j1 rule="hyper" parents="16380 17334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(14089(a,2),17351(a,1,1,2))].">
      <j1 rule="para" parents="14089 17351"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * (y * (v5 * K(z,K(u,w))))) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(16091(a,1),17335(a,1,2,2))].">
      <j1 rule="para" parents="16091 17335"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(K(u,w),v5)) = L(x,K(v5,K(u,w)) * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4788,a(flip),b,17350,a)].">
      <j1 rule="hyper" parents="64 4788 17350"/>
    </justification>
  </clause>

  <clause id="17356">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,K(v5,K(u,w)) * y,z)
    ]]></literal>
    <justification jstring="[para(6705(a,1),17355(a,1,3))].">
      <j1 rule="para" parents="6705 17355"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(16143,a,17356,a),flip(a)].">
      <j1 rule="hyper" parents="16143 17356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      L(x,y * K(z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(5933(a,1),17357(a,1,2))].">
      <j1 rule="para" parents="5933 17357"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(6045(a,1),17357(a,1,2))].">
      <j1 rule="para" parents="6045 17357"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ (w * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(12327(a,1),17359(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12327 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,9557,a,b,17360,a),flip(a)].">
      <j1 rule="hyper" parents="319 9557 17360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15711,a(flip),b,17360,a),flip(a)].">
      <j1 rule="hyper" parents="64 15711 17360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(17363(a,2),9627(a,1))].">
      <j1 rule="para" parents="17363 9627"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z * K(x,K(y,u)),K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(15709(a,2),17365(a,1))].">
      <j1 rule="para" parents="15709 17365"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = (u * z) / (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14493,a,b,17364,a)].">
      <j1 rule="hyper" parents="64 14493 17364"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w,K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16093(a,2),17354(a,1,1))].">
      <j1 rule="para" parents="16093 17354"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) = L(z,y,K(u,K(w,v5)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16402,a(flip),b,17369,a)].">
      <j1 rule="hyper" parents="64 16402 17369"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,((z * u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(11146(a,1),16389(a,1,2))].">
      <j1 rule="para" parents="11146 16389"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16388,a(flip),b,17371,a),flip(a)].">
      <j1 rule="hyper" parents="64 16388 17371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,(y * (T((y \ 1) \ z,u) / T(y,K(v5,v6)))) \ w)
    ]]></literal>
    <justification jstring="[para(16439(a,1),16586(a,2,2,1))].">
      <j1 rule="para" parents="16439 16586"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * ((v5 \ z) / z))) = K(x,y * T(v5 \ (z * K(u,w)),z))
    ]]></literal>
    <justification jstring="[hyper(15431,a,16655,a),flip(a)].">
      <j1 rule="hyper" parents="15431 16655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * ((v5 \ z) / z))) = K(x,y * (z / (K(w,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17177,a(flip),b,17374,a),flip(a)].">
      <j1 rule="hyper" parents="319 17177 17374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,(y * K(w,u)) \ ((z / y) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11424,a(flip),b,16720,a),flip(a)].">
      <j1 rule="hyper" parents="319 11424 16720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17377">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(4162(a,1),16730(a,2,1,1))].">
      <j1 rule="para" parents="4162 16730"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((T(x,z) * (y * K(x,z))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(4081(a,1),17377(a,1,2,1))].">
      <j1 rule="para" parents="4081 17377"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(16729,a,17378,a)].">
      <j1 rule="hyper" parents="16729 17378"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(4367(a,1),17379(a,1,1))].">
      <j1 rule="para" parents="4367 17379"/>
    </justification>
  </clause>

  <clause id="17381">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(9234,a,17380,a)].">
      <j1 rule="hyper" parents="9234 17380"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(17380(a,1),9198(a,1))].">
      <j1 rule="para" parents="17380 9198"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17381(a,1,2,2))].">
      <j1 rule="para" parents="9 17381"/>
    </justification>
  </clause>

  <clause id="17384">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17368,a(flip),b,17383,a),flip(a)].">
      <j1 rule="hyper" parents="64 17368 17383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * (K(z,T(y,x)) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9232,a(flip),b,17383,a),flip(a)].">
      <j1 rule="hyper" parents="64 9232 17383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(9191(a,1),17385(a,1,2))].">
      <j1 rule="para" parents="9191 17385"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5189,a,17386,a)].">
      <j1 rule="hyper" parents="5189 17386"/>
    </justification>
  </clause>

  <clause id="17388">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,17386,a),flip(a)].">
      <j1 rule="hyper" parents="145 17386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17389">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,15710,a(flip),b,17387,a),flip(a)].">
      <j1 rule="hyper" parents="64 15710 17387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17390">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(12363(a,1),17387(a,1,3))].">
      <j1 rule="para" parents="12363 17387"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(17387(a,1),15714(a,1,1))].">
      <j1 rule="para" parents="17387 15714"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(4363(a,1),17388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 17388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) * u = T(z,K(y,x)) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(5966(a,1),17391(a,2,1))].">
      <j1 rule="para" parents="5966 17391"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      (x * K(y,z)) * (x \ u) = x * ((x * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(4379(a,1),17392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4379 17392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,L(K(w,v5) * v6,K(v5,w),u)))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(17392(a,1),15398(a,1,2,2,2,1))].">
      <j1 rule="para" parents="17392 15398"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * L(u \ 1,u,u \ (x * K(z,y)))) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[hyper(127,a,9240,a,b,17394,a)].">
      <j1 rule="hyper" parents="127 9240 17394"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17364,a(flip),b,17389,a),flip(a)].">
      <j1 rule="hyper" parents="64 17364 17389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,155,a(flip),b,17397,a)].">
      <j1 rule="hyper" parents="130 155 17397"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      (K(x,L(y,z * (u * K(w,v5)),u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(17397(a,1),12903(a,2,2))].">
      <j1 rule="para" parents="17397 12903"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12006,a(flip),b,17398,a),flip(a)].">
      <j1 rule="hyper" parents="319 12006 17398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(5925(a,1),17398(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5925 17398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6125,a(flip),b,17401,a),flip(a)].">
      <j1 rule="hyper" parents="64 6125 17401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(11924(a,1),17402(a,2,2))].">
      <j1 rule="para" parents="11924 17402"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6791(a,1),17384(a,1,2,2))].">
      <j1 rule="para" parents="6791 17384"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(u,K(y,z)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(5885(a,2),17404(a,1,2))].">
      <j1 rule="para" parents="5885 17404"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(11924(a,1),17403(a,1,1,2))].">
      <j1 rule="para" parents="11924 17403"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(y,K(z,u)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6748(a,2),17405(a,1,2,1,2,2))].">
      <j1 rule="para" parents="6748 17405"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(14250(a,1),17407(a,1,2,1))].">
      <j1 rule="para" parents="14250 17407"/>
    </justification>
  </clause>

  <clause id="17409">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(6851(a,1),17408(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6851 17408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      (x * K(y,z)) \ (x / u) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[para(16775(a,1),17396(a,1,2))].">
      <j1 rule="para" parents="16775 17396"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * (x \ ((x * K(u,z)) / y))
    ]]></literal>
    <justification jstring="[para(17410(a,1),16879(a,2,2))].">
      <j1 rule="para" parents="17410 16879"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = (x * K(u,z)) / y
    ]]></literal>
    <justification jstring="[hyper(319,a,10,a(flip),b,17412,a),flip(a)].">
      <j1 rule="hyper" parents="319 10 17412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),K(z,u) * y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17297,a(flip),b,17032,a)].">
      <j1 rule="hyper" parents="64 17297 17032"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,y \ z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11188,a(flip),b,17055,a)].">
      <j1 rule="hyper" parents="64 11188 17055"/>
    </justification>
  </clause>

  <clause id="17418">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u \ 1)) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16693,a,b,17325,a)].">
      <j1 rule="hyper" parents="64 16693 17325"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,K(w,u) \ (y \ ((z / y) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11424,a(flip),b,17376,a),flip(a)].">
      <j1 rule="hyper" parents="319 11424 17376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17097,a(flip),b,17416,a)].">
      <j1 rule="hyper" parents="64 17097 17416"/>
    </justification>
  </clause>

  <clause id="17422">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / v5) * v6) = K(x,((u / (K(z,y) * w)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17027,a(flip),b,17420,a)].">
      <j1 rule="hyper" parents="64 17027 17420"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15632,a(flip),b,17418,a)].">
      <j1 rule="hyper" parents="64 15632 17418"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * ((T(z,u \ 1) \ 1) * y))
    ]]></literal>
    <justification jstring="[para(33(a,1),17423(a,2,2))].">
      <j1 rule="para" parents="33 17423"/>
    </justification>
  </clause>

  <clause id="17425">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(w,u) \ y) \ v5),x) = a(x,K(u,w) \ (y \ ((z / y) \ v5)),x)
    ]]></literal>
    <justification jstring="[para(6791(a,1),17419(a,1,2,1,2))].">
      <j1 rule="para" parents="6791 17419"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      a(x,T(y,K(z,u)) \ (w * ((K(u,z) \ w) \ v5)),x) = a(x,K(z,u) \ (w \ ((y / w) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11425,a(flip),b,17425,a)].">
      <j1 rule="hyper" parents="64 11425 17425"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      K((x * K(y,z)) * L(u,x,K(y,z)),w) = K(w,K(z,y) \ (u * x)) \ K(w,K(u,x))
    ]]></literal>
    <justification jstring="[para(15205(a,1),16180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15205 16180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,w)) = K(K(y,T(z,w)) \ (w * u),x)
    ]]></literal>
    <justification jstring="[para(16723(a,1),17427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16723 17427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,w)) = K(K(y,z) \ (w * u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,16403,a(flip),b,17430,a),flip(a)].">
      <j1 rule="hyper" parents="319 16403 17430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(K(y,z) \ (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17273,a,b,17431,a)].">
      <j1 rule="hyper" parents="64 17273 17431"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / x)),w) = K(z * (u / T(x,T(y,u))),w)
    ]]></literal>
    <justification jstring="[para(7236(a,1),17433(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7236 17433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / x)),w) = K(z * (u / T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,15405,a(flip),b,17434,a),flip(a)].">
      <j1 rule="hyper" parents="319 15405 17434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / y)),w) = K(z * (u / T(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(14427,a,17435,a)].">
      <j1 rule="hyper" parents="14427 17435"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(u * (x / T(y,z)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(17436(a,1),15758(a,1,2))].">
      <j1 rule="para" parents="17436 15758"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      ((x / T(y,z)) * u) \ T(u * (x / T(y,z)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9193,a(flip),b,17438,a)].">
      <j1 rule="hyper" parents="64 9193 17438"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      a(x,y \ (K(y \ 1,z) \ u),x) = a(x,u / T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(8686,a,17439,a),flip(a)].">
      <j1 rule="hyper" parents="8686 17439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      a(x,y \ (K(y \ 1,z) \ u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z) \ u,x) = w
    ]]></literal>
    <justification jstring="[para(17440(a,2),10995(a,1))].">
      <j1 rule="para" parents="17440 10995"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      (x * (y * (K(z,K(u,w)) * v5))) \ ((x * y) * (K(z,K(u,w)) * v5)) = a(x,y * K(z,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(16378(a,1),16375(a,1,2))].">
      <j1 rule="para" parents="16378 16375"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(16339(a,1),16376(a,1,2,1))].">
      <j1 rule="para" parents="16339 16376"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,(T(L(y,u,w),z) \ v5) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,17300,a(flip),b,16426,a),flip(a)].">
      <j1 rule="hyper" parents="319 17300 16426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,(L(T(y,z),u,w) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),17446(a,2,2,1,1))].">
      <j1 rule="para" parents="25 17446"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / (((u \ z) \ 1) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(12496(a,1),17333(a,1,2,2))].">
      <j1 rule="para" parents="12496 17333"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,K(u,w)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17444(a,1),713(a,1))].">
      <j1 rule="para" parents="17444 713"/>
    </justification>
  </clause>

  <clause id="17450">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * (K(y,K(z,u)) * v5)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(16584(a,1),17445(a,1,2))].">
      <j1 rule="para" parents="16584 17445"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      ((x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * v5)) * K(y,K(z,u)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16582,a(flip),b,17450,a)].">
      <j1 rule="hyper" parents="64 16582 17450"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      (K(x,K(y,z)) * ((u * (w * v5)) \ ((u * w) * v5))) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(17353(a,1),17451(a,1,1))].">
      <j1 rule="para" parents="17353 17451"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      (K(x,K(y,z)) * a(u,w,v5)) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(14(a,2),17452(a,1,1,2))].">
      <j1 rule="para" parents="14 17452"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(14318,a,17453,a),flip(a)].">
      <j1 rule="hyper" parents="14318 17453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6405(a,1),17454(a,1,1))].">
      <j1 rule="para" parents="6405 17454"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11735,a(flip),b,17456,a),flip(a)].">
      <j1 rule="hyper" parents="64 11735 17456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17460">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10915,a(flip),b,17458,a),flip(a)].">
      <j1 rule="hyper" parents="64 10915 17458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(12368(a,1),17460(a,1,1,2))].">
      <j1 rule="para" parents="12368 17460"/>
    </justification>
  </clause>

  <clause id="17463">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,x \ y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,10919,a(flip),b,17462,a)].">
      <j1 rule="hyper" parents="64 10919 17462"/>
    </justification>
  </clause>

  <clause id="17464">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17462,a(flip),b,17463,a),flip(a)].">
      <j1 rule="hyper" parents="64 17462 17463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17465">
    <literal><![CDATA[
      (x * y) / a(T(x,z) / z,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(17464(a,1),11502(a,1,2))].">
      <j1 rule="para" parents="17464 11502"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(10914(a,1),17465(a,1,2))].">
      <j1 rule="para" parents="10914 17465"/>
    </justification>
  </clause>

  <clause id="17467">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(12929(a,1),17466(a,1,2))].">
      <j1 rule="para" parents="12929 17466"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(855,a,17467,a),flip(a)].">
      <j1 rule="hyper" parents="855 17467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(130,a,17468,a,b,11,a)].">
      <j1 rule="hyper" parents="130 17468 11"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(16769(a,1),17469(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16769 17469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(12986(a,1),17470(a,2,1,2))].">
      <j1 rule="para" parents="12986 17470"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      T(x * K(T(y,K(z,u)),K(w,v5) \ (y \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(4921(a,1),16391(a,1,1))].">
      <j1 rule="para" parents="4921 16391"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      T(x * K(y,K(z,u) \ (y \ x)),K(z,u)) = y * T(x / y,K(z,u))
    ]]></literal>
    <justification jstring="[para(1327(a,1),17472(a,1,1,2,1))].">
      <j1 rule="para" parents="1327 17472"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      T(K(x \ (y / K(z,u)),x) \ y,K(z,u)) = x * T(y / x,K(z,u))
    ]]></literal>
    <justification jstring="[para(9377(a,2),17474(a,1,1))].">
      <j1 rule="para" parents="9377 17474"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      T(K(x \ (y * K(z,u)),x) \ y,K(u,z)) = x * T(y / x,K(u,z))
    ]]></literal>
    <justification jstring="[para(5174(a,1),17475(a,1,1,1,1,2))].">
      <j1 rule="para" parents="5174 17475"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      T(K(x \ (K(y,z) \ u),x) \ u,K(y,z)) = x * T(u / x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14607(a,2),17476(a,1,1,1))].">
      <j1 rule="para" parents="14607 17476"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ T(u,K(y,z)) = x * T(u / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15189,a(flip),b,17477,a)].">
      <j1 rule="hyper" parents="64 15189 17477"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ ((K(u,z) * y) / w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17422,a(flip),b,16398,a)].">
      <j1 rule="hyper" parents="64 17422 16398"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ ((u \ (u / y)) * w),x) = a(x,T(T(u \ (u / y),z),y \ 1) * w,x)
    ]]></literal>
    <justification jstring="[para(4993(a,1),16786(a,1,2,1))].">
      <j1 rule="para" parents="4993 16786"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16861,a(flip),b,16965,a)].">
      <j1 rule="hyper" parents="64 16861 16965"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (y \ (z * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(17482(a,2),15016(a,1))].">
      <j1 rule="para" parents="17482 15016"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(u * z,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17204,a(flip),b,17147,a),flip(a)].">
      <j1 rule="hyper" parents="319 17204 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(z * u,u)))
    ]]></literal>
    <justification jstring="[para(4281(a,2),17485(a,2,2,2,2))].">
      <j1 rule="para" parents="4281 17485"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((T(u,z) * w) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17210,a(flip),b,17486,a),flip(a)].">
      <j1 rule="hyper" parents="319 17210 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) = K(x,y * ((u * w) \ 1))
    ]]></literal>
    <justification jstring="[para(11996(a,1),17487(a,2,2,2))].">
      <j1 rule="para" parents="11996 17487"/>
    </justification>
  </clause>

  <clause id="17490">
    <literal><![CDATA[
      K(x,y / (((T(z,u) / (z / (u \ 1))) \ 1) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(17488(a,2),12279(a,1))].">
      <j1 rule="para" parents="17488 12279"/>
    </justification>
  </clause>

  <clause id="17491">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * (K(w,T(v5,v6)) \ (v7 * K(z,T(y,u))))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(16152(a,2),17292(a,1,2,1,2))].">
      <j1 rule="para" parents="16152 17292"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * w) / v5)) * v6) = K(x,(y \ (w / (K(u,z) * v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,15478,a(flip),b,17479,a),flip(a)].">
      <j1 rule="hyper" parents="64 15478 17479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      K(x,(y * K(z,T(u,w))) \ v5) = K(x,y \ (K(z,T(u,w)) \ v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),17491(a,1,2,1))].">
      <j1 rule="para" parents="10 17491"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13681,a,16214,a)].">
      <j1 rule="hyper" parents="13681 16214"/>
    </justification>
  </clause>

  <clause id="17496">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(3327(a,1),17494(a,1,2,1,1))].">
      <j1 rule="para" parents="3327 17494"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(11337,a,17496,a)].">
      <j1 rule="hyper" parents="11337 17496"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * T(w,K(y,x) * v5)) / (K(x,L(y,z,u)) * w) = K(w,v5 * K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(14472(a,1),16491(a,1,1))].">
      <j1 rule="para" parents="14472 16491"/>
    </justification>
  </clause>

  <clause id="17500">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,K(z,L(y,w,v5)))) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(7091,a,17498,a)].">
      <j1 rule="hyper" parents="7091 17498"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(16187(a,1),17500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16187 17500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16926,a(flip),b,17501,a)].">
      <j1 rule="hyper" parents="64 16926 17501"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ v5) * K(z,y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(17501(a,1),16936(a,1))].">
      <j1 rule="para" parents="17501 16936"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14259,a,b,17502,a),flip(a)].">
      <j1 rule="hyper" parents="319 14259 17502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      K(x,(y \ (z * T(u,z))) * K(w,v5)) = K(x,y \ ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15434,a(flip),b,17502,a),flip(a)].">
      <j1 rule="hyper" parents="64 15434 17502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(6113(a,1),17506(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6113 17506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,(y \ (w * v5)) * K(u,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),17507(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 17507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14259,a,b,17509,a),flip(a)].">
      <j1 rule="hyper" parents="319 14259 17509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ (u * (w * v5))) * K(z,y)) = K(x,L(v5,w,K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(18(a,2),17509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 17509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(4081(a,1),17510(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4081 17510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17513">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(15040,a,17508,a),flip(a)].">
      <j1 rule="hyper" parents="15040 17508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * (y \ (z * v5))) = v6
    ]]></literal>
    <justification jstring="[para(17508(a,1),15040(a,1))].">
      <j1 rule="para" parents="17508 15040"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[hyper(16457,a,17513,a),flip(a)].">
      <j1 rule="hyper" parents="16457 17513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(9183(a,1),17513(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9183 17513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * K(w,v5)) * u) * v6)) = K(x,y \ ((u * z) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,17046,a(flip),b,17512,a),flip(a)].">
      <j1 rule="hyper" parents="64 17046 17512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(4314(a,1),17515(a,1,2))].">
      <j1 rule="para" parents="4314 17515"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(13492,a,17518,a),flip(a)].">
      <j1 rule="hyper" parents="13492 17518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,17012,a(flip),b,17521,a),flip(a)].">
      <j1 rule="hyper" parents="319 17012 17521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(8486(a,1),17522(a,1,2,2,1))].">
      <j1 rule="para" parents="8486 17522"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(189(a,1),17519(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="189 17519"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,11244,a(flip),b,17523,a),flip(a)].">
      <j1 rule="hyper" parents="319 11244 17523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16635,a,b,17526,a)].">
      <j1 rule="hyper" parents="64 16635 17526"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(17504,a,17511,a),flip(a)].">
      <j1 rule="hyper" parents="17504 17511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),17528(a,2,2))].">
      <j1 rule="para" parents="18 17528"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,K(z,u) * w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(12767,a,17529,a)].">
      <j1 rule="hyper" parents="12767 17529"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,12788,a,b,17529,a),flip(a)].">
      <j1 rule="hyper" parents="319 12788 17529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5933(a,1),17529(a,1,2,3))].">
      <j1 rule="para" parents="5933 17529"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (K(w,v5) * u)) = (K(x,y) * z) * (K(w,v5) * u)
    ]]></literal>
    <justification jstring="[para(17529(a,1),12796(a,1,1))].">
      <j1 rule="para" parents="17529 12796"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w)) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13247,a(flip),b,17533,a),flip(a)].">
      <j1 rule="hyper" parents="64 13247 17533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5047(a,1),17533(a,1,2,3))].">
      <j1 rule="para" parents="5047 17533"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(T(w,v5),v6,v7))) = K(x,L(y,z,u \ L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(12383(a,1),17533(a,1,2,3))].">
      <j1 rule="para" parents="12383 17533"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(17533(a,1),12531(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17533 12531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (u * K(w,v5))) = (K(x,y) * z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[para(17533(a,1),12796(a,1,1))].">
      <j1 rule="para" parents="17533 12796"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[para(17533(a,1),14454(a,1,1,1))].">
      <j1 rule="para" parents="17533 14454"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,12531,a(flip),b,17538,a),flip(a)].">
      <j1 rule="hyper" parents="319 12531 17538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17538(a,2),12653(a,1))].">
      <j1 rule="para" parents="17538 12653"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(12596,a,17541,a)].">
      <j1 rule="hyper" parents="12596 17541"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(12774(a,1),17541(a,1,3,1))].">
      <j1 rule="para" parents="12774 17541"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(15625(a,1),17541(a,1,3))].">
      <j1 rule="para" parents="15625 17541"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(16423,a,17543,a)].">
      <j1 rule="hyper" parents="16423 17543"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16236,a(flip),b,17543,a)].">
      <j1 rule="hyper" parents="64 16236 17543"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      L(1 / (x * K(y,z)),u,K(w,v5)) = a(w,u,K(x,v5)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17543(a,1),13277(a,2,1))].">
      <j1 rule="para" parents="17543 13277"/>
    </justification>
  </clause>

  <clause id="17549">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16952,a(flip),b,17547,a)].">
      <j1 rule="hyper" parents="64 16952 17547"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      a(x,y,K(z \ T(u,w),v5)) = a(v5,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(4522(a,1),17547(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4522 17547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(17547(a,1),12543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17547 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * T(a(x,y,K(w,v5)),K(w,v5) * y)
    ]]></literal>
    <justification jstring="[para(17547(a,1),15617(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17547 15617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(v5,y,K(x,(z / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16757,a,b,17550,a)].">
      <j1 rule="hyper" parents="64 16757 17550"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(10304(a,1),17551(a,2,2))].">
      <j1 rule="para" parents="10304 17551"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z * (w \ u),v5)) = v6
    ]]></literal>
    <justification jstring="[para(5047(a,1),17542(a,1,3,1))].">
      <j1 rule="para" parents="5047 17542"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,u,K(z,w)) = v6
    ]]></literal>
    <justification jstring="[para(16232(a,2),17542(a,1))].">
      <j1 rule="para" parents="16232 17542"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(17544(a,1),12551(a,1,2))].">
      <j1 rule="para" parents="17544 12551"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,y) * a(x,z,K(v6 * u,y))
    ]]></literal>
    <justification jstring="[para(17549(a,1),12679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17549 12679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17531(a,2),12838(a,1))].">
      <j1 rule="para" parents="17531 12838"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(3999(a,1),17562(a,1,2,3))].">
      <j1 rule="para" parents="3999 17562"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(4314(a,1),17562(a,1,2,3))].">
      <j1 rule="para" parents="4314 17562"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(w * u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(9187(a,1),17562(a,1,2,3))].">
      <j1 rule="para" parents="9187 17562"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ 1))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(17563,a,12981,a)].">
      <j1 rule="hyper" parents="17563 12981"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w \ 1))) = K(x,L(y,z,w \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(16630,a,17566,a)].">
      <j1 rule="hyper" parents="16630 17566"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,y \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(17564,a,13035,a)].">
      <j1 rule="hyper" parents="17564 13035"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((T(z,u) \ 1) * y) \ ((z \ 1) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(17564,a,8904,a)].">
      <j1 rule="hyper" parents="17564 8904"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w \ 1))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),17567(a,2,2,3))].">
      <j1 rule="para" parents="9 17567"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13132,a,17570,a),flip(a)].">
      <j1 rule="hyper" parents="13132 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      K(x,(y * z) / a(u \ 1,u,z)) = K(x,y / (a(u \ 1,u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12910,a(flip),b,17571,a)].">
      <j1 rule="hyper" parents="64 12910 17571"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(17562,a,17530,a)].">
      <j1 rule="hyper" parents="17562 17530"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9244,a(flip),b,17535,a)].">
      <j1 rule="hyper" parents="64 9244 17535"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ u,v5)) = a(v5,y,K(x,(w / z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17545,a(flip),b,17553,a)].">
      <j1 rule="hyper" parents="64 17545 17553"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = x * T(y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,11572,a(flip),b,17554,a),flip(a)].">
      <j1 rule="hyper" parents="319 11572 17554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(8217(a,1),17559(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="8217 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      T(x,a(y \ (z / u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y \ (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17559(a,1),12564(a,1))].">
      <j1 rule="para" parents="17559 12564"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(12893,a,17577,a),flip(a)].">
      <j1 rule="hyper" parents="12893 17577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17533,a(flip),b,17583,a)].">
      <j1 rule="hyper" parents="64 17533 17583"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),17584(a,2,2,2))].">
      <j1 rule="para" parents="9 17584"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      K(x,L(y,z \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9554(a,1),17584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9554 17584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(232(a,1),17586(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="232 17586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      K(x,L(y,L(T(z,u),w,v5),v6)) = K(x,L(y,L(z,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),17588(a,1,2,2))].">
      <j1 rule="para" parents="25 17588"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(11747(a,1),17588(a,1,2))].">
      <j1 rule="para" parents="11747 17588"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      K(x,L(y,L(z,u,K(w,v5)),v6)) = K(x,L(y,z,v6))
    ]]></literal>
    <justification jstring="[para(13261(a,2),17588(a,1,2,2))].">
      <j1 rule="para" parents="13261 17588"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(17594(a,1),12768(a,1))].">
      <j1 rule="para" parents="17594 12768"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,v6)) = K(x,L(y,w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(4378(a,1),17595(a,1,2,2))].">
      <j1 rule="para" parents="4378 17595"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,12551,a(flip),b,17581,a),flip(a)].">
      <j1 rule="hyper" parents="319 12551 17581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17555,a,12552,a)].">
      <j1 rule="hyper" parents="17555 12552"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      a(x,y,K(z,u * (w / v5))) = a(x,y,K(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12553,a(flip),b,17599,a),flip(a)].">
      <j1 rule="hyper" parents="64 12553 17599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5 * (v6 \ v7))) = a(v5 * (v7 / v6),u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(17557,a,17600,a),flip(a)].">
      <j1 rule="hyper" parents="17557 17600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17602">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(17582,a,17598,a)].">
      <j1 rule="hyper" parents="17582 17598"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12690,a(flip),b,17602,a)].">
      <j1 rule="hyper" parents="64 12690 17602"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),17603(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 17603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16448,a(flip),b,17604,a),flip(a)].">
      <j1 rule="hyper" parents="64 16448 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      T(x * y,a(K(z,x) * y,u,w)) = T(x * y,a(w,u,T(x,z)))
    ]]></literal>
    <justification jstring="[para(4312(a,1),17605(a,1,2,1))].">
      <j1 rule="para" parents="4312 17605"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      T(x * y,a(K(z,x) * y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * y,a(w,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(17606(a,2),16272(a,1))].">
      <j1 rule="para" parents="17606 16272"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(17607,a,17580,a)].">
      <j1 rule="hyper" parents="17607 17580"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(13261(a,2),17608(a,2,2))].">
      <j1 rule="para" parents="13261 17608"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(16147(a,1),17608(a,2,2))].">
      <j1 rule="para" parents="16147 17608"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      T(T(x,y) * K(z,u),a(w,v5,x)) = T(x,y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(16272,a,17610,a)].">
      <j1 rule="hyper" parents="16272 17610"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      L(x * K(y,z),u,K(x,w)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(13307,a,17610,a)].">
      <j1 rule="hyper" parents="13307 17610"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * K(a(u,w,x),v5),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17610(a,1),12094(a,2,2))].">
      <j1 rule="para" parents="17610 12094"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      K(x,y) * (z * T(x * K(u,w),K(x,y) * z)) = (x * K(u,w)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(17612(a,1),646(a,2,1))].">
      <j1 rule="para" parents="17612 646"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(13295,a,17609,a)].">
      <j1 rule="hyper" parents="13295 17609"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      K(x,L(y / z,L(T(u,w),v5,v6),y \ L(u,v5,v6))) = K(x,L(T(u,w),v5,v6) / (z * (y \ L(T(u,w),v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(64,a,13033,a(flip),b,17537,a),flip(a)].">
      <j1 rule="hyper" parents="64 13033 17537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = L(K(v5,w) / z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(12023(a,1),17548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12023 17548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(16131(a,1),17552(a,2,2))].">
      <j1 rule="para" parents="16131 17552"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,13273,a(flip),b,17618,a),flip(a)].">
      <j1 rule="hyper" parents="319 13273 17618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(13308,a,17620,a)].">
      <j1 rule="hyper" parents="13308 17620"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(K(y,z) * u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(13309,a,17622,a)].">
      <j1 rule="hyper" parents="13309 17622"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,4220,a,b,17622,a),flip(a)].">
      <j1 rule="hyper" parents="319 4220 17622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17624(a,2),4221(a,1))].">
      <j1 rule="para" parents="17624 4221"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(17625,a,17623,a)].">
      <j1 rule="hyper" parents="17625 17623"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12557,a(flip),b,17561,a),flip(a)].">
      <j1 rule="hyper" parents="319 12557 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,y / (a(z \ 1,z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z \ 1,z,u) \ (y * u)) = w
    ]]></literal>
    <justification jstring="[para(17573(a,1),16207(a,1))].">
      <j1 rule="para" parents="17573 16207"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17574,a(flip),b,17597,a),flip(a)].">
      <j1 rule="hyper" parents="64 17574 17597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(12893,a,17631,a)].">
      <j1 rule="hyper" parents="12893 17631"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = K(w,v5) * K(v5,L(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,17631,a(flip),b,12710,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 17631 12710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17636">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5381,a(flip),b,17632,a),flip(a)].">
      <j1 rule="hyper" parents="64 5381 17632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) * v5,v6)) = K(x,L(y,w * v5,v6))
    ]]></literal>
    <justification jstring="[para(5457(a,1),17632(a,1,2,2))].">
      <j1 rule="para" parents="5457 17632"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10097,a,17636,a)].">
      <j1 rule="hyper" parents="10097 17636"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = v5 / (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,4359,a,b,17636,a),flip(a)].">
      <j1 rule="hyper" parents="319 4359 17636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,17636,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17636 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,10133,a,b,17636,a)].">
      <j1 rule="hyper" parents="64 10133 17636"/>
    </justification>
  </clause>

  <clause id="17646">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13068,a(flip),b,17636,a),flip(a)].">
      <j1 rule="hyper" parents="64 13068 17636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12804,a(flip),b,17636,a),flip(a)].">
      <j1 rule="hyper" parents="64 12804 17636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10111,a(flip),b,17636,a),flip(a)].">
      <j1 rule="hyper" parents="64 10111 17636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(4379(a,1),17636(a,1,2))].">
      <j1 rule="para" parents="4379 17636"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(17636(a,1),10115(a,1,2))].">
      <j1 rule="para" parents="17636 10115"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * w = K(x,y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(17636(a,1),12796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17636 12796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17653">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(15707(a,1),17636(a,1,2))].">
      <j1 rule="para" parents="15707 17636"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      x \ (K(y,z) * (x * K(u,w))) = K(u,w) * T(K(y,z),x * K(u,w))
    ]]></literal>
    <justification jstring="[para(17640(a,1),647(a,1,2,1))].">
      <j1 rule="para" parents="17640 647"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4716(a,1),17640(a,1,2))].">
      <j1 rule="para" parents="4716 17640"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (T(z,u) * K(w / z,v5))) = T(x,y * K(v5,z \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15748,a(flip),b,17643,a)].">
      <j1 rule="hyper" parents="64 15748 17643"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      T(x,(y / z) / K(u,w)) = T(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12829,a(flip),b,17643,a),flip(a)].">
      <j1 rule="hyper" parents="64 12829 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,12637,a,b,17643,a)].">
      <j1 rule="hyper" parents="41 12637 17643"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,13290,a(flip),b,17643,a),flip(a)].">
      <j1 rule="hyper" parents="41 13290 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17668">
    <literal><![CDATA[
      R(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13007,a,b,17666,a)].">
      <j1 rule="hyper" parents="64 13007 17666"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17666(a,1),50(a,2))].">
      <j1 rule="para" parents="17666 50"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(u,z) * (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,4775,a(flip),b,17667,a)].">
      <j1 rule="hyper" parents="64 4775 17667"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(z,u) \ (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,302,a(flip),b,17667,a)].">
      <j1 rule="hyper" parents="64 302 17667"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17667(a,1),51(a,2))].">
      <j1 rule="para" parents="17667 51"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      T(x / (K(y,z) * K(u,w)),K(u,w)) = K(w,u) * (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14953,a(flip),b,17668,a)].">
      <j1 rule="hyper" parents="64 14953 17668"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15721,a(flip),b,17645,a)].">
      <j1 rule="hyper" parents="64 15721 17645"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      K(x,y) * ((x * K(z,u)) * w) = (T(x,y) * K(z,u)) * w
    ]]></literal>
    <justification jstring="[para(17645(a,1),12832(a,1,1))].">
      <j1 rule="para" parents="17645 12832"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(12635(a,1),17669(a,1))].">
      <j1 rule="para" parents="12635 17669"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      T(x * K(y,z),a(u,x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = v5
    ]]></literal>
    <justification jstring="[para(12715(a,1),17669(a,1))].">
      <j1 rule="para" parents="12715 17669"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,L(K(z,u),w,v5) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,10117,a(flip),b,17660,a)].">
      <j1 rule="hyper" parents="64 10117 17660"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      T(x,(y * z) / (K(u,w) * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,u) * y) = v5
    ]]></literal>
    <justification jstring="[para(14789(a,1),17695(a,1))].">
      <j1 rule="para" parents="14789 17695"/>
    </justification>
  </clause>

  <clause id="17701">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(16211(a,2),17695(a,1))].">
      <j1 rule="para" parents="16211 17695"/>
    </justification>
  </clause>

  <clause id="17702">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17642(a,2),4377(a,1))].">
      <j1 rule="para" parents="17642 4377"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(4379(a,1),17702(a,1,2))].">
      <j1 rule="para" parents="4379 17702"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      K((K(x,y) * z) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((u / z) \ K(x,y),w) = v5
    ]]></literal>
    <justification jstring="[para(14256(a,1),17702(a,1))].">
      <j1 rule="para" parents="14256 17702"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ (w \ v5)) = K(x,w \ (K(y,T(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17493,a(flip),b,17646,a),flip(a)].">
      <j1 rule="hyper" parents="64 17493 17646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u * y) \ w)) = K(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(4922(a,1),17646(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4922 17646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5163(a,1),17646(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5163 17646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(4356(a,2),17647(a,2,2,2))].">
      <j1 rule="para" parents="4356 17647"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,16925,a(flip),b,17648,a),flip(a)].">
      <j1 rule="hyper" parents="319 16925 17648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16925,a,b,17649,a),flip(a)].">
      <j1 rule="hyper" parents="319 16925 17649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17715">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14991,a,b,17649,a)].">
      <j1 rule="hyper" parents="64 14991 17649"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14121,a,b,17651,a),flip(a)].">
      <j1 rule="hyper" parents="319 14121 17651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      (L(K(x,y) * K(z,u),w,K(v5,v6)) * a(v5,w,v6)) / K(z,u) = a(v5,w,v6) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,13298,a,b,17651,a)].">
      <j1 rule="hyper" parents="128 13298 17651"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(w,v5) = x * (K(z,L(u,x,y \ x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17471,a,b,17651,a)].">
      <j1 rule="hyper" parents="64 17471 17651"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,17651,a(flip),b,8189,a)].">
      <j1 rule="hyper" parents="128 17651 8189"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      T(x * (K(y,z) * K(u,w)),K(w,u)) = K(u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17651(a,1),5175(a,1,1))].">
      <j1 rule="para" parents="17651 5175"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(w,u) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(14116(a,2),17651(a,2,2))].">
      <j1 rule="para" parents="14116 17651"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(319,a,14115,a,b,17653,a),flip(a)].">
      <j1 rule="hyper" parents="319 14115 17653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      T(x,(y / z) / K(u,w)) = T(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(4356(a,2),17665(a,2,2,2))].">
      <j1 rule="para" parents="4356 17665"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      (K(x,y) \ (K(z,u) \ w)) / w = K(y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(206,a,74,a(flip),b,17670,a)].">
      <j1 rule="hyper" parents="206 74 17670"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      (K(x,y) \ K(z,u)) \ w = K(z,u) \ (K(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(4356(a,2),17672(a,1,1))].">
      <j1 rule="para" parents="4356 17672"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(y / (x * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(15149,a,17690,a),flip(a)].">
      <j1 rule="hyper" parents="15149 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(14666,a,17690,a)].">
      <j1 rule="hyper" parents="14666 17690"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16310,a(flip),b,17690,a)].">
      <j1 rule="hyper" parents="64 16310 17690"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(12363(a,1),17690(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12363 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K((y \ x) * K(u,z),v6))
    ]]></literal>
    <justification jstring="[para(17690(a,1),12546(a,2,3))].">
      <j1 rule="para" parents="17690 12546"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      K(x \ K((y \ z) * K(u \ w,u),y * K(u,w)),v5) = K(x \ K(y * K(u,u \ w),z),v5)
    ]]></literal>
    <justification jstring="[para(17690(a,1),13762(a,1,1,2))].">
      <j1 rule="para" parents="17690 13762"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      x * K(a(y,x,z),L(x,u,w)) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[hyper(17696,a,14564,a)].">
      <j1 rule="hyper" parents="17696 14564"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (u \ T(z * u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(w,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(16210(a,1),17701(a,1))].">
      <j1 rule="para" parents="16210 17701"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(14217,a,17712,a),flip(a)].">
      <j1 rule="hyper" parents="14217 17712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * (z \ u)) \ u)) = K(x,T((y * (z \ u)) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(15511,a,17713,a),flip(a)].">
      <j1 rule="hyper" parents="15511 17713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17745">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,13458,a(flip),b,17713,a),flip(a)].">
      <j1 rule="hyper" parents="319 13458 17713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,z)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(4314(a,1),17713(a,2,2))].">
      <j1 rule="para" parents="4314 17713"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,17745,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17745 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,w)) \ v5) = K(x,(v5 \ y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17087,a,17746,a),flip(a)].">
      <j1 rule="hyper" parents="17087 17746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14689,a(flip),b,17747,a)].">
      <j1 rule="hyper" parents="64 14689 17747"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,y \ (K(w,y) * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16866,a,b,17714,a)].">
      <j1 rule="hyper" parents="64 16866 17714"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) = K(x,K(u,z) * ((z \ y) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5421,a(flip),b,17715,a)].">
      <j1 rule="hyper" parents="64 5421 17715"/>
    </justification>
  </clause>

  <clause id="17752">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4314(a,1),17715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4314 17715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17755">
    <literal><![CDATA[
      ((x \ y) * K(x,K(y,z))) * K(x,x \ y) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(319,a,9753,a(flip),b,17716,a),flip(a)].">
      <j1 rule="hyper" parents="319 9753 17716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * (K(x,y) \ K(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16449,a,b,17723,a)].">
      <j1 rule="hyper" parents="64 16449 17723"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15059,a,17728,a),flip(a)].">
      <j1 rule="hyper" parents="15059 17728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12086,a(flip),b,17728,a),flip(a)].">
      <j1 rule="hyper" parents="64 12086 17728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (w \ T(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(17728(a,1),15059(a,1))].">
      <j1 rule="para" parents="17728 15059"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(14229,a,17729,a),flip(a)].">
      <j1 rule="hyper" parents="14229 17729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      (K(x,y) \ (K(z,u) \ w)) / w = K(x,y) \ K(u,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a,b,17731,a),flip(a)].">
      <j1 rule="hyper" parents="319 4356 17731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = (K(z,u) \ K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,14116,a,b,17731,a),flip(a)].">
      <j1 rule="hyper" parents="130 14116 17731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = (K(x,y) \ K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,4356,a,b,17731,a),flip(a)].">
      <j1 rule="hyper" parents="130 4356 17731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ u = K(x,T(y,z)) \ (K(x,y) \ u)
    ]]></literal>
    <justification jstring="[para(14386(a,1),17733(a,1,1))].">
      <j1 rule="para" parents="14386 17733"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(w,v5)) \ v6 = K(L(y,z,u),x) \ (K(w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(14326(a,2),17733(a,1,1))].">
      <j1 rule="para" parents="14326 17733"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(12262,a,17735,a)].">
      <j1 rule="hyper" parents="12262 17735"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x,K(y,z)) * K((x \ z) * K(u,w),y) = K(z / (K(w,u) * x),y)
    ]]></literal>
    <justification jstring="[para(17735(a,1),15232(a,1,2))].">
      <j1 rule="para" parents="17735 15232"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,13735,a,b,17737,a),flip(a)].">
      <j1 rule="hyper" parents="319 13735 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      K(x,K(y \ 1,z * y) \ (u / z)) = K(x,u / ((y \ 1) * (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,7983,a(flip),b,17743,a),flip(a)].">
      <j1 rule="hyper" parents="64 7983 17743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ T(w,u))) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15392,a,17761,a)].">
      <j1 rule="hyper" parents="15392 17761"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(129,a,17761,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17761 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(16613,a,17763,a)].">
      <j1 rule="hyper" parents="16613 17763"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = K(z,u) \ (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,17765,a,b,17766,a)].">
      <j1 rule="hyper" parents="319 17765 17766"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * (x \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(17769(a,2),14410(a,1))].">
      <j1 rule="para" parents="17769 14410"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      K(x,K(y,z)) * K((x \ z) * K(u,w),y) = K((K(w,u) * z) / x,y)
    ]]></literal>
    <justification jstring="[para(17771(a,1),15215(a,1,2))].">
      <j1 rule="para" parents="17771 15215"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),v5)) = T(x,y * (T(z,v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17103,a(flip),b,17774,a)].">
      <j1 rule="hyper" parents="64 17103 17774"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(4313(a,1),17775(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4313 17775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ y) = K(z,u) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4030(a,2),17776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4030 17776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ T(w,K(x,y))) = K(z,u) \ (w * K(y,x))
    ]]></literal>
    <justification jstring="[para(6806(a,1),17776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6806 17776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,12531,a(flip),b,17633,a),flip(a)].">
      <j1 rule="hyper" parents="319 12531 17633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,10125,a(flip),b,17633,a),flip(a)].">
      <j1 rule="hyper" parents="319 10125 17633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9694,a(flip),b,17784,a),flip(a)].">
      <j1 rule="hyper" parents="64 9694 17784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = w \ L(w,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,13284,a,b,17785,a),flip(a)].">
      <j1 rule="hyper" parents="319 13284 17785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(39,a,13284,a,b,17789,a(flip))].">
      <j1 rule="hyper" parents="39 13284 17789"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),K(v5,v6)) = L(x,y,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(13261(a,2),17790(a,1,2))].">
      <j1 rule="para" parents="13261 17790"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(v5,v6)) = L(x,u \ (K(z,y) * w),K(v5,v6))
    ]]></literal>
    <justification jstring="[para(4378(a,1),17791(a,1,2))].">
      <j1 rule="para" parents="4378 17791"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,17594,a,b,17639,a)].">
      <j1 rule="hyper" parents="64 17594 17639"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u * z) \ w)) = K(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(14421,a,17710,a)].">
      <j1 rule="hyper" parents="14421 17710"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11236,a(flip),b,17711,a),flip(a)].">
      <j1 rule="hyper" parents="64 11236 17711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11214,a(flip),b,17711,a),flip(a)].">
      <j1 rule="hyper" parents="64 11214 17711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(3266(a,2),17795(a,1,2,1))].">
      <j1 rule="para" parents="3266 17795"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K(x,((L(y,z,y) * z) \ y) \ u) = K(x,(y / (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(3370(a,1),17795(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3370 17795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      K(x / (y * K(z,z \ u)),w) = K(K(u,z) * (y \ x),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(14286,a,17734,a),flip(a)].">
      <j1 rule="hyper" parents="14286 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(y * (x \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14667,a(flip),b,17734,a),flip(a)].">
      <j1 rule="hyper" parents="319 14667 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(y,u),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(13736,a,17738,a)].">
      <j1 rule="hyper" parents="13736 17738"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      x * a(y,x,K(z,L(x,u,w))) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[para(11589(a,2),17741(a,1,2))].">
      <j1 rule="para" parents="11589 17741"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,17745,a(flip),b,17748,a),flip(a)].">
      <j1 rule="hyper" parents="319 17745 17748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      K(x,T((y * z) * (1 / y),y) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14307,a(flip),b,17803,a),flip(a)].">
      <j1 rule="hyper" parents="64 14307 17803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(13454,a,17752,a)].">
      <j1 rule="hyper" parents="13454 17752"/>
    </justification>
  </clause>

  <clause id="17806">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(15021,a,17760,a),flip(a)].">
      <j1 rule="hyper" parents="15021 17760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      T(x,y / (z \ T(u,K(w,v5)))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,17806,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17806 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(5175(a,1),17806(a,1,2,2,2))].">
      <j1 rule="para" parents="5175 17806"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(x,y / (z \ (u * T(z,K(w,v5))))) = K(x,y / T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(13423(a,1),17806(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13423 17806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      T(x,y / (z \ (((z * K(u,w)) * v5) * z))) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15746,a(flip),b,17807,a),flip(a)].">
      <j1 rule="hyper" parents="64 15746 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14447,a,b,17780,a)].">
      <j1 rule="hyper" parents="64 14447 17780"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(5933(a,1),17793(a,1,2,2,2))].">
      <j1 rule="para" parents="5933 17793"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      K(K(x,y) * (z \ u),T(w,z)) = K(u * (z \ K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(14410,a,17800,a)].">
      <j1 rule="hyper" parents="14410 17800"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(x * (y \ K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) * K(z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(17800(a,1),6938(a,1))].">
      <j1 rule="para" parents="17800 6938"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15625,a(flip),b,17801,a),flip(a)].">
      <j1 rule="hyper" parents="64 15625 17801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7398,a,b,17815,a)].">
      <j1 rule="hyper" parents="64 7398 17815"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x * 1
    ]]></literal>
    <justification jstring="[para(8858(a,1),17802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8858 17802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      a(x,y,a(z,x,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(12921,a,17818,a)].">
      <j1 rule="hyper" parents="12921 17818"/>
    </justification>
  </clause>

  <clause id="17820">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,8,a(flip),b,17818,a),flip(a)].">
      <j1 rule="hyper" parents="319 8 17818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,y) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(53,a,17819,a)].">
      <j1 rule="hyper" parents="53 17819"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      T(x,L(a(y,x,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,12923,a(flip),b,17820,a)].">
      <j1 rule="hyper" parents="64 12923 17820"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = (y * a(x,y,z)) / y
    ]]></literal>
    <justification jstring="[para(17823(a,1),12621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17823 12621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,y))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10395,a,b,17822,a)].">
      <j1 rule="hyper" parents="64 10395 17822"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(17826(a,1),12558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17826 12558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,11598,a(flip),b,17825,a),flip(a)].">
      <j1 rule="hyper" parents="319 11598 17825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17829">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(12625,a,17828,a)].">
      <j1 rule="hyper" parents="12625 17828"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      T(a(x,y,z),a(u,x,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,17828,a)].">
      <j1 rule="hyper" parents="55 17828"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      T(a(x,y,z),a(u,z,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,17829,a)].">
      <j1 rule="hyper" parents="55 17829"/>
    </justification>
  </clause>

  <clause id="17832">
    <literal><![CDATA[
      L(a(x,y,z),x,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13295,a,17830,a)].">
      <j1 rule="hyper" parents="13295 17830"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      L(a(x,y,z),z,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13295,a,17831,a)].">
      <j1 rule="hyper" parents="13295 17831"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      R(K(x,y),z,L(a(z,u,w),z,K(x,y))) = (K(x,y) * (z * a(z,u,w))) / (z * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(17832(a,1),486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17832 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      R(K(x,y),z,L(a(u,w,z),z,K(x,y))) = (K(x,y) * (z * a(u,w,z))) / (z * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(17833(a,1),486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17833 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12558,a(flip),b,17827,a),flip(a)].">
      <j1 rule="hyper" parents="319 12558 17827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      K(x,L(y,z,(z * u) \ w)) = K(x,L(y,z,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(302(a,1),17837(a,1,2,3))].">
      <j1 rule="para" parents="302 17837"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11222,a(flip),b,17805,a),flip(a)].">
      <j1 rule="hyper" parents="64 11222 17805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(11232,a,17839,a),flip(a)].">
      <j1 rule="hyper" parents="11232 17839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,17839,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 17839 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17842">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ T(u \ z,u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[para(6836(a,1),17841(a,1,2,1,1))].">
      <j1 rule="para" parents="6836 17841"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / T(w,(u / z) \ y)) = K(x,w \ (y / (T(z,u) \ u)))
    ]]></literal>
    <justification jstring="[para(17841(a,1),15068(a,1,2,2))].">
      <j1 rule="para" parents="17841 15068"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(6326(a,1),17811(a,1,2,1))].">
      <j1 rule="para" parents="6326 17811"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14650,a(flip),b,17845,a)].">
      <j1 rule="hyper" parents="64 14650 17845"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(11168,a,17846,a),flip(a)].">
      <j1 rule="hyper" parents="11168 17846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      K(x,L(y,z,(u * z) \ w)) = K(x,L(y,z,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(17565,a,17838,a)].">
      <j1 rule="hyper" parents="17565 17838"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(11229,a,17840,a),flip(a)].">
      <j1 rule="hyper" parents="11229 17840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(17840(a,1),11229(a,1))].">
      <j1 rule="para" parents="17840 11229"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      K(T(x,y),T(z,y) / (y / x)) = K(T(x,y),y \ (z * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13550,a(flip),b,17850,a),flip(a)].">
      <j1 rule="hyper" parents="64 13550 17850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (w \ T(u,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((w \ T(u,w)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(11178(a,1),17851(a,1,2,2,1))].">
      <j1 rule="para" parents="11178 17851"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(11161,a,17847,a),flip(a)].">
      <j1 rule="hyper" parents="11161 17847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = (T(x,y \ (u \ z)) * R(x \ 1,x,w)) / ((w / (x * w)) * x)
    ]]></literal>
    <justification jstring="[para(17854(a,1),4332(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17854 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * z) \ u)) = K(x \ 1,L(y,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13122,a(flip),b,17848,a),flip(a)].">
      <j1 rule="hyper" parents="319 13122 17848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      T(x,(y * z) * (z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(12137(a,1),17700(a,1))].">
      <j1 rule="para" parents="12137 17700"/>
    </justification>
  </clause>

  <clause id="17859">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17777,a,16799,a)].">
      <j1 rule="hyper" parents="17777 16799"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,z \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(z \ u,w) = v6
    ]]></literal>
    <justification jstring="[para(17859(a,2),6466(a,1))].">
      <j1 rule="para" parents="17859 6466"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      K(x,((y * z) \ R(y,z,y)) \ u) = K(x,(y / (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(10838(a,1),17798(a,1,2,1))].">
      <j1 rule="para" parents="10838 17798"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      K(x,(y / (z * y)) \ u) = K(x,((y * z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11148,a(flip),b,17861,a),flip(a)].">
      <j1 rule="hyper" parents="64 11148 17861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u * z) \ u) \ y) = K(x,y / (u / (z * u)))
    ]]></literal>
    <justification jstring="[para(17862(a,1),7301(a,1,2))].">
      <j1 rule="para" parents="17862 7301"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) = K(x,K(z,u) \ (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(15045,a,17709,a),flip(a)].">
      <j1 rule="hyper" parents="15045 17709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ (y \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(17709(a,1),15047(a,1))].">
      <j1 rule="para" parents="17709 15047"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      K(x,(y * z) \ (K(z,T(u,w)) \ v5)) = K(x,(y * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,17710,a(flip),b,17866,a),flip(a)].">
      <j1 rule="hyper" parents="319 17710 17866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16413,a(flip),b,17866,a),flip(a)].">
      <j1 rule="hyper" parents="64 16413 17866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      K(x,y \ (K(L(z,u,w),v5) \ v6)) = K(x,K(v5,z) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(16552,a,17870,a),flip(a)].">
      <j1 rule="hyper" parents="16552 17870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(14421,a,17870,a)].">
      <j1 rule="hyper" parents="14421 17870"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      K(x,y \ (K(z \ 1,u) \ w)) = K(x,K(u,z) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14483,a(flip),b,17870,a),flip(a)].">
      <j1 rule="hyper" parents="64 14483 17870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (T(y,z) * w))) = K(x,u \ (y * w))
    ]]></literal>
    <justification jstring="[para(4100(a,1),17870(a,2,2,2))].">
      <j1 rule="para" parents="4100 17870"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x,y \ (K(z,L(u,w,v5)) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(16552,a,17872,a),flip(a)].">
      <j1 rule="hyper" parents="16552 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17877">
    <literal><![CDATA[
      K(x,K(y,z) \ ((T(z,y) \ u) \ w)) = K(x,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,16345,a(flip),b,17872,a),flip(a)].">
      <j1 rule="hyper" parents="319 16345 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (y * w))) = K(x,K(u,z) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),17872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ (y * u))) = K(x,K(z,x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(16718,a,17878,a)].">
      <j1 rule="hyper" parents="16718 17878"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16346,a(flip),b,17874,a),flip(a)].">
      <j1 rule="hyper" parents="64 16346 17874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17030,a(flip),b,17875,a)].">
      <j1 rule="hyper" parents="64 17030 17875"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) * T(w,z))) = K(x,y \ (w * z))
    ]]></literal>
    <justification jstring="[para(109(a,1),17881(a,2,2,2))].">
      <j1 rule="para" parents="109 17881"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      K(x,K(y,z) * ((T(y,z) \ u) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4356(a,1),17877(a,1,2))].">
      <j1 rule="para" parents="4356 17877"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      K(x,y \ (z * T(T(u,w),w))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(6894(a,1),17882(a,1,2,2))].">
      <j1 rule="para" parents="6894 17882"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      K(x,y \ (z * T(u \ w,u))) = K(x,y \ (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(111(a,1),17884(a,1,2,2,2,1))].">
      <j1 rule="para" parents="111 17884"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ v5,v6)) = a(v6,y,K(x,(z \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(17883(a,1),17547(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17883 17547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      K(x,K(y,z) \ (x * (u / y))) \ T(x,u / T(y,z)) = R(x,y \ ((y \ u) * T(y,z)),x)
    ]]></literal>
    <justification jstring="[para(17885(a,1),16689(a,1,1))].">
      <j1 rule="para" parents="17885 16689"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,K(y,z) \ (v5 \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,16348,a,b,17871,a)].">
      <j1 rule="hyper" parents="64 16348 17871"/>
    </justification>
  </clause>

  <clause id="17889">
    <literal><![CDATA[
      K(x,y \ (L(K(z,u),w,v5) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[para(5377(a,1),17876(a,1,2,2,1))].">
      <j1 rule="para" parents="5377 17876"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      K(x,K(y,z) \ ((L(K(y,z),u,w) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,16663,a(flip),b,17889,a),flip(a)].">
      <j1 rule="hyper" parents="64 16663 17889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(L(y,u,w),z) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(5363(a,1),17891(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5363 17891"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15380,a(flip),b,17720,a),flip(a)].">
      <j1 rule="hyper" parents="64 15380 17720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8897,a(flip),b,17894,a)].">
      <j1 rule="hyper" parents="64 8897 17894"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * T(z,K(x,y))) / (z * K(x,y)),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(417,a,17397,a,b,17895,a),flip(a)].">
      <j1 rule="hyper" parents="417 17397 17895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,17681,a,b,17722,a)].">
      <j1 rule="hyper" parents="41 17681 17722"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,T(y,w) \ K(u,z))
    ]]></literal>
    <justification jstring="[para(4309(a,1),17750(a,2,2))].">
      <j1 rule="para" parents="4309 17750"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,T(y \ K(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(319,a,15684,a,b,17901,a),flip(a)].">
      <j1 rule="hyper" parents="319 15684 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) \ y)) = K(x,T(z \ K(w,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6317,a(flip),b,17902,a)].">
      <j1 rule="hyper" parents="64 6317 17902"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K(x,y / (z * (y * K(u,w)))) = K(x,T(T(z,y) \ K(w,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17148,a(flip),b,17903,a)].">
      <j1 rule="hyper" parents="64 17148 17903"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16961,a(flip),b,17751,a),flip(a)].">
      <j1 rule="hyper" parents="64 16961 17751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ (K(x,y) \ T(T(x,y),x \ T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15813,a,b,17767,a)].">
      <j1 rule="hyper" parents="64 15813 17767"/>
    </justification>
  </clause>

  <clause id="17907">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ (u * K(z,y)) = K(y,z) \ (x * T(u / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17478(a,1),17782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17478 17782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,17711,a(flip),b,17796,a),flip(a)].">
      <j1 rule="hyper" parents="319 17711 17796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,(y / ((z \ u) \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(110(a,1),17908(a,1,2,1,2))].">
      <j1 rule="para" parents="110 17908"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(x / (y * K(z,z \ u)),w) = K(x * (y \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,17813,a(flip),b,17799,a),flip(a)].">
      <j1 rule="hyper" parents="319 17813 17799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      K(x * (y \ K(z \ u,z)),w) = K(x * (y \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(14668,a,17910,a)].">
      <j1 rule="hyper" parents="14668 17910"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      K(x / (K(y,y \ z) / u),w) = K(x * ((u \ 1) \ K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(12457,a,17911,a)].">
      <j1 rule="hyper" parents="12457 17911"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,T(T(z,y) / (y / x),y))
    ]]></literal>
    <justification jstring="[hyper(6244,a,17852,a),flip(a)].">
      <j1 rule="hyper" parents="6244 17852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,u \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12840,a(flip),b,17856,a),flip(a)].">
      <j1 rule="hyper" parents="64 12840 17856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      K(x,T(y,z) \ (K(z,T(u,w)) \ v5)) = K(x,((z \ y) * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11172,a(flip),b,17869,a)].">
      <j1 rule="hyper" parents="64 11172 17869"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) \ v5)) = a(x,y,K(z,(w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17579,a(flip),b,17886,a)].">
      <j1 rule="hyper" parents="64 17579 17886"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,(v5 \ v6) \ v7)) = a((v6 / v5) \ v7,u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(17557,a,17916,a),flip(a)].">
      <j1 rule="hyper" parents="17557 17916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      K(x,y / (z * (y * K(u,w)))) = K(x,T(T(z \ K(w,u),y),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,15725,a,b,17904,a),flip(a)].">
      <j1 rule="hyper" parents="319 15725 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(17905(a,2),17029(a,1))].">
      <j1 rule="para" parents="17905 17029"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      K(x / (K(y,y \ z) / u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(319,a,12025,a(flip),b,17912,a),flip(a)].">
      <j1 rule="hyper" parents="319 12025 17912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      K(x * (y * K(z \ u,z)),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(12274,a,17921,a)].">
      <j1 rule="hyper" parents="12274 17921"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x * (K(y \ z,y) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(14635,a,17922,a)].">
      <j1 rule="hyper" parents="14635 17922"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x * (y * K(z,z * u)),w) = K(x * (K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),17923(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 17923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      K((x \ K(y,y * z)) * (K(z,y) * u),w) = K(T(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16794,a(flip),b,17924,a),flip(a)].">
      <j1 rule="hyper" parents="64 16794 17924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,T(T(z,y) / (x \ y),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,7100,a(flip),b,17913,a),flip(a)].">
      <j1 rule="hyper" parents="319 7100 17913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      K(x,y / (z * (y * K(u,w)))) = K(x,z \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6845,a(flip),b,17919,a),flip(a)].">
      <j1 rule="hyper" parents="319 6845 17919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,(w / y) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(17413(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="17413 17927"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,(z / y) \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(16360,a,17929,a)].">
      <j1 rule="hyper" parents="16360 17929"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(w / y) \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(15058,a,17930,a)].">
      <j1 rule="hyper" parents="15058 17930"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,w)) = K(x,K(u,w) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17728,a(flip),b,17931,a),flip(a)].">
      <j1 rule="hyper" parents="64 17728 17931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(17932(a,2),14266(a,1))].">
      <j1 rule="para" parents="17932 14266"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u / (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,L((u / v5) / w,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(12804(a,1),17933(a,1,2,2))].">
      <j1 rule="para" parents="12804 17933"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,y \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,7848,a(flip),b,17926,a),flip(a)].">
      <j1 rule="hyper" parents="319 7848 17926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / z) = K(x,z \ (x * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6996,a,17935,a)].">
      <j1 rule="hyper" parents="6996 17935"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      K(x,y \ (x * T(z,y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(17936(a,1),7439(a,1))].">
      <j1 rule="para" parents="17936 7439"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      K(x,(y / T(z,u)) \ (x * T(w,y / ((z \ u) \ u)))) = K(x,w / (x \ (y / ((z \ u) \ u))))
    ]]></literal>
    <justification jstring="[hyper(17937,a,17909,a),flip(a)].">
      <j1 rule="hyper" parents="17937 17909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      K(x,((y * z) * (1 / z)) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2176(a,1),17804(a,1,2,1))].">
      <j1 rule="para" parents="2176 17804"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      K(x,((y * z) * (z \ 1)) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4696,a(flip),b,17940,a)].">
      <j1 rule="hyper" parents="64 4696 17940"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(266(a,1),17941(a,1,2,1))].">
      <j1 rule="para" parents="266 17941"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12928,a(flip),b,17942,a),flip(a)].">
      <j1 rule="hyper" parents="64 12928 17942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1168(a,1),17943(a,1,2))].">
      <j1 rule="para" parents="1168 17943"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13102,a(flip),b,17914,a),flip(a)].">
      <j1 rule="hyper" parents="64 13102 17914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),17946(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 17946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(17947(a,1),4359(a,1,2,1))].">
      <j1 rule="para" parents="17947 4359"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z \ (u * (w \ z)),y))) / x) = K(y,T((w * (u \ z)) \ z,x))
    ]]></literal>
    <justification jstring="[para(17947(a,1),7480(a,1,2,1,2,2))].">
      <j1 rule="para" parents="17947 7480"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) = K(x,u \ (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(14219,a,17949,a),flip(a)].">
      <j1 rule="hyper" parents="14219 17949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(17920,a,16939,a(flip))].">
      <j1 rule="hyper" parents="17920 16939"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      a(x * (y / z),u,K(w,v5)) = a(x * (z \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(17557,a,17601,a),flip(a)].">
      <j1 rule="hyper" parents="17557 17601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16277,a(flip),b,17956,a),flip(a)].">
      <j1 rule="hyper" parents="64 16277 17956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16276,a(flip),b,17957,a)].">
      <j1 rule="hyper" parents="64 16276 17957"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * T(K(z,y),x * K(u,w))
    ]]></literal>
    <justification jstring="[para(4356(a,2),17658(a,1,2))].">
      <j1 rule="para" parents="4356 17658"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(319,a,16518,a(flip),b,17697,a),flip(a)].">
      <j1 rule="hyper" parents="319 16518 17697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ (y \ v6)) = v7
    ]]></literal>
    <justification jstring="[para(17697(a,2),16519(a,1))].">
      <j1 rule="para" parents="17697 16519"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(u,w) \ ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(94(a,1),17960(a,1,2,1))].">
      <j1 rule="para" parents="94 17960"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x,(K(y,z) \ (u * L(K(w,v5),v6,v7))) \ v8) = K(x,K(w,v5) \ ((K(y,z) \ u) \ v8))
    ]]></literal>
    <justification jstring="[para(16206(a,2),17960(a,1,2,1))].">
      <j1 rule="para" parents="16206 17960"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x,(y * (K(z,u) \ w)) \ v5) = K(x,K(u,z) \ ((y * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16415,a,b,17963,a)].">
      <j1 rule="hyper" parents="64 16415 17963"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(4356(a,1),17963(a,2,2))].">
      <j1 rule="para" parents="4356 17963"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(x,K(y,z) \ (((z \ u) * z) \ w)) = K(x,(z * (u / T(z,y))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13537,a(flip),b,17965,a),flip(a)].">
      <j1 rule="hyper" parents="64 13537 17965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K(y \ x,v6))
    ]]></literal>
    <justification jstring="[hyper(319,a,17541,a(flip),b,17739,a),flip(a)].">
      <j1 rule="hyper" parents="319 17541 17739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,(T(y,z) * (z \ u)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17011,a(flip),b,17744,a),flip(a)].">
      <j1 rule="hyper" parents="64 17011 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,17136,a(flip),b,17970,a),flip(a)].">
      <j1 rule="hyper" parents="319 17136 17970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14555(a,1),17759(a,2,2))].">
      <j1 rule="para" parents="14555 17759"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = a(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(319,a,16258,a,b,17972,a),flip(a)].">
      <j1 rule="hyper" parents="319 16258 17972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      a(K(x * y,x),z,u) \ T(x,y) = R(T(x,L(x * y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10284,a(flip),b,17973,a),flip(a)].">
      <j1 rule="hyper" parents="64 10284 17973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      R(T(x,L(x * y,z,u)),y,x) = a(K(y,x),z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10903(a,1),17974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10903 17974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      R(T(x,L(x * y,z,u)),y,x) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12695,a(flip),b,17975,a),flip(a)].">
      <j1 rule="hyper" parents="319 12695 17975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      L(K(x,x * y),z,u) \ T(x,L(y,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(17976(a,1),10158(a,1,2))].">
      <j1 rule="para" parents="17976 10158"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      L(K(x,x * (y / (z / ((u \ 1) \ 1)))),u \ z,u) \ T(x,(y * u) / z) = R(x,y / (z / ((u \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(13386(a,1),17977(a,1,2))].">
      <j1 rule="para" parents="13386 17977"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(w,v5)) \ v6 = L(K(y,x),z,u) \ (K(w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(10129(a,2),17768(a,2,1))].">
      <j1 rule="para" parents="10129 17768"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,K(y,z)) * K((x \ z) * K(u,w),y) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * (x \ K(u,w)),y) = v5
    ]]></literal>
    <justification jstring="[para(17770(a,2),12275(a,1))].">
      <j1 rule="para" parents="17770 12275"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17626,a(flip),b,17792,a),flip(a)].">
      <j1 rule="hyper" parents="64 17626 17792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(13310,a,17981,a)].">
      <j1 rule="hyper" parents="13310 17981"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(17982(a,1),4388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17982 4388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5933(a,1),17982(a,1,2))].">
      <j1 rule="para" parents="5933 17982"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      L(x,K(y,z) * u,a(w,v5,K(v6,v7))) = L(x,u,K(a(w,v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(11589(a,2),17982(a,1,3))].">
      <j1 rule="para" parents="11589 17982"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      T(x,a(y,z * K(u,w),v5)) = L(x,z,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(13303,a,17984,a)].">
      <j1 rule="hyper" parents="13303 17984"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x,K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9722,a(flip),b,17984,a),flip(a)].">
      <j1 rule="hyper" parents="64 9722 17984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(13074(a,1),17984(a,1,2))].">
      <j1 rule="para" parents="13074 17984"/>
    </justification>
  </clause>

  <clause id="17989">
    <literal><![CDATA[
      T(x,a(y,z * K(u,w),v5)) = T(x,a(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a(flip),b,17986,a),flip(a)].">
      <j1 rule="hyper" parents="319 13261 17986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      T(x,a(y,z * u,w)) = T(x,a(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(88(a,1),17989(a,1,2,2))].">
      <j1 rule="para" parents="88 17989"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(13307,a,17990,a),flip(a)].">
      <j1 rule="hyper" parents="13307 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12688,a,17990,a),flip(a)].">
      <j1 rule="hyper" parents="12688 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      L(x,y * z,K(u,y)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(13295,a,17992,a)].">
      <j1 rule="hyper" parents="13295 17992"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12686,a(flip),b,17993,a)].">
      <j1 rule="hyper" parents="64 12686 17993"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16288,a(flip),b,17994,a),flip(a)].">
      <j1 rule="hyper" parents="64 16288 17994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(17996(a,2),9696(a,1))].">
      <j1 rule="para" parents="17996 9696"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,12686,a(flip),b,17995,a),flip(a)].">
      <j1 rule="hyper" parents="319 12686 17995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a,b,17998,a),flip(a)].">
      <j1 rule="hyper" parents="319 13261 17998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13295,a,17999,a)].">
      <j1 rule="hyper" parents="13295 17999"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11407,a(flip),b,18000,a),flip(a)].">
      <j1 rule="hyper" parents="64 11407 18000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(17674,a,18001,a),flip(a)].">
      <j1 rule="hyper" parents="17674 18001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      L(L(x,y,z),y,K(L(u \ 1,u,w),((w * u) \ w) * z)) = L(x,y,(((w * u) \ w) * z) / L(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(427(a,1),18001(a,1,1,3))].">
      <j1 rule="para" parents="427 18001"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(78(a,1),18002(a,1,3)),flip(a)].">
      <j1 rule="para" parents="78 18002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      a(T(x,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(17997,a,17833,a)].">
      <j1 rule="hyper" parents="17997 17833"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10915,a(flip),b,18005,a),flip(a)].">
      <j1 rule="hyper" parents="64 10915 18005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      a(x,y,z) * (x * (T(y,x) * z)) = (y * x) * z
    ]]></literal>
    <justification jstring="[para(18006(a,1),13031(a,1,1))].">
      <j1 rule="para" parents="18006 13031"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,18008,a)].">
      <j1 rule="hyper" parents="134 18008"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,T(y,x),x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,646,a(flip),b,18009,a),flip(a)].">
      <j1 rule="hyper" parents="319 646 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      T((x / y) * L(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[hyper(417,a,17983,a,b,1528,a)].">
      <j1 rule="hyper" parents="417 17983 1528"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,17983,a(flip),b,9181,a)].">
      <j1 rule="hyper" parents="131 17983 9181"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,17361,a,b,17988,a)].">
      <j1 rule="hyper" parents="64 17361 17988"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,16973,a(flip),b,18014,a),flip(a)].">
      <j1 rule="hyper" parents="64 16973 18014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,K(a(v6,v7,v8),v9))
    ]]></literal>
    <justification jstring="[para(11447(a,1),17985(a,1,2,1))].">
      <j1 rule="para" parents="11447 17985"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),u)) = K(x,y / T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(4913(a,2),17809(a,1,2,2))].">
      <j1 rule="para" parents="4913 17809"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) = K(x,y / ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7898,a(flip),b,17864,a),flip(a)].">
      <j1 rule="hyper" parents="64 7898 17864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(L(x,y,z) * K(u \ 1,x),w / ((v5 * u) \ v5)) = K(x,L((v5 / (u * v5)) \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16363,a(flip),b,18019,a),flip(a)].">
      <j1 rule="hyper" parents="64 16363 18019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y) \ (T(z,y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(17915(a,1),17867(a,1))].">
      <j1 rule="para" parents="17915 17867"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      a((x / y) \ z,u,K(w,v5)) = a((y \ x) \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(17557,a,17917,a),flip(a)].">
      <j1 rule="hyper" parents="17557 17917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(18022(a,1),16280(a,1,2))].">
      <j1 rule="para" parents="18022 16280"/>
    </justification>
  </clause>

  <clause id="18024">
    <literal><![CDATA[
      K(K(x * y,x) * (z \ (K(y,x) * u)),w) = K(T(z,K(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17777,a,17925,a)].">
      <j1 rule="hyper" parents="17777 17925"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * T(K(z,y),K(w,u) \ x)
    ]]></literal>
    <justification jstring="[para(14165(a,2),17959(a,2,2))].">
      <j1 rule="para" parents="14165 17959"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) \ w) = K(x,(y * (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17794,a(flip),b,17967,a)].">
      <j1 rule="hyper" parents="64 17794 17967"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (K(y,x) \ w) = a(K(x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(12682(a,1),17979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12682 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (K(x,y) \ w) = L(K(x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(4365(a,1),18027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4365 18027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * (K(z,y) \ w))) = T(x,u * (a(K(y,z),v5,v6) \ w))
    ]]></literal>
    <justification jstring="[para(18027(a,1),16706(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18027 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(16587,a,18018,a),flip(a)].">
      <j1 rule="hyper" parents="16587 18018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(129,a,18030,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 18030 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13601,a(flip),b,18030,a),flip(a)].">
      <j1 rule="hyper" parents="64 13601 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y / T(K(z,u) * w,w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16981,a,b,18032,a)].">
      <j1 rule="hyper" parents="64 16981 18032"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      T(x,y / T((z * K(u,w)) * v5,z)) = T(x,y / (v5 * (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,15127,a(flip),b,18032,a),flip(a)].">
      <j1 rule="hyper" parents="64 15127 18032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12353,a(flip),b,18032,a)].">
      <j1 rule="hyper" parents="64 12353 18032"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(4646(a,1),18032(a,1,2,2,2))].">
      <j1 rule="para" parents="4646 18032"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,12353,a(flip),b,18036,a),flip(a)].">
      <j1 rule="hyper" parents="319 12353 18036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18039">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) \ w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),18038(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(4292(a,1),18038(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4292 18038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      T(x,y \ T(K(z,u) \ y,w)) = T(x,K(z,u) \ K(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17050,a(flip),b,18039,a)].">
      <j1 rule="hyper" parents="64 17050 18039"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(14680,a,18037,a),flip(a)].">
      <j1 rule="hyper" parents="14680 18037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * T(z,u),w)) = v6
    ]]></literal>
    <justification jstring="[para(18037(a,1),14646(a,1))].">
      <j1 rule="para" parents="18037 14646"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      T(x,(y \ (z / T(u,w))) \ K(u \ z,v5)) = T(x,T(z / T(u,w),v5) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17749,a(flip),b,18040,a),flip(a)].">
      <j1 rule="hyper" parents="64 17749 18040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      K(K(x,y) * (z \ (K(x,y) * u)),w) = K(T(z,K(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(11272,a,18024,a)].">
      <j1 rule="hyper" parents="11272 18024"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      K(K(x,y) * (z \ (K(x,y) * u)),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14584,a(flip),b,18046,a),flip(a)].">
      <j1 rule="hyper" parents="319 14584 18046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      K(x,(y * z) * K(u \ w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(K(v7,v8) * (u \ (K(v7,v8) * w)),v5))) = v6
    ]]></literal>
    <justification jstring="[para(18047(a,1),16573(a,1,2,2))].">
      <j1 rule="para" parents="18047 16573"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * K(z,T(y,K(w,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(319,a,6112,a,b,18025,a),flip(a)].">
      <j1 rule="hyper" parents="319 6112 18025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K((K(y,z) * u) \ w,u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(13610,a,18033,a)].">
      <j1 rule="hyper" parents="13610 18033"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17156,a(flip),b,18033,a)].">
      <j1 rule="hyper" parents="64 17156 18033"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(4356(a,1),18052(a,1,2,2,1))].">
      <j1 rule="para" parents="4356 18052"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,K(x,y) \ w)) = w \ (K(u,z) \ (w * K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(319,a,4356,a,b,18050,a)].">
      <j1 rule="hyper" parents="319 4356 18050"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(w,u) \ K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(15135(a,1),18055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15135 18055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,x * y)) = (x * y) \ (K(u,z) \ (y * x))
    ]]></literal>
    <justification jstring="[para(88(a,1),18056(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="88 18056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,y \ x)) = (x * y) \ (K(u,z) \ (y * x))
    ]]></literal>
    <justification jstring="[para(14012(a,2),18057(a,1,2))].">
      <j1 rule="para" parents="14012 18057"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      K(x,y) \ (K(T(z,y \ x),u) \ w) = ((x * y) \ (K(z,u) \ (y * x))) * w
    ]]></literal>
    <justification jstring="[hyper(130,a,18059,a(flip),b,17764,a),flip(a)].">
      <j1 rule="hyper" parents="130 18059 17764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      K(x,y) \ (y * K(z,T(u,y \ x))) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(18059(a,1),4458(a,2,2))].">
      <j1 rule="para" parents="18059 4458"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      K(x,y \ (x \ (x * T(z,y * x)))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(5731,a,17952,a)].">
      <j1 rule="hyper" parents="5731 17952"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(13319(a,1),18011(a,1,1))].">
      <j1 rule="para" parents="13319 18011"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(253,a,18063,a)].">
      <j1 rule="hyper" parents="253 18063"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),u) = u \ (K(y,z) * ((K(z,y) * x) * u))
    ]]></literal>
    <justification jstring="[para(12524(a,2),18063(a,1,1,2))].">
      <j1 rule="para" parents="12524 18063"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12598(a,1),18064(a,2,2))].">
      <j1 rule="para" parents="12598 18064"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,a(v6,v7,K(v8,v9)))
    ]]></literal>
    <justification jstring="[para(11589(a,2),18017(a,2,3))].">
      <j1 rule="para" parents="11589 18017"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) \ w) = K(x,K(u,y) \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(18021,a,18026,a),flip(a)].">
      <j1 rule="hyper" parents="18021 18026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,K(K(v5,v6),y) \ (T(T((y \ 1) \ z,u),y) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17373,a,b,18068,a)].">
      <j1 rule="hyper" parents="64 17373 18068"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      T(x,y * (a(K(z,u),w,v5) \ v6)) = T(x,y * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,16514,a(flip),b,18029,a),flip(a)].">
      <j1 rule="hyper" parents="64 16514 18029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ T(v5,x),x) = K(x,v5) \ T(x,x * v5)
    ]]></literal>
    <justification jstring="[para(18070(a,1),17258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18070 17258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ T(v5,x),x) = L(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4460,a(flip),b,18072,a),flip(a)].">
      <j1 rule="hyper" parents="319 4460 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ v5,x) = L(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10226,a(flip),b,18073,a)].">
      <j1 rule="hyper" parents="64 10226 18073"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      a(x,a(K(y,z),u,w) \ v5,x) = (v6 / x) \ (v6 / L(x,v5,x))
    ]]></literal>
    <justification jstring="[para(18075(a,1),8381(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18075 8381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      a(x,a(K(y,z),u,w) \ v5,x) = a(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8381,a(flip),b,18077,a),flip(a)].">
      <j1 rule="hyper" parents="319 8381 18077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18079">
    <literal><![CDATA[
      a(x,(y * a(K(z,u),w,v5)) \ v6,x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11424,a,b,18078,a)].">
      <j1 rule="hyper" parents="64 11424 18078"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      a(x,L(K(y,z),u,w) \ v5,x) = a(x,K(y,z) \ v5,x)
    ]]></literal>
    <justification jstring="[para(18028(a,1),18078(a,1,2))].">
      <j1 rule="para" parents="18028 18078"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      a(x,(a(K(y,z),u,w) \ v5) \ v6,x) = a(x,v5 \ v6,x)
    ]]></literal>
    <justification jstring="[para(16141(a,1),18079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16141 18079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      a(x,K(y,(z \ u) \ w) \ v5,x) = a(x,K(y,u \ (z * w)) \ v5,x)
    ]]></literal>
    <justification jstring="[para(5275(a,1),18080(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5275 18080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      a(x,y \ (a(K(z,u),w,v5) * v6),x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11425,a(flip),b,18081,a)].">
      <j1 rule="hyper" parents="64 11425 18081"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      a(x,y \ (a(K(z,u),w,v5) \ v6),x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),18083(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      a(x,y \ (z * a(u,w,K(v5,v6))),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(16257(a,1),18084(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16257 18084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      a(x,y \ (L(K(z,u),w,v5) \ v6),x) = a(x,y \ (K(z,u) \ v6),x)
    ]]></literal>
    <justification jstring="[para(18028(a,1),18084(a,1,2,2))].">
      <j1 rule="para" parents="18028 18084"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      a(x,y \ ((z * u) * K(w,v5)),x) = a(x,y \ (z * (u * K(w,v5))),x)
    ]]></literal>
    <justification jstring="[para(85(a,1),18085(a,1,2,2))].">
      <j1 rule="para" parents="85 18085"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      a(x,y \ (z * ((K(u,w) \ z) \ v5)),x) = a(x,y \ (K(w,u) \ v5),x)
    ]]></literal>
    <justification jstring="[para(12866(a,1),18086(a,1,2,2))].">
      <j1 rule="para" parents="12866 18086"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      a(x,T(y \ (y / (z \ u)),w) * T(y,(z \ u) \ 1),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[para(5539(a,2),18082(a,1,2))].">
      <j1 rule="para" parents="5539 18082"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),18062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 18062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(11128,a,18090,a),flip(a)].">
      <j1 rule="hyper" parents="11128 18090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(12392(a,1),18091(a,2,2))].">
      <j1 rule="para" parents="12392 18091"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(11965(a,1),18093(a,1,2,2))].">
      <j1 rule="para" parents="11965 18093"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(12249,a,18094,a),flip(a)].">
      <j1 rule="hyper" parents="12249 18094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(241(a,1),18095(a,2,2))].">
      <j1 rule="para" parents="241 18095"/>
    </justification>
  </clause>

  <clause id="18097">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12144,a(flip),b,18096,a),flip(a)].">
      <j1 rule="hyper" parents="64 12144 18096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,9309,a(flip),b,18097,a),flip(a)].">
      <j1 rule="hyper" parents="319 9309 18097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(319,a,5968,a,b,18098,a),flip(a)].">
      <j1 rule="hyper" parents="319 5968 18098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18100">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(5057(a,1),18099(a,1,2,1))].">
      <j1 rule="para" parents="5057 18099"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13678,a(flip),b,18100,a)].">
      <j1 rule="hyper" parents="64 13678 18100"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(14481,a,18101,a)].">
      <j1 rule="hyper" parents="14481 18101"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(u,(z * u) * y)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(18103(a,1),6861(a,1,2,2))].">
      <j1 rule="para" parents="18103 6861"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(16808,a,18066,a)].">
      <j1 rule="hyper" parents="16808 18066"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      (K(x,y) * (K(K(y,x),z) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12213(a,1),18105(a,1,1,2))].">
      <j1 rule="para" parents="12213 18105"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / T(z * K(z \ u,w),u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(14852(a,2),17664(a,1,2,2))].">
      <j1 rule="para" parents="14852 17664"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      (T(x,K(y,z)) \ y) * K(x,x \ y) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(14242(a,1),17755(a,1,1))].">
      <j1 rule="para" parents="14242 17755"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      T(x \ y,K(y,z)) * K(x,x \ y) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(7224(a,2),18109(a,1,1))].">
      <j1 rule="para" parents="7224 18109"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      T((x \ y) * K(x,x \ y),K(y,z)) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(15187,a,18110,a)].">
      <j1 rule="hyper" parents="15187 18110"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      (x / y) * K(z,K(y,y \ x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(4097(a,1),18111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4097 18111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      (x \ y) * K(x,T(x \ y,z)) = T(y / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7066,a(flip),b,18112,a)].">
      <j1 rule="hyper" parents="64 7066 18112"/>
    </justification>
  </clause>

  <clause id="18114">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / ((z \ 1) * (y / (1 / z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,14486,a(flip),b,17772,a)].">
      <j1 rule="hyper" parents="64 14486 17772"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (u / (1 / z)))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14325,a,18114,a),flip(a)].">
      <j1 rule="hyper" parents="14325 18114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      K(x,y / T(z,u \ 1)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14548,a(flip),b,18115,a)].">
      <j1 rule="hyper" parents="64 14548 18115"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      K(x,(1 / y) / T(z,y)) = K(x,z \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(15070,a,18116,a),flip(a)].">
      <j1 rule="hyper" parents="15070 18116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      K(x,(1 / y) / (z / y)) = K(x,(y \ z) \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13601,a(flip),b,18117,a)].">
      <j1 rule="hyper" parents="64 13601 18117"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,(y \ 1) / (z / y)) = K(x,(y \ z) \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4603,a(flip),b,18118,a)].">
      <j1 rule="hyper" parents="64 4603 18118"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x,(y \ 1) / (z / y)) = K(x,(y \ z) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,4622,a(flip),b,18119,a),flip(a)].">
      <j1 rule="hyper" parents="319 4622 18119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      T(x,y / T((z * K(u,w)) * v5,z)) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(22(a,2),17810(a,1,2,2))].">
      <j1 rule="para" parents="22 17810"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      T(x,y / (z * (K(u,w) * v5))) = T(x,y / (z * (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18035,a(flip),b,18122,a),flip(a)].">
      <j1 rule="hyper" parents="64 18035 18122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      T(x,y / (z * (K(u,w) * v5))) = T(x,y * ((z * v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17305,a(flip),b,18123,a),flip(a)].">
      <j1 rule="hyper" parents="319 17305 18123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) \ K(z * u,w))) = T(x,y / (T(u,z) * K(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14936,a(flip),b,18124,a),flip(a)].">
      <j1 rule="hyper" parents="64 14936 18124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ (z / u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17096,a(flip),b,17842,a)].">
      <j1 rule="hyper" parents="64 17096 17842"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17841,a(flip),b,18126,a),flip(a)].">
      <j1 rule="hyper" parents="64 17841 18126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(3324(a,1),18127(a,1,2,1,1))].">
      <j1 rule="para" parents="3324 18127"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17295,a(flip),b,18128,a)].">
      <j1 rule="hyper" parents="64 17295 18128"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17022,a(flip),b,18129,a),flip(a)].">
      <j1 rule="hyper" parents="64 17022 18129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13692,a(flip),b,18130,a),flip(a)].">
      <j1 rule="hyper" parents="64 13692 18130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(8473(a,1),18131(a,1,2,1))].">
      <j1 rule="para" parents="8473 18131"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12321,a,18132,a),flip(a)].">
      <j1 rule="hyper" parents="12321 18132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(12322,a,18133,a),flip(a)].">
      <j1 rule="hyper" parents="12322 18133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17257,a(flip),b,18134,a)].">
      <j1 rule="hyper" parents="64 17257 18134"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      K(x,K(y,(z \ u) \ (z \ 1)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[para(18120(a,1),17880(a,1,2,1))].">
      <j1 rule="para" parents="18120 17880"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y * T(w \ K(u,z),w \ v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,14780,a(flip),b,18034,a),flip(a)].">
      <j1 rule="hyper" parents="319 14780 18034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ K(y \ z,w)) = T(x,T(z / T(y,u),w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,18135,a,b,18044,a)].">
      <j1 rule="hyper" parents="64 18135 18044"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      K(x,y) \ (K(z,T(u,y \ x)) \ w) = ((x * y) \ (K(z,u) \ (y * x))) * w
    ]]></literal>
    <justification jstring="[para(6102(a,1),18060(a,1,2,1))].">
      <j1 rule="para" parents="6102 18060"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * T(z \ K(w,z \ u),u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14786,a(flip),b,18108,a)].">
      <j1 rule="hyper" parents="64 14786 18108"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      K(x,K(y,z * (z \ u)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14485,a(flip),b,18136,a)].">
      <j1 rule="hyper" parents="64 14485 18136"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      K(x,K(y,z) \ ((z / u) \ w)) = K(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),18142(a,1,2,1,2))].">
      <j1 rule="para" parents="10 18142"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / u) \ w)) = K(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(14421,a,18143,a)].">
      <j1 rule="hyper" parents="14421 18143"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),z \ v5)) = T(x,y / T(K(w,u) * z,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14614,a(flip),b,18138,a),flip(a)].">
      <j1 rule="hyper" parents="64 14614 18138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),z \ v5)) = T(x,y * T(z \ K(u,w),v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,14780,a(flip),b,18145,a),flip(a)].">
      <j1 rule="hyper" parents="319 14780 18145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z \ w),w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17250,a(flip),b,18146,a),flip(a)].">
      <j1 rule="hyper" parents="64 17250 18146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      T(x,T(((y \ z) / z) \ K(y \ z,u),w)) = T(x,T(z / T(y,w),u) \ z)
    ]]></literal>
    <justification jstring="[hyper(15616,a,18139,a)].">
      <j1 rule="hyper" parents="15616 18139"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      ((x * y) \ (K(z,u) \ (y * x))) * y = K(z,T(u,y \ x)) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17781,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="64 17781 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (T(z \ u,w) \ u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18147,a(flip),b,18141,a)].">
      <j1 rule="hyper" parents="64 18147 18141"/>
    </justification>
  </clause>

  <clause id="18151">
    <literal><![CDATA[
      T(x,T(y / T(z \ y,u),w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13850,a(flip),b,18148,a)].">
      <j1 rule="hyper" parents="64 13850 18148"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(6306(a,1),18151(a,1,2,1))].">
      <j1 rule="para" parents="6306 18151"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(319,a,17146,a(flip),b,18152,a),flip(a)].">
      <j1 rule="hyper" parents="319 17146 18152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,T(T(y / z,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,9384,a,b,18153,a)].">
      <j1 rule="hyper" parents="319 9384 18153"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      T(x,T(y * T((y * (z / y)) / y,u),w)) = T(x,T(T(y / z,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17151,a,b,18154,a)].">
      <j1 rule="hyper" parents="64 17151 18154"/>
    </justification>
  </clause>

  <clause id="18156">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(T(z / y,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9363,a(flip),b,18155,a),flip(a)].">
      <j1 rule="hyper" parents="64 9363 18155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y * T(y \ z,u),w))
    ]]></literal>
    <justification jstring="[para(443(a,1),18156(a,2,2,1))].">
      <j1 rule="para" parents="443 18156"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      T(x,T(y * T(y \ z,u),w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18153,a(flip),b,18157,a),flip(a)].">
      <j1 rule="hyper" parents="64 18153 18157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17630,a,16901,a),flip(a)].">
      <j1 rule="hyper" parents="17630 16901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * L(z,y,y \ 1)) = w
    ]]></literal>
    <justification jstring="[para(18159(a,1),14438(a,1))].">
      <j1 rule="para" parents="18159 14438"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(12532(a,1),17718(a,2,2))].">
      <j1 rule="para" parents="12532 17718"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(189(a,1),17860(a,1,2))].">
      <j1 rule="para" parents="189 17860"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K((K(x,y) * z) / u,w) = K(z * (u \ K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(17980,a,17778,a),flip(a)].">
      <j1 rule="hyper" parents="17980 17778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      K((x / y) \ K(z,u),w) = K(y * (x \ K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(17706,a,18164,a)].">
      <j1 rule="hyper" parents="17706 18164"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      K(x * (y \ K(z,u)),T(w,y)) = K((x \ y) \ K(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(14800,a,18165,a),flip(a)].">
      <j1 rule="hyper" parents="14800 18165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      K((x \ y) \ K(z,u),w) = K((y \ x) * K(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(17814,a,18166,a),flip(a)].">
      <j1 rule="hyper" parents="17814 18166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,y) * (z * T(x * K(u,w),z)) = (x * K(u,w)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15525(a,1),17614(a,1,2,2))].">
      <j1 rule="para" parents="15525 17614"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x,y) * ((x * K(z,u)) * w) = (x * K(z,u)) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(584,a,18168,a)].">
      <j1 rule="hyper" parents="584 18168"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      (x * K(y,z)) * (K(x,u) * w) = (T(x,u) * K(y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,17694,a(flip),b,18169,a),flip(a)].">
      <j1 rule="hyper" parents="64 17694 18169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = (x * K(z,u)) * (K(x,y) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,16721,a,b,18171,a)].">
      <j1 rule="hyper" parents="319 16721 18171"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) * K(z,u)) \ w) = (x * K(z,u)) \ w
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,18171,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 18171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17229,a(flip),b,17843,a)].">
      <j1 rule="hyper" parents="64 17229 17843"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(15070,a,18174,a),flip(a)].">
      <j1 rule="hyper" parents="15070 18174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z / (w / u))) = v5
    ]]></literal>
    <justification jstring="[para(18174(a,1),15070(a,1))].">
      <j1 rule="para" parents="18174 15070"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(78(a,1),18175(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="78 18175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(78(a,1),18177(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="78 18177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18179">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (z / T(z / (z * u),w)))
    ]]></literal>
    <justification jstring="[para(8496(a,1),18177(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8496 18177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13803,a(flip),b,18178,a)].">
      <j1 rule="hyper" parents="64 13803 18178"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(4702(a,1),18180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4702 18180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18182">
    <literal><![CDATA[
      K(x,y) \ (z * T(u / z,K(x,y))) = z * ((u * K(y,x)) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14671,a(flip),b,17907,a),flip(a)].">
      <j1 rule="hyper" parents="64 14671 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18183">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ (z * (u / z)) = z * ((u * K(y,x)) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14567,a,b,18182,a)].">
      <j1 rule="hyper" parents="64 14567 18182"/>
    </justification>
  </clause>

  <clause id="18184">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(z * y,u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(14526,a,18104,a)].">
      <j1 rule="hyper" parents="14526 18104"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      K(x,y * ((T(z,y) * u) * K(z * y,u))) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(16573,a,18184,a)].">
      <j1 rule="hyper" parents="16573 18184"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      K(x,y * (T(z,y) * (u * K(z * y,u)))) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16909,a(flip),b,18185,a)].">
      <j1 rule="hyper" parents="64 16909 18185"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(12416(a,1),18186(a,1,2,2))].">
      <j1 rule="para" parents="12416 18186"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15670,a(flip),b,18187,a),flip(a)].">
      <j1 rule="hyper" parents="64 15670 18187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),18188(a,2,2,1,2))].">
      <j1 rule="para" parents="11 18188"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(16199,a,18189,a)].">
      <j1 rule="hyper" parents="16199 18189"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,18190,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 18190 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(9221(a,1),18190(a,1,2,1))].">
      <j1 rule="para" parents="9221 18190"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      T(x,L(y,z \ K(u,z \ 1),u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(4185(a,1),18191(a,1,2,2))].">
      <j1 rule="para" parents="4185 18191"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) = K(x,T(z * u,y * z))
    ]]></literal>
    <justification jstring="[hyper(9313,a,18192,a),flip(a)].">
      <j1 rule="hyper" parents="9313 18192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18196">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17174,a(flip),b,18195,a)].">
      <j1 rule="hyper" parents="64 17174 18195"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(14215,a,18196,a),flip(a)].">
      <j1 rule="hyper" parents="14215 18196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13472,a(flip),b,18197,a),flip(a)].">
      <j1 rule="hyper" parents="319 13472 18197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      T(x,y / (T(z,u) * K(u * z,w))) = T(x,y * (T(z,u) \ K(u * z,w)))
    ]]></literal>
    <justification jstring="[hyper(16748,a,18125,a),flip(a)].">
      <j1 rule="hyper" parents="16748 18125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      T(x,y / (T(z,u) * K(u * z,w))) = T(x,y * T(z \ K(u * z,w),u))
    ]]></literal>
    <justification jstring="[hyper(319,a,17779,a,b,18199,a),flip(a)].">
      <j1 rule="hyper" parents="319 17779 18199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18201">
    <literal><![CDATA[
      T(x,y / T(z * K(z * u,w),u)) = T(x,y * T(z \ K(u * z,w),u))
    ]]></literal>
    <justification jstring="[para(14844(a,2),18200(a,1,2,2))].">
      <j1 rule="para" parents="14844 18200"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      T(x,y * T(z \ K(u * z,w),u)) = T(x,y * T(z \ K(w,z * u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14786,a(flip),b,18201,a),flip(a)].">
      <j1 rule="hyper" parents="64 14786 18201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      T(x,y * T(z \ K(u * z,w),u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15471,a(flip),b,18202,a),flip(a)].">
      <j1 rule="hyper" parents="319 15471 18202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (y \ T(z * y,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17103,a,b,18203,a)].">
      <j1 rule="hyper" parents="64 17103 18203"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      T(x,y / (T(z \ u,w) \ u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17131,a(flip),b,18204,a)].">
      <j1 rule="hyper" parents="64 17131 18204"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (u \ T(z * u,w))) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18150,a(flip),b,18205,a),flip(a)].">
      <j1 rule="hyper" parents="64 18150 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18207">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(17742,a,18206,a),flip(a)].">
      <j1 rule="hyper" parents="17742 18206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      (x \ T(y * x,z * K(u,w * v5))) * (T(y,x) \ 1) = K(x * y,z * K(u,v5 \ w))
    ]]></literal>
    <justification jstring="[para(18207(a,1),13194(a,1,1,2))].">
      <j1 rule="para" parents="18207 13194"/>
    </justification>
  </clause>

  <clause id="18209">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (T((z * u) \ z,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14935,a(flip),b,18179,a),flip(a)].">
      <j1 rule="hyper" parents="319 14935 18179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(3424(a,1),18181(a,2,2,2,2))].">
      <j1 rule="para" parents="3424 18181"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ ((u * K(w,u \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11150,a(flip),b,18209,a),flip(a)].">
      <j1 rule="hyper" parents="64 11150 18209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(4550(a,1),18211(a,2,2,2))].">
      <j1 rule="para" parents="4550 18211"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17513,a(flip),b,18212,a),flip(a)].">
      <j1 rule="hyper" parents="319 17513 18212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13633,a(flip),b,18213,a),flip(a)].">
      <j1 rule="hyper" parents="319 13633 18213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,16960,a(flip),b,18214,a),flip(a)].">
      <j1 rule="hyper" parents="319 16960 18214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(1 / u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13775,a(flip),b,18215,a)].">
      <j1 rule="hyper" parents="64 13775 18215"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4762,a(flip),b,18216,a),flip(a)].">
      <j1 rule="hyper" parents="319 4762 18216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11150,a(flip),b,18217,a)].">
      <j1 rule="hyper" parents="64 11150 18217"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,4689,a(flip),b,18218,a),flip(a)].">
      <j1 rule="hyper" parents="64 4689 18218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ (T(y \ 1,z \ u) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,10201,a(flip),b,18219,a),flip(a)].">
      <j1 rule="hyper" parents="319 10201 18219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,L(u \ (y * z),y * z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(10152,a,17569,a),flip(a)].">
      <j1 rule="hyper" parents="10152 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13081,a(flip),b,17569,a),flip(a)].">
      <j1 rule="hyper" parents="64 13081 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(17853,a,17233,a),flip(a)].">
      <j1 rule="hyper" parents="17853 17233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18224">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(17851,a,18223,a),flip(a)].">
      <j1 rule="hyper" parents="17851 18223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18225">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7833,a,b,18224,a)].">
      <j1 rule="hyper" parents="64 7833 18224"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ (K(v6,v7) \ v8)) = K(x,K(z,u) \ ((K(v7,v6) \ y) \ v8))
    ]]></literal>
    <justification jstring="[hyper(64,a,16308,a(flip),b,17964,a)].">
      <j1 rule="hyper" parents="64 16308 17964"/>
    </justification>
  </clause>

  <clause id="18227">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(13321,a,18015,a)].">
      <j1 rule="hyper" parents="13321 18015"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      (K(x,y) * (z \ (K(y,x) * u))) \ u = ((z \ u) * K(x,y)) \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15810,a(flip),b,18227,a),flip(a)].">
      <j1 rule="hyper" parents="64 15810 18227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ (K(u,z) * y),K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(18229(a,1),13299(a,1,1))].">
      <j1 rule="para" parents="18229 13299"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(u,w) \ v5) \ v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ (v5 \ (K(w,u) \ v6))) = v7
    ]]></literal>
    <justification jstring="[para(18226(a,1),17961(a,1))].">
      <j1 rule="para" parents="18226 17961"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (K(z,L(y,w,v5)) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(18231,a,17893,a)].">
      <j1 rule="hyper" parents="18231 17893"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (L(K(z,y),w,v5) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[para(5377(a,1),18232(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5377 18232"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (L(K(u,z),w,v5) \ v6))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17870,a(flip),b,18233,a)].">
      <j1 rule="hyper" parents="64 17870 18233"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      K(x,y \ (a(K(z,u),w,v5) \ v6)) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(17973(a,1),18234(a,1,2,2))].">
      <j1 rule="para" parents="17973 18234"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,K(v5,v6)))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(16257(a,1),18235(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16257 18235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      K(x,y \ K(z,L(u,w,v5))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(10106(a,1),18236(a,1,2,2))].">
      <j1 rule="para" parents="10106 18236"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      K(x,y \ K(z,(u / w) / v5)) = K(x,y \ K(z,u / (v5 * w)))
    ]]></literal>
    <justification jstring="[para(12804(a,1),18237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12804 18237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      K(x,y \ K(z,u / (w * v5))) = K(x,y \ K(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[hyper(15099,a,18238,a),flip(a)].">
      <j1 rule="hyper" parents="15099 18238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u \ (w / v5))) = K(x,z / T(y,L((w / v5) / u,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(17934,a,18239,a),flip(a)].">
      <j1 rule="hyper" parents="17934 18239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      K(x,y / T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(17933,a,18240,a),flip(a)].">
      <j1 rule="hyper" parents="17933 18240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z \ 1,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14764,a(flip),b,18241,a)].">
      <j1 rule="hyper" parents="64 14764 18241"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y * T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14764,a(flip),b,18242,a),flip(a)].">
      <j1 rule="hyper" parents="319 14764 18242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(12829(a,1),18243(a,1,2,2))].">
      <j1 rule="para" parents="12829 18243"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(15052,a,18244,a)].">
      <j1 rule="hyper" parents="15052 18244"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(18245(a,2),15432(a,1))].">
      <j1 rule="para" parents="18245 15432"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      K(K(x,y) * L(y,z,u),w / ((v5 * x) \ v5)) = K(y,L((v5 / (x * v5)) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(14411,a,18020,a)].">
      <j1 rule="hyper" parents="14411 18020"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      K(x,L(T(y / ((z * u) \ z),u),w,v5)) = K(x,L((z / (u * z)) \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16362,a(flip),b,18247,a)].">
      <j1 rule="hyper" parents="64 16362 18247"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ u,w,v5)) = K(x,L(((y * z) \ y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,7315,a(flip),b,18248,a),flip(a)].">
      <j1 rule="hyper" parents="64 7315 18248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,13924,a(flip),b,18249,a),flip(a)].">
      <j1 rule="hyper" parents="64 13924 18249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      K(x,L(y / (z / (u * z)),w,v5)) = K(x,L(y / ((z * u) \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,13923,a(flip),b,18250,a),flip(a)].">
      <j1 rule="hyper" parents="64 13923 18250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / ((w * u) \ w),(w * u) \ w,z)) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16212,a(flip),b,18251,a),flip(a)].">
      <j1 rule="hyper" parents="64 16212 18251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15658,a(flip),b,18042,a)].">
      <j1 rule="hyper" parents="64 15658 18042"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      T(x,y \ T(z * (u * K(w,u)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z * T(u,w),v5)) = v6
    ]]></literal>
    <justification jstring="[para(18253(a,1),18043(a,1))].">
      <j1 rule="para" parents="18253 18043"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(u * T(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(15649(a,1),18254(a,1))].">
      <j1 rule="para" parents="15649 18254"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) = K(x * y,z * K(u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(13195,a,18208,a),flip(a)].">
      <j1 rule="hyper" parents="13195 18208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z * K(u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(18208(a,1),13195(a,1))].">
      <j1 rule="para" parents="18208 13195"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,u * z)) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17860,a,18256,a),flip(a)].">
      <j1 rule="hyper" parents="17860 18256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      K(x \ y,z * K(u,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(18163,a,18258,a)].">
      <j1 rule="hyper" parents="18163 18258"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = w / (K(u \ z,x) * w)
    ]]></literal>
    <justification jstring="[para(18259(a,1),4359(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18259 4359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(319,a,14118,a(flip),b,18260,a),flip(a)].">
      <j1 rule="hyper" parents="319 14118 18260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      K(x * K(y,T(z,u \ w) * v5),v5 \ T(z,w * u)) = K(x,v5 \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(15599,a,18261,a)].">
      <j1 rule="hyper" parents="15599 18261"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      K(x * K(y,T(z,u * w) * v5),v5 \ T(z,w * u)) = K(x,v5 \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(15049,a,18261,a)].">
      <j1 rule="hyper" parents="15049 18261"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ (w \ v5),u)),K(w \ (u \ v5),u) \ z) = K(x,K(w \ (u \ v5),u) \ z)
    ]]></literal>
    <justification jstring="[para(8221(a,1),18261(a,1,1,2,2))].">
      <j1 rule="para" parents="8221 18261"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w \ v5)),K(u,v5 / w) \ z) = K(x,K(u,v5 / w) \ z)
    ]]></literal>
    <justification jstring="[para(15026(a,1),18261(a,1,1,2))].">
      <j1 rule="para" parents="15026 18261"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(16148(a,1),17540(a,1,1,1))].">
      <j1 rule="para" parents="16148 17540"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v6,v5) * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17897,a(flip),b,18267,a)].">
      <j1 rule="hyper" parents="64 17897 18267"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z * (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(17897(a,1),18269(a,2,2))].">
      <j1 rule="para" parents="17897 18269"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8829,a,18271,a)].">
      <j1 rule="hyper" parents="8829 18271"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      ((K(x,y) * K(z,u)) * a(w,v5,v6)) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(18272(a,1),17717(a,1,1,1))].">
      <j1 rule="para" parents="18272 17717"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      (K(x,y) * (K(z,u) * a(w,v5,v6))) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(17652(a,1),18274(a,1,1))].">
      <j1 rule="para" parents="17652 18274"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6823,a,18275,a)].">
      <j1 rule="hyper" parents="6823 18275"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * a(u,w,K(x,v5)),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11589(a,2),17613(a,1,2,1,2))].">
      <j1 rule="para" parents="11589 17613"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      R(K(x,y),z,L(a(z,u,w),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,11,a(flip),b,17834,a),flip(a)].">
      <j1 rule="hyper" parents="319 11 17834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      R(K(x,y),z,a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17832(a,1),18279(a,1,3))].">
      <j1 rule="para" parents="17832 18279"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      K(x,L(y,z,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12814,a,18281,a)].">
      <j1 rule="hyper" parents="12814 18281"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13179,a,b,18282,a)].">
      <j1 rule="hyper" parents="64 13179 18282"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,v5,a(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(319,a,18282,a,b,18284,a),flip(a)].">
      <j1 rule="hyper" parents="319 18282 18284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(18285(a,2),5384(a,1))].">
      <j1 rule="para" parents="18285 5384"/>
    </justification>
  </clause>

  <clause id="18288">
    <literal><![CDATA[
      R(K(x,y),z,L(a(u,w,z),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,11,a(flip),b,17836,a),flip(a)].">
      <j1 rule="hyper" parents="319 11 17836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      R(K(x,y),z,a(u,w,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17833(a,1),18288(a,1,3))].">
      <j1 rule="para" parents="17833 18288"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12814,a,18290,a)].">
      <j1 rule="hyper" parents="12814 18290"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = K(x,y) * (z / a(u,w,z))
    ]]></literal>
    <justification jstring="[para(18291(a,1),12903(a,1,1,1))].">
      <j1 rule="para" parents="18291 12903"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16246,a(flip),b,18293,a)].">
      <j1 rule="hyper" parents="64 16246 18293"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(13316(a,1),18294(a,2,2))].">
      <j1 rule="para" parents="13316 18294"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,4332,a(flip),b,17855,a),flip(a)].">
      <j1 rule="hyper" parents="319 4332 17855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(3266(a,2),18296(a,1,2,2))].">
      <j1 rule="para" parents="3266 18296"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (T(w,u) \ u))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[para(11182(a,1),18297(a,1,2,2,1))].">
      <j1 rule="para" parents="11182 18297"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18176,a,18298,a)].">
      <j1 rule="hyper" parents="18176 18298"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18297,a(flip),b,18299,a),flip(a)].">
      <j1 rule="hyper" parents="64 18297 18299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(12251,a,18300,a),flip(a)].">
      <j1 rule="hyper" parents="12251 18300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(18301(a,1),12190(a,1))].">
      <j1 rule="para" parents="18301 12190"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(3270(a,2),18302(a,1,2,2,1))].">
      <j1 rule="para" parents="3270 18302"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      R(x,y \ ((y \ z) * T(y,u)),x) = K(x,x * (z / T(y,u))) \ T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[para(16537(a,1),17887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16537 17887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      R(x,y \ ((y \ z) * T(y,u)),x) = R(x,z / T(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4461,a(flip),b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="319 4461 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      R(x,y \ ((y \ z) * T(y,u)),x) = R(x,T(y,u) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10972,a(flip),b,18305,a),flip(a)].">
      <j1 rule="hyper" parents="319 10972 18305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      R(x,y \ (y \ (T(y,z) * u)),x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10974,a,b,18306,a)].">
      <j1 rule="hyper" parents="64 10974 18306"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      R(x,(K(y,z) \ y) \ u,x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(4504(a,1),18307(a,1,2))].">
      <j1 rule="para" parents="4504 18307"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      R(x,((y * z) / y) \ u,x) = R(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[para(4155(a,1),18308(a,1,2,1))].">
      <j1 rule="para" parents="4155 18308"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16279,a(flip),b,18023,a),flip(a)].">
      <j1 rule="hyper" parents="64 16279 18023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,12749,a(flip),b,18221,a),flip(a)].">
      <j1 rule="hyper" parents="319 12749 18221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18222,a(flip),b,18311,a),flip(a)].">
      <j1 rule="hyper" parents="64 18222 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17340,a(flip),b,18312,a)].">
      <j1 rule="hyper" parents="64 17340 18312"/>
    </justification>
  </clause>

  <clause id="18314">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,13549,a(flip),b,18313,a),flip(a)].">
      <j1 rule="hyper" parents="319 13549 18313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17951,a(flip),b,18313,a)].">
      <j1 rule="hyper" parents="64 17951 18313"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18313(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 18313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * (u * K(w,L(v5,u,z)))) \ y) = K(x,((z \ u) * K(w,v5)) \ y)
    ]]></literal>
    <justification jstring="[para(12766(a,1),18313(a,2,2,1))].">
      <j1 rule="para" parents="12766 18313"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ u,K(v5,v6)) \ y) = w
    ]]></literal>
    <justification jstring="[para(18313(a,2),15015(a,1))].">
      <j1 rule="para" parents="18313 15015"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(18316(a,1),8232(a,1,1))].">
      <j1 rule="para" parents="18316 8232"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(5064(a,1),18314(a,1,2,1))].">
      <j1 rule="para" parents="5064 18314"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17951,a(flip),b,18320,a)].">
      <j1 rule="hyper" parents="64 17951 18320"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(81(a,1),18321(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="81 18321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18323">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),18321(a,1,2,2,1))].">
      <j1 rule="para" parents="109 18321"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(12204(a,1),18321(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12204 18321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15350,a,b,18322,a)].">
      <j1 rule="hyper" parents="64 15350 18322"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      K(x,(y / T(a(z \ 1,z,u),L(u,z,z \ 1))) \ L(u,z,z \ 1)) = K(x,L(u,z,z \ 1) \ (u * (y \ L(u,z,z \ 1))))
    ]]></literal>
    <justification jstring="[para(3949(a,1),18323(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3949 18323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11246,a(flip),b,18315,a)].">
      <j1 rule="hyper" parents="64 11246 18315"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17075,a(flip),b,18327,a),flip(a)].">
      <j1 rule="hyper" parents="64 17075 18327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(81(a,1),18328(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="81 18328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * (u * y))) = K(x,(u \ (z * y)) \ y)
    ]]></literal>
    <justification jstring="[para(381(a,1),18328(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="381 18328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),18329(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 18329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18333">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(16650,a,18332,a),flip(a)].">
      <j1 rule="hyper" parents="16650 18332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13141,a(flip),b,18330,a),flip(a)].">
      <j1 rule="hyper" parents="64 13141 18330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18335">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(18334(a,1),6846(a,1,1))].">
      <j1 rule="para" parents="18334 6846"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13110,a,b,18335,a)].">
      <j1 rule="hyper" parents="64 13110 18335"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((((v7 * y) \ v7) * z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(18318,a,17966,a)].">
      <j1 rule="hyper" parents="18318 17966"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12880,a(flip),b,18319,a),flip(a)].">
      <j1 rule="hyper" parents="64 12880 18319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(13047,a,18333,a),flip(a)].">
      <j1 rule="hyper" parents="13047 18333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15383,a(flip),b,18339,a),flip(a)].">
      <j1 rule="hyper" parents="64 15383 18339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18341">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * ((((v5 * u) \ v5) * z) \ v5)) = K(x,((u \ z) * K(w,y)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,17966,a(flip),b,18317,a)].">
      <j1 rule="hyper" parents="64 17966 18317"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((((v5 * w) \ v5) * u) \ v5)) = K(x,((w \ u) * K(z,y)) \ v5)
    ]]></literal>
    <justification jstring="[para(10133(a,1),18341(a,1,2,1))].">
      <j1 rule="para" parents="10133 18341"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16892,a(flip),b,18342,a)].">
      <j1 rule="hyper" parents="64 16892 18342"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * ((w \ v5) \ u)) = v6
    ]]></literal>
    <justification jstring="[para(18343(a,2),17704(a,1))].">
      <j1 rule="para" parents="18343 17704"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((y \ z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(18345,a,18337,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18345 18337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(15022,a,18346,a)].">
      <j1 rule="hyper" parents="15022 18346"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      1 / T(T(x,a(y,z,u)) * K(w,v5),a(y,z,x)) = K(u,a(y,z,x)) / (x * K(w,v5))
    ]]></literal>
    <justification jstring="[para(16422(a,1),18278(a,1,2,1))].">
      <j1 rule="para" parents="16422 18278"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = 1 / (T(u,a(y,z,x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(17611(a,1),18348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17611 18348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18350">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = K(v5,w) / T(u,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12023,a(flip),b,18349,a),flip(a)].">
      <j1 rule="hyper" parents="319 12023 18349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / T(z,a(u,y,x))
    ]]></literal>
    <justification jstring="[para(12525(a,2),18350(a,1,1))].">
      <j1 rule="para" parents="12525 18350"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(13261(a,2),18352(a,2,2))].">
      <j1 rule="para" parents="13261 18352"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      L(K(x,y) / z,u,K(w,v5)) = K(x,y) / L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17617,a(flip),b,18353,a)].">
      <j1 rule="hyper" parents="64 17617 18353"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      L(K(x,y) / (z \ 1),u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,16614,a(flip),b,18354,a),flip(a)].">
      <j1 rule="hyper" parents="319 16614 18354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(11929(a,1),18355(a,1,1))].">
      <j1 rule="para" parents="11929 18355"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      L(K(x,y) * (K(y,T(x,z)) * (z / a(u,w,v5))),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,13406,a(flip),b,18356,a),flip(a)].">
      <j1 rule="hyper" parents="319 13406 18356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(L(K(w,v5) * x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(18356(a,2),15729(a,1,2,1))].">
      <j1 rule="para" parents="18356 15729"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8551(a,1),18357(a,1,1))].">
      <j1 rule="para" parents="8551 18357"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      L(T(x,K(y,z)) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10444(a,1),18359(a,1,1))].">
      <j1 rule="para" parents="10444 18359"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(13288,a,18360,a),flip(a)].">
      <j1 rule="hyper" parents="13288 18360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      T(a(x,y,z) \ (a(x,y,z) * u),K(w,v5)) = u * K(w,K(v5,u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14237,a(flip),b,18361,a),flip(a)].">
      <j1 rule="hyper" parents="319 14237 18361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),18362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 18362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(w,v5)) = a(x,y,z) * T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(131,a,18363,a(flip),b,14237,a),flip(a)].">
      <j1 rule="hyper" parents="131 18363 14237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18365">
    <literal><![CDATA[
      x \ T(a(y,z,u) * (a(y,z,u) \ x),K(w,v5)) = K(w,K(v5,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(127,a,18364,a,b,6766,a(flip))].">
      <j1 rule="hyper" parents="127 18364 6766"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = v5 \ T(v5,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),18365(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = K(v5,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,4012,a,b,18366,a),flip(a)].">
      <j1 rule="hyper" parents="319 4012 18366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) = u * K(y,T(z,a(w,v5,v6) \ x))
    ]]></literal>
    <justification jstring="[para(18367(a,1),14172(a,1,1))].">
      <j1 rule="para" parents="18367 14172"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(14708,a,18368,a),flip(a)].">
      <j1 rule="hyper" parents="14708 18368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18370">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(14425,a,18369,a)].">
      <j1 rule="hyper" parents="14425 18369"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      K(x,T(y,z * a(u,w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14424,a,18369,a)].">
      <j1 rule="hyper" parents="14424 18369"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(12701(a,1),18370(a,1,2,2))].">
      <j1 rule="para" parents="12701 18370"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(18371(a,1),6837(a,1,1,2))].">
      <j1 rule="para" parents="18371 6837"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15351,a,b,18372,a)].">
      <j1 rule="hyper" parents="64 15351 18372"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7254,a,18373,a),flip(a)].">
      <j1 rule="hyper" parents="7254 18373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(85(a,1),18376(a,1,2,2))].">
      <j1 rule="para" parents="85 18376"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * a(w,v5,v6))) = T(y,K(u * a(w,v5,v6),z) * x)
    ]]></literal>
    <justification jstring="[para(18376(a,1),13423(a,1,2,1,2))].">
      <j1 rule="para" parents="18376 13423"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      K(x,T(y,T(z * a(u,w,v5),v6) * v7)) = K(x,T(y,z * v7))
    ]]></literal>
    <justification jstring="[hyper(319,a,18370,a(flip),b,18374,a),flip(a)].">
      <j1 rule="hyper" parents="319 18370 18374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(15166,a,18379,a)].">
      <j1 rule="hyper" parents="15166 18379"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,18372,a(flip),b,18380,a)].">
      <j1 rule="hyper" parents="64 18372 18380"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16248,a(flip),b,18381,a),flip(a)].">
      <j1 rule="hyper" parents="64 16248 18381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18384">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = v6 \ T(x * T(v6,K(v5,y)),K(v5,y))
    ]]></literal>
    <justification jstring="[para(18376(a,1),18378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18376 18378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(319,a,13423,a(flip),b,18384,a),flip(a)].">
      <j1 rule="hyper" parents="319 13423 18384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(4314(a,1),18385(a,1,2))].">
      <j1 rule="para" parents="4314 18385"/>
    </justification>
  </clause>

  <clause id="18388">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(4314(a,1),18387(a,2,2))].">
      <j1 rule="para" parents="4314 18387"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) = T(x,z / T(y,T(a(w,v5,v6),v7) * u))
    ]]></literal>
    <justification jstring="[hyper(16717,a,18388,a),flip(a)].">
      <j1 rule="hyper" parents="16717 18388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(14183,a,18389,a),flip(a)].">
      <j1 rule="hyper" parents="14183 18389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(9307(a,1),18390(a,1,2,2))].">
      <j1 rule="para" parents="9307 18390"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) = (x * v7) \ (T(x,y / T(z,u)) * v7)
    ]]></literal>
    <justification jstring="[para(18391(a,1),6435(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18391 6435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / T(z,u),v7)) = v8
    ]]></literal>
    <justification jstring="[para(18392(a,2),6438(a,1))].">
      <j1 rule="para" parents="18392 6438"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(18393,a,18382,a)].">
      <j1 rule="hyper" parents="18393 18382"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,15455,a(flip),b,18394,a),flip(a)].">
      <j1 rule="hyper" parents="64 15455 18394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(K(w,v5) * x,L(y,z,u)) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(13290(a,1),18358(a,1,2))].">
      <j1 rule="para" parents="13290 18358"/>
    </justification>
  </clause>

  <clause id="18397">
    <literal><![CDATA[
      K(x,T(y,L(z * u,w,K(v5,z)))) = K(x,T(y,L(z,w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14056,a(flip),b,18396,a),flip(a)].">
      <j1 rule="hyper" parents="64 14056 18396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(16208,a,18397,a),flip(a)].">
      <j1 rule="hyper" parents="16208 18397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(14223,a,18398,a)].">
      <j1 rule="hyper" parents="14223 18398"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15177,a(flip),b,18398,a)].">
      <j1 rule="hyper" parents="64 15177 18398"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14027,a,b,18399,a),flip(a)].">
      <j1 rule="hyper" parents="319 14027 18399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(18402(a,1),6837(a,1,1,2))].">
      <j1 rule="para" parents="18402 6837"/>
    </justification>
  </clause>

  <clause id="18404">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(14223,a,18401,a)].">
      <j1 rule="hyper" parents="14223 18401"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),18404(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x * ((z * y) \ y))) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15603,a(flip),b,18406,a),flip(a)].">
      <j1 rule="hyper" parents="64 15603 18406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      T(x,K(y,z * L(u,w,v5))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(7254,a,18403,a),flip(a)].">
      <j1 rule="hyper" parents="7254 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      T(x,K(y,z * ((u * w) \ v5))) = T(x,K(y,z * (w \ (u \ v5))))
    ]]></literal>
    <justification jstring="[para(302(a,1),18408(a,1,2,2,2))].">
      <j1 rule="para" parents="302 18408"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      T(x,K(y,z * ((u * z) \ w))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),18409(a,2,2,2))].">
      <j1 rule="para" parents="10 18409"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(12(a,1),18410(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(16455,a,18411,a)].">
      <j1 rule="hyper" parents="16455 18411"/>
    </justification>
  </clause>

  <clause id="18413">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(16319,a,18412,a)].">
      <j1 rule="hyper" parents="16319 18412"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z * (u \ T(w,z)))) = x * K(y,T(x,w \ (T(z,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17021,a(flip),b,18413,a),flip(a)].">
      <j1 rule="hyper" parents="64 17021 18413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z * (u \ w))) = x * K(y,T(x,w \ (T(z,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15274,a(flip),b,18414,a)].">
      <j1 rule="hyper" parents="64 15274 18414"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      x * K(y,T(x,z \ (T(u,z) \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7077,a(flip),b,18415,a),flip(a)].">
      <j1 rule="hyper" parents="64 7077 18415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(17018(a,1),18417(a,1,2))].">
      <j1 rule="para" parents="17018 18417"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(286,a,18418,a),flip(a)].">
      <j1 rule="hyper" parents="286 18418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) \ w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16451,a(flip),b,18419,a),flip(a)].">
      <j1 rule="hyper" parents="64 16451 18419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18422,a(flip),b,18407,a)].">
      <j1 rule="hyper" parents="64 18422 18407"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      K(K(x \ (y \ z),x) * z,T(u,y)) = K(((y * x) \ z) * (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16674,a(flip),b,18423,a)].">
      <j1 rule="hyper" parents="64 16674 18423"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(9369(a,1),18425(a,1,1))].">
      <j1 rule="para" parents="9369 18425"/>
    </justification>
  </clause>

  <clause id="18427">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(14286,a,18426,a)].">
      <j1 rule="hyper" parents="14286 18426"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(4984(a,1),18427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4984 18427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(319,a,9304,a(flip),b,18428,a),flip(a)].">
      <j1 rule="hyper" parents="319 9304 18428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(9321,a,18429,a)].">
      <j1 rule="hyper" parents="9321 18429"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15285,a(flip),b,18430,a)].">
      <j1 rule="hyper" parents="64 15285 18430"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14687,a,18431,a)].">
      <j1 rule="hyper" parents="14687 18431"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = (x * w) / (K(z * T(y / z,u),x) * w)
    ]]></literal>
    <justification jstring="[para(18432(a,1),14850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18432 14850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,4316,a(flip),b,18433,a),flip(a)].">
      <j1 rule="hyper" parents="319 4316 18433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(14845(a,1),18434(a,1,2))].">
      <j1 rule="para" parents="14845 18434"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14649,a(flip),b,18435,a)].">
      <j1 rule="hyper" parents="64 14649 18435"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      T(x,y * T(T(z,z * y) / y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14898,a(flip),b,18436,a),flip(a)].">
      <j1 rule="hyper" parents="64 14898 18436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17151,a,b,18437,a)].">
      <j1 rule="hyper" parents="64 17151 18437"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15597,a(flip),b,18438,a)].">
      <j1 rule="hyper" parents="64 15597 18438"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(9273,a,18439,a),flip(a)].">
      <j1 rule="hyper" parents="9273 18439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(443(a,1),18440(a,2,2))].">
      <j1 rule="para" parents="443 18440"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(18255,a,18441,a)].">
      <j1 rule="hyper" parents="18255 18441"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(109(a,1),18442(a,1,2,2,1))].">
      <j1 rule="para" parents="109 18442"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      K(x \ K(K(y,z) * (u \ w),u * K(z,y)),v5) = K(x \ K(u * K(z,z \ y),w),v5)
    ]]></literal>
    <justification jstring="[para(14278(a,1),17740(a,1,1,2))].">
      <j1 rule="para" parents="14278 17740"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x \ K(K(y,z) * (u \ w),u),v5) = K(x \ K(u * K(z,z \ y),w),v5)
    ]]></literal>
    <justification jstring="[hyper(16850,a,18444,a)].">
      <j1 rule="hyper" parents="16850 18444"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x \ K(y * K(z,z \ u),w),v5) = K(x \ K(y,K(u,z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13761,a(flip),b,18445,a),flip(a)].">
      <j1 rule="hyper" parents="64 13761 18445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x \ K(y * K(z,z \ u),w),v5) = K(x \ K(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,16851,a(flip),b,18446,a),flip(a)].">
      <j1 rule="hyper" parents="319 16851 18446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18450">
    <literal><![CDATA[
      K(x \ K(K(y,z) * u,w),v5) = K(x \ K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(14276(a,1),18447(a,1,1,2))].">
      <j1 rule="para" parents="14276 18447"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      K((x \ 1) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(K(v5,v6) * y,z),u) = w
    ]]></literal>
    <justification jstring="[para(18450(a,1),12261(a,1))].">
      <j1 rule="para" parents="18450 12261"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) = K((1 \ x) * K(w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(18451,a,18167,a)].">
      <j1 rule="hyper" parents="18451 18167"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) = K(x * K(w,u),v5)
    ]]></literal>
    <justification jstring="[para(66(a,1),18452(a,2,1,1))].">
      <j1 rule="para" parents="66 18452"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(x * K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(14288,a,18453,a)].">
      <j1 rule="hyper" parents="14288 18453"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      K(x * K(y,T(z,u) * w),v5) = K(x * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(4636(a,1),18454(a,1,1,2,2))].">
      <j1 rule="para" parents="4636 18454"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ T(z,w * v5)) = K(x,u \ T(z,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18263,a(flip),b,18455,a),flip(a)].">
      <j1 rule="hyper" parents="64 18263 18455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ T(z,w * v5)) = K(x,u \ T(z,v5 \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18262,a(flip),b,18455,a),flip(a)].">
      <j1 rule="hyper" parents="64 18262 18455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18456,a(flip),b,18457,a),flip(a)].">
      <j1 rule="hyper" parents="64 18456 18457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y * z)) = K(x,v5 / (y \ (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(17484,a,18460,a),flip(a)].">
      <j1 rule="hyper" parents="17484 18460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17057,a(flip),b,18460,a)].">
      <j1 rule="hyper" parents="64 17057 18460"/>
    </justification>
  </clause>

  <clause id="18463">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18460,a(flip),b,18462,a),flip(a)].">
      <j1 rule="hyper" parents="64 18460 18462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16860,a(flip),b,18463,a),flip(a)].">
      <j1 rule="hyper" parents="319 16860 18463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18465">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 / (u \ (w * K(z,y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18347,a(flip),b,18461,a)].">
      <j1 rule="hyper" parents="64 18347 18461"/>
    </justification>
  </clause>

  <clause id="18466">
    <literal><![CDATA[
      K(x,(y / T(z,u)) \ (x * T(w,y / T(z,u)))) = K(x,w / (x \ (y / ((z \ u) \ u))))
    ]]></literal>
    <justification jstring="[para(11110(a,1),17938(a,1,2,2,2))].">
      <j1 rule="para" parents="11110 17938"/>
    </justification>
  </clause>

  <clause id="18467">
    <literal><![CDATA[
      K(x,y / (x \ (z / ((u \ w) \ w)))) = K(x,y / (x \ (z / T(u,w))))
    ]]></literal>
    <justification jstring="[hyper(17937,a,18466,a),flip(a)].">
      <j1 rule="hyper" parents="17937 18466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      K(x,((y / ((z \ u) \ u)) / w) \ x) = K(x,w / (x \ (y / T(z,u))))
    ]]></literal>
    <justification jstring="[hyper(7215,a,18467,a)].">
      <j1 rule="hyper" parents="7215 18467"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,((y / ((z \ u) \ u)) / w) \ x) = K(x,((y / T(z,u)) / w) \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,7213,a(flip),b,18468,a),flip(a)].">
      <j1 rule="hyper" parents="319 7213 18468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,w)) = K(x,T(u \ (z * (y \ u)),w))
    ]]></literal>
    <justification jstring="[hyper(7481,a,17950,a),flip(a)].">
      <j1 rule="hyper" parents="7481 17950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,y / ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17971,a(flip),b,18470,a),flip(a)].">
      <j1 rule="hyper" parents="64 17971 18470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,((y / z) * u) / y) = K(x,y / ((y / u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15500,a(flip),b,18471,a)].">
      <j1 rule="hyper" parents="64 15500 18471"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(u \ (K(z,y) * w),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(16151(a,1),18051(a,1,2,2))].">
      <j1 rule="para" parents="16151 18051"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      K(x,T(T((y \ 1) \ z,u),y) \ w) = K(x,T((T(y,z) \ 1) \ z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(319,a,14979,a(flip),b,18069,a)].">
      <j1 rule="hyper" parents="319 14979 18069"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x,T((T(x,y) \ 1) \ y,z) \ u) = K(x,T((x \ 1) \ y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(5869,a,18474,a),flip(a)].">
      <j1 rule="hyper" parents="5869 18474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,T(z / (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14496,a(flip),b,18474,a),flip(a)].">
      <j1 rule="hyper" parents="64 14496 18474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(x,T((T(x,y) \ 1) \ y,z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,7741,a(flip),b,18475,a),flip(a)].">
      <j1 rule="hyper" parents="319 7741 18475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      K(x,T(y / (x \ 1),z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18478,a(flip),b,18477,a),flip(a)].">
      <j1 rule="hyper" parents="64 18478 18477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,K(y,x * z) \ ((z / (x \ 1)) \ u)) = K(x,T(x * z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15365,a,b,18479,a)].">
      <j1 rule="hyper" parents="64 15365 18479"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(K(z,y) * (u \ w),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(8261(a,1),18473(a,1,2,2))].">
      <j1 rule="para" parents="8261 18473"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(w * K(z,y),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15337,a(flip),b,18481,a)].">
      <j1 rule="hyper" parents="64 15337 18481"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(u,w)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16854,a(flip),b,18482,a)].">
      <j1 rule="hyper" parents="64 16854 18482"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) = K(x,u / (z / (K(w,v5) * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17932,a(flip),b,18483,a)].">
      <j1 rule="hyper" parents="64 17932 18483"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ T(v5,w))) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(17762,a,18485,a)].">
      <j1 rule="hyper" parents="17762 18485"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) = K(x,y / (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16906,a(flip),b,18486,a)].">
      <j1 rule="hyper" parents="64 16906 18486"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,z \ 1)) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16640,a(flip),b,17568,a)].">
      <j1 rule="hyper" parents="64 16640 17568"/>
    </justification>
  </clause>

  <clause id="18490">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,L(T(z,y \ 1) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,12871,a(flip),b,18488,a),flip(a)].">
      <j1 rule="hyper" parents="64 12871 18488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16632,a(flip),b,18490,a),flip(a)].">
      <j1 rule="hyper" parents="319 16632 18490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17113,a(flip),b,18491,a)].">
      <j1 rule="hyper" parents="64 17113 18491"/>
    </justification>
  </clause>

  <clause id="18493">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16839,a(flip),b,18492,a),flip(a)].">
      <j1 rule="hyper" parents="64 16839 18492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17239,a,b,18493,a)].">
      <j1 rule="hyper" parents="64 17239 18493"/>
    </justification>
  </clause>

  <clause id="18495">
    <literal><![CDATA[
      (K(x,y) * (K(x,K(y,z)) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6746(a,1),18106(a,1,1,2,1))].">
      <j1 rule="para" parents="6746 18106"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      K(x,y / (((z * u) \ z) * T(w,u \ 1))) = K(x,y / (w * (z / (u * z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16213,a(flip),b,18252,a)].">
      <j1 rule="hyper" parents="64 16213 18252"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      K(x,y / (z * (u / (w * u)))) = K(x,y / (z * ((u * w) \ u)))
    ]]></literal>
    <justification jstring="[para(5064(a,1),18496(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5064 18496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      K(x,y / (z * ((y * u) \ y))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16838,a(flip),b,18497,a),flip(a)].">
      <j1 rule="hyper" parents="64 16838 18497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      K(x,((y / ((y * z) \ y)) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18472,a,b,18498,a)].">
      <j1 rule="hyper" parents="64 18472 18498"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      K(x,((y * z) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[para(78(a,1),18499(a,1,2,1,1))].">
      <j1 rule="para" parents="78 18499"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      K(x,T(y,z) / ((T(y,z) / u) / (K(z,y) * w))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(4317(a,1),18500(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4317 18500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      K(x,((y * z) * (u * K(y,w))) / y) = K(x,y / ((K(w,y) * (y / u)) / z))
    ]]></literal>
    <justification jstring="[para(12403(a,1),18500(a,2,2,2,1))].">
      <j1 rule="para" parents="12403 18500"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) * (y \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17106,a,18503,a),flip(a)].">
      <j1 rule="hyper" parents="17106 18503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,16568,a(flip),b,18504,a),flip(a)].">
      <j1 rule="hyper" parents="319 16568 18504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      (x * (T(T(x,K(y,z)),y) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14084(a,1),18495(a,1,1))].">
      <j1 rule="para" parents="14084 18495"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      (x * (T(x,T(y,z)) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6391(a,1),18506(a,1,1,2,1))].">
      <j1 rule="para" parents="6391 18506"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      (K(T(x,y),z) * u) * (u \ (y * K(z,x))) = y * a(u \ (y * K(z,x)),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4040(a,1),18507(a,1,1))].">
      <j1 rule="para" parents="4040 18507"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,T(u,x)) * y) \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(17382,a,18508,a),flip(a)].">
      <j1 rule="hyper" parents="17382 18508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,u) * y) \ (K(z,u) * x))
    ]]></literal>
    <justification jstring="[para(15159(a,1),18509(a,2,2))].">
      <j1 rule="para" parents="15159 18509"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(17968(a,1),18510(a,1,2))].">
      <j1 rule="para" parents="17968 18510"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(y,u,K(u \ (x * y),z))
    ]]></literal>
    <justification jstring="[para(6222(a,1),18511(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6222 18511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(z,u,K(y,u \ x))
    ]]></literal>
    <justification jstring="[para(12597(a,1),18512(a,2,2))].">
      <j1 rule="para" parents="12597 18512"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(16289(a,1),18514(a,1,2))].">
      <j1 rule="para" parents="16289 18514"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(998,a,18515,a),flip(a)].">
      <j1 rule="hyper" parents="998 18515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(17615(a,2),18516(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17615 18516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(10(a,1),18517(a,1,2,1))].">
      <j1 rule="para" parents="10 18517"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(10308(a,2),18518(a,2,2))].">
      <j1 rule="para" parents="10308 18518"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ T(x,T(x \ T(y,z),y))
    ]]></literal>
    <justification jstring="[para(6265(a,1),17906(a,2,2))].">
      <j1 rule="para" parents="6265 17906"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ T(x,x \ T(T(y,z),y))
    ]]></literal>
    <justification jstring="[para(9392(a,1),18521(a,2,2))].">
      <j1 rule="para" parents="9392 18521"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ T(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(186(a,1),18522(a,2,2,2,2))].">
      <j1 rule="para" parents="186 18522"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = R(x,x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,4477,a(flip),b,18523,a),flip(a)].">
      <j1 rule="hyper" parents="319 4477 18523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),K(x,T(y,z))) = R(x,x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(6099(a,2),18524(a,1,3))].">
      <j1 rule="para" parents="6099 18524"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      R(x,x \ T(y,z),x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(17674,a,18525,a),flip(a)].">
      <j1 rule="hyper" parents="17674 18525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) = x \ R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,18526,a(flip),b,8312,a),flip(a)].">
      <j1 rule="hyper" parents="127 18526 8312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,8309,a(flip),b,18528,a),flip(a)].">
      <j1 rule="hyper" parents="319 8309 18528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18530">
    <literal><![CDATA[
      a(x,x \ (y * z),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11505,a(flip),b,18529,a)].">
      <j1 rule="hyper" parents="64 11505 18529"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      a(x,x \ (y / z),x) = a(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(111(a,1),18529(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 18529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (((x \ z) * u) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11818,a,b,18531,a)].">
      <j1 rule="hyper" parents="64 11818 18531"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (u \ ((x \ z) \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11356,a(flip),b,18532,a),flip(a)].">
      <j1 rule="hyper" parents="319 11356 18532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      a(x,x \ (((y / x) * z) \ u),x) = a(x,x \ (z \ ((x \ y) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18531,a(flip),b,18533,a)].">
      <j1 rule="hyper" parents="64 18531 18533"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      a(x,x \ (y \ ((z / x) \ u)),x) = a(x,x \ (y \ ((x \ z) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11356,a(flip),b,18534,a)].">
      <j1 rule="hyper" parents="64 11356 18534"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[para(9215(a,1),18010(a,2,1))].">
      <j1 rule="para" parents="9215 18010"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(319,a,229,a(flip),b,18536,a),flip(a)].">
      <j1 rule="hyper" parents="319 229 18536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),18537(a,1,1,3,2))].">
      <j1 rule="para" parents="109 18537"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),K(u \ (v5 \ w),v5) \ z) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[para(11152(a,1),18264(a,1,1,2))].">
      <j1 rule="para" parents="11152 18264"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),K(v5,u \ (v5 \ w)) * z) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[para(4356(a,1),18539(a,1,2))].">
      <j1 rule="para" parents="4356 18539"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),z * K(v5,u \ w)) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14860,a(flip),b,18540,a)].">
      <j1 rule="hyper" parents="64 14860 18540"/>
    </justification>
  </clause>

  <clause id="18542">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),z * K(v5,w * u)) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(18257,a,18541,a)].">
      <j1 rule="hyper" parents="18257 18541"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),z) \ w) = K(x,w * K(z,u * y))
    ]]></literal>
    <justification jstring="[hyper(6062,a,18542,a),flip(a)].">
      <j1 rule="hyper" parents="6062 18542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(4356(a,1),18543(a,1,2))].">
      <j1 rule="para" parents="4356 18543"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14860,a(flip),b,18544,a)].">
      <j1 rule="hyper" parents="64 14860 18544"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x,y * K(z,(u \ z) * w)) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[hyper(14519,a,18545,a),flip(a)].">
      <j1 rule="hyper" parents="14519 18545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6 \ v7))) = K(x,(y * z) * K(u,v7 * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,16541,a,b,18545,a)].">
      <j1 rule="hyper" parents="64 16541 18545"/>
    </justification>
  </clause>

  <clause id="18548">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(u,w / v5) \ z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[para(18545(a,1),18265(a,1,1,2))].">
      <j1 rule="para" parents="18545 18265"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x,y * K(z,z * (u \ w))) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[para(12874(a,1),18546(a,1,2,2))].">
      <j1 rule="para" parents="12874 18546"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(14440,a,18549,a)].">
      <j1 rule="hyper" parents="14440 18549"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      K(x,y * (z * K(K(u,w) * (v5 \ (K(u,w) * v6)),v7))) = K(x,(y * z) * K(v5 * v6,v7))
    ]]></literal>
    <justification jstring="[hyper(18049,a,18550,a)].">
      <j1 rule="hyper" parents="18049 18550"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6 \ v7))) = K(x,y * (z * K(u,v7 * v6)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16535,a(flip),b,18547,a),flip(a)].">
      <j1 rule="hyper" parents="319 16535 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(189(a,1),18552(a,1,2,2,2,1))].">
      <j1 rule="para" parents="189 18552"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16636,a,18553,a)].">
      <j1 rule="hyper" parents="16636 18553"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17265,a(flip),b,18553,a),flip(a)].">
      <j1 rule="hyper" parents="64 17265 18553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(15054,a,18554,a),flip(a)].">
      <j1 rule="hyper" parents="15054 18554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(15054,a,18556,a),flip(a)].">
      <j1 rule="hyper" parents="15054 18556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15079,a(flip),b,18557,a)].">
      <j1 rule="hyper" parents="64 15079 18557"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(18558(a,1),16841(a,1))].">
      <j1 rule="para" parents="18558 16841"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(v5 \ w,u) * z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(15794,a,18548,a)].">
      <j1 rule="hyper" parents="15794 18548"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(w * v5,u) * z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(15563,a,18560,a)].">
      <j1 rule="hyper" parents="15563 18560"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(6062,a,18561,a),flip(a)].">
      <j1 rule="hyper" parents="6062 18561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15794,a,18562,a)].">
      <j1 rule="hyper" parents="15794 18562"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x,K(y * z,u) * (w * v5)) * K(x,K(w,v5)) = K(x,v5 * (K(u,z \ y) * w))
    ]]></literal>
    <justification jstring="[para(18563(a,1),17067(a,1,1))].">
      <j1 rule="para" parents="18563 17067"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17067,a(flip),b,18564,a),flip(a)].">
      <j1 rule="hyper" parents="64 17067 18564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w * v5) * (v6 * (u / z)))) = K(x,y * (v6 * T(u / z,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15767,a(flip),b,18565,a),flip(a)].">
      <j1 rule="hyper" parents="64 15767 18565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      K(x,y * (z * K(K(u,w) * (v5 \ (K(u,w) * v6)),v7))) = K(x,y * (z * K(v5 * v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16535,a(flip),b,18551,a),flip(a)].">
      <j1 rule="hyper" parents="319 16535 18551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15767,a(flip),b,18566,a),flip(a)].">
      <j1 rule="hyper" parents="64 15767 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(18047(a,1),18567(a,1,2,2,2))].">
      <j1 rule="para" parents="18047 18567"/>
    </justification>
  </clause>

  <clause id="18570">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(15391,a,18569,a),flip(a)].">
      <j1 rule="hyper" parents="15391 18569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16834,a(flip),b,18569,a),flip(a)].">
      <j1 rule="hyper" parents="64 16834 18569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(15391,a,18570,a),flip(a)].">
      <j1 rule="hyper" parents="15391 18570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18573">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 * ((u \ w) \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17773,a(flip),b,18572,a),flip(a)].">
      <j1 rule="hyper" parents="64 17773 18572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18555,a(flip),b,18571,a)].">
      <j1 rule="hyper" parents="64 18555 18571"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(15101,a,18574,a)].">
      <j1 rule="hyper" parents="15101 18574"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      K(x,T(y,z * z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(213(a,1),18574(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="213 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18577">
    <literal><![CDATA[
      T(x,T(y,z * z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,18576,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 18576 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[para(700(a,1),18577(a,1,2))].">
      <j1 rule="para" parents="700 18577"/>
    </justification>
  </clause>

  <clause id="18579">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(12317,a,18578,a)].">
      <j1 rule="hyper" parents="12317 18578"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      T(x,(y * z) * ((y * y) \ u)) = T(x,((1 / y) * z) * u)
    ]]></literal>
    <justification jstring="[para(449(a,1),18578(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="449 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      T(T(x,y * ((z * z) \ u)),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(18579(a,1),14919(a,1,1))].">
      <j1 rule="para" parents="18579 14919"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      T(x,(y * z) * ((y * y) \ u)) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,3756,a(flip),b,18580,a),flip(a)].">
      <j1 rule="hyper" parents="319 3756 18580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      T(x,((y \ 1) * z) * (y * y)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(178(a,1),18582(a,1,2)),flip(a)].">
      <j1 rule="para" parents="178 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),18583(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18585">
    <literal><![CDATA[
      T(x,(y / (z * u)) * (z * z)) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14026,a(flip),b,18584,a),flip(a)].">
      <j1 rule="hyper" parents="64 14026 18584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      T(x,y * ((z * u) \ (z * z))) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12345,a(flip),b,18585,a)].">
      <j1 rule="hyper" parents="64 12345 18585"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      T(x,y / ((1 / z) * u)) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(703(a,1),18585(a,1,2))].">
      <j1 rule="para" parents="703 18585"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      T(x,y / (((z \ y) \ 1) * z)) = T(x,(z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14861,a(flip),b,18587,a),flip(a)].">
      <j1 rule="hyper" parents="64 14861 18587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      T(x,y / ((z \ 1) * (u / z))) = T(x,y * T(u \ (z * z),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17329,a(flip),b,18586,a),flip(a)].">
      <j1 rule="hyper" parents="64 17329 18586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18465,a(flip),b,18573,a)].">
      <j1 rule="hyper" parents="64 18465 18573"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17808,a,b,18590,a)].">
      <j1 rule="hyper" parents="64 17808 18590"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18487,a(flip),b,18591,a),flip(a)].">
      <j1 rule="hyper" parents="64 18487 18591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z / v5) \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(18593(a,1),18302(a,1))].">
      <j1 rule="para" parents="18593 18302"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      K(x,T(y,z) * (((T(y,z) / u) / w) \ K(z,y))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(18594,a,18502,a)].">
      <j1 rule="hyper" parents="18594 18502"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(18594,a,18053,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18594 18053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / v5) \ K(u,z))) = v6
    ]]></literal>
    <justification jstring="[para(18053(a,2),18594(a,1))].">
      <j1 rule="para" parents="18053 18594"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4314(a,1),18596(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4314 18596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / ((T(y,z) / u) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16354,a(flip),b,18595,a)].">
      <j1 rule="hyper" parents="64 16354 18595"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      K(x,((y * z) * u) / T(y,w)) = K(x,y / ((T(y,w) / u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13511,a(flip),b,18599,a),flip(a)].">
      <j1 rule="hyper" parents="64 13511 18599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18505,a,b,18600,a)].">
      <j1 rule="hyper" parents="64 18505 18600"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      K(x,y * (((y / z) / u) \ K(y,w))) = K(x,y / ((T(y,w) / z) / u))
    ]]></literal>
    <justification jstring="[hyper(18597,a,18602,a)].">
      <j1 rule="hyper" parents="18597 18602"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15088,a(flip),b,18603,a)].">
      <j1 rule="hyper" parents="64 15088 18603"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18325,a(flip),b,18604,a),flip(a)].">
      <j1 rule="hyper" parents="64 18325 18604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      T(x,K(y,z \ ((u * z) * x))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(6970(a,1),18336(a,1,1))].">
      <j1 rule="para" parents="6970 18336"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      T(x,K(y,((z * u) * x) * u)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(14728(a,1),18606(a,1,1))].">
      <j1 rule="para" parents="14728 18606"/>
    </justification>
  </clause>

  <clause id="18608">
    <literal><![CDATA[
      T(x,K(y,(z * u) * (x * u))) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(18377(a,1),18607(a,1,1))].">
      <j1 rule="para" parents="18377 18607"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(14062(a,1),18608(a,1,1))].">
      <j1 rule="para" parents="14062 18608"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(14737(a,1),18609(a,1,1))].">
      <j1 rule="para" parents="14737 18609"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      x \ (y \ ((K(z,u) * y) * T(x,K(z,u)))) = K(z,x / ((u * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16831,a(flip),b,18610,a)].">
      <j1 rule="hyper" parents="64 16831 18610"/>
    </justification>
  </clause>

  <clause id="18613">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(17404(a,1),18611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17404 18611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (z * K(w,v5)))) / z = K(x,y) * ((u * z) / (z * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(17812(a,1),17399(a,1,1,1))].">
      <j1 rule="para" parents="17812 17399"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(12733(a,1),18614(a,1,1,1))].">
      <j1 rule="para" parents="12733 18614"/>
    </justification>
  </clause>

  <clause id="18617">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(17539(a,1),18615(a,1,1))].">
      <j1 rule="para" parents="17539 18615"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17397,a(flip),b,18617,a)].">
      <j1 rule="hyper" parents="64 17397 18617"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (u * K(x,T(y,z)))) = L(z * K(x,K(y,u)),K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(17366,a,18618,a),flip(a)].">
      <j1 rule="hyper" parents="17366 18618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      K(x,y) * (z \ ((K(y,x) * z) * u)) = L(u * K(x,K(y,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(17409(a,1),18619(a,1,2))].">
      <j1 rule="para" parents="17409 18619"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) * (u \ 1)) \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16443,a(flip),b,18220,a),flip(a)].">
      <j1 rule="hyper" parents="64 16443 18220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) / u) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13208,a(flip),b,18621,a),flip(a)].">
      <j1 rule="hyper" parents="319 13208 18621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(u \ (y \ z)) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(319,a,17797,a(flip),b,18622,a),flip(a)].">
      <j1 rule="hyper" parents="319 17797 18622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(17564,a,18623,a),flip(a)].">
      <j1 rule="hyper" parents="17564 18623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      T(K(x,L(T(y,z * y),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(429,a,10242,a(flip),b,18624,a)].">
      <j1 rule="hyper" parents="429 10242 18624"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(K(y,z) / u,w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(12079(a,1),16968(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12079 16968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      K(x,(T(y,(z \ 1) \ 1) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(3421(a,1),17039(a,1,2,1,1))].">
      <j1 rule="para" parents="3421 17039"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(2758(a,1),18627(a,1,2,1,1))].">
      <j1 rule="para" parents="2758 18627"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15635,a(flip),b,18628,a)].">
      <j1 rule="hyper" parents="64 15635 18628"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((z \ 1) \ u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),18630(a,2,2,1))].">
      <j1 rule="para" parents="12 18630"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / ((z \ 1) \ 1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13173,a(flip),b,18631,a)].">
      <j1 rule="hyper" parents="64 13173 18631"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / T(z,1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15496,a(flip),b,18632,a)].">
      <j1 rule="hyper" parents="64 15496 18632"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((((u * y) \ u) \ u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[para(208(a,1),18634(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="208 18634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18636">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(319,a,15516,a(flip),b,18635,a),flip(a)].">
      <j1 rule="hyper" parents="319 15516 18635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18637">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(319,a,17169,a(flip),b,18636,a),flip(a)].">
      <j1 rule="hyper" parents="319 17169 18636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17052,a(flip),b,18637,a)].">
      <j1 rule="hyper" parents="64 17052 18637"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(208(a,1),18638(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="208 18638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (z / y),w,v5))) = K(x,u * L(((z * y) / z) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(4168(a,1),17160(a,1,2,1))].">
      <j1 rule="para" parents="4168 17160"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ z),(x * y) \ y) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13746,a(flip),b,17417,a)].">
      <j1 rule="hyper" parents="64 13746 17417"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14884,a(flip),b,18641,a)].">
      <j1 rule="hyper" parents="64 14884 18641"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6982,a,18642,a),flip(a)].">
      <j1 rule="hyper" parents="6982 18642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      a(x,T(y \ (y / (z \ u)),w) * T(y,u \ z),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[para(5058(a,1),18089(a,1,2,2))].">
      <j1 rule="para" parents="5058 18089"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) = K(x,L(y / v5,L(T(y,z),u,w),a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13177,a(flip),b,17616,a),flip(a)].">
      <j1 rule="hyper" parents="64 13177 17616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) = K(x,L(y / v5,L(y,u,w),a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17592,a(flip),b,18666,a),flip(a)].">
      <j1 rule="hyper" parents="319 17592 18666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / v5) = v6
    ]]></literal>
    <justification jstring="[para(18667(a,2),18287(a,1))].">
      <j1 rule="para" parents="18667 18287"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      L(L(x,y,z),y,K(u \ 1,((w * u) \ w) * z)) = L(x,y,(((w * u) \ w) * z) / L(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(5024(a,1),18003(a,1,3))].">
      <j1 rule="para" parents="5024 18003"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      L(L(x,y,z),y,K(((u * w) \ u) * z,w)) = L(x,y,(((u * w) \ u) * z) / L(w \ 1,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12330,a(flip),b,18670,a)].">
      <j1 rule="hyper" parents="64 12330 18670"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,(((w * u) \ w) * z) / L(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12448,a(flip),b,18671,a)].">
      <j1 rule="hyper" parents="64 12448 18671"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,((u \ 1) * z) / (u \ 1))
    ]]></literal>
    <justification jstring="[para(10672(a,1),18673(a,2,3))].">
      <j1 rule="para" parents="10672 18673"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,(u \ 1) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,10813,a(flip),b,18675,a),flip(a)].">
      <j1 rule="hyper" parents="319 10813 18675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,1 \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,10878,a(flip),b,18676,a),flip(a)].">
      <j1 rule="hyper" parents="319 10878 18676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),18677(a,2,3,2))].">
      <j1 rule="para" parents="66 18677"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16143,a,18678,a),flip(a)].">
      <j1 rule="hyper" parents="16143 18678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30,a,b,18678,a)].">
      <j1 rule="hyper" parents="64 30 18678"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6223,a(flip),b,18678,a),flip(a)].">
      <j1 rule="hyper" parents="64 6223 18678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10238,a(flip),b,18679,a),flip(a)].">
      <j1 rule="hyper" parents="64 10238 18679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(11761,a,18681,a),flip(a)].">
      <j1 rule="hyper" parents="11761 18681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,10852,a(flip),b,18680,a),flip(a)].">
      <j1 rule="hyper" parents="319 10852 18680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(18682(a,1),12342(a,1,2))].">
      <j1 rule="para" parents="18682 12342"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      x / L(K(y,z),(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(15322(a,2),18687(a,1,2,3,1))].">
      <j1 rule="para" parents="15322 18687"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,16679,a(flip),b,18684,a)].">
      <j1 rule="hyper" parents="64 16679 18684"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11792,a(flip),b,18689,a),flip(a)].">
      <j1 rule="hyper" parents="64 11792 18689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,(y * z) / y,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(1294(a,1),18690(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1294 18690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18692">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12328(a,1),18685(a,1,1))].">
      <j1 rule="para" parents="12328 18685"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(10793(a,1),18692(a,1,1))].">
      <j1 rule="para" parents="10793 18692"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      ((x * y) * (z * L(u,z,K(y,x)))) / T((x * y) * z,L(u,z,K(y,x))) = L(u,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12200,a(flip),b,18693,a)].">
      <j1 rule="hyper" parents="64 12200 18693"/>
    </justification>
  </clause>

  <clause id="18695">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,11774,a(flip),b,18691,a),flip(a)].">
      <j1 rule="hyper" parents="319 11774 18691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(3126(a,1),18695(a,1,3,1))].">
      <j1 rule="para" parents="3126 18695"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11774,a(flip),b,18696,a),flip(a)].">
      <j1 rule="hyper" parents="64 11774 18696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(319,a,11793,a(flip),b,18697,a),flip(a)].">
      <j1 rule="hyper" parents="319 11793 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18699">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,(y \ z) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(18698(a,1),8563(a,1,2))].">
      <j1 rule="para" parents="18698 8563"/>
    </justification>
  </clause>

  <clause id="18700">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,L(u,z,K(x,y))) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(18012(a,1),18694(a,1,1))].">
      <j1 rule="para" parents="18012 18694"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(16130(a,1),18700(a,1,2))].">
      <j1 rule="para" parents="16130 18700"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(12355,a,18701,a)].">
      <j1 rule="hyper" parents="12355 18701"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18702(a,1,3))].">
      <j1 rule="para" parents="12 18702"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(4175(a,1),18704(a,1,2,1))].">
      <j1 rule="para" parents="4175 18704"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12431,a(flip),b,18705,a)].">
      <j1 rule="hyper" parents="64 12431 18705"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),18706(a,2,3))].">
      <j1 rule="para" parents="12 18706"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(4363(a,1),18707(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 18707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(12186(a,1),18708(a,1,2))].">
      <j1 rule="para" parents="12186 18708"/>
    </justification>
  </clause>

  <clause id="18711">
    <literal><![CDATA[
      T(x,L(y,z \ 1,u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(18710(a,1),18194(a,1,2,1))].">
      <j1 rule="para" parents="18710 18194"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(12136(a,1),18711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12136 18711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14669,a(flip),b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="319 14669 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18715">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,z \ y))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15636,a(flip),b,18714,a),flip(a)].">
      <j1 rule="hyper" parents="64 15636 18714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,z \ y)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(12994,a,18699,a)].">
      <j1 rule="hyper" parents="12994 18699"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,L(T(z,y) \ u,z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(13622,a,18716,a),flip(a)].">
      <j1 rule="hyper" parents="13622 18716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,11326,a(flip),b,18717,a),flip(a)].">
      <j1 rule="hyper" parents="319 11326 18717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13548,a,18718,a)].">
      <j1 rule="hyper" parents="13548 18718"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13208,a(flip),b,18719,a)].">
      <j1 rule="hyper" parents="64 13208 18719"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(4702(a,1),18720(a,1,2))].">
      <j1 rule="para" parents="4702 18720"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((y \ z) * T(u,z / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18210,a,b,18721,a)].">
      <j1 rule="hyper" parents="64 18210 18721"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (K(y,u) * w))) = K(x,y \ ((T(y,u) \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17041,a(flip),b,18721,a),flip(a)].">
      <j1 rule="hyper" parents="64 17041 18721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(4309(a,1),18721(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4309 18721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(18721(a,1),8231(a,1,2))].">
      <j1 rule="para" parents="18721 8231"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(17514,a,18723,a)].">
      <j1 rule="hyper" parents="17514 18723"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(12061(a,1),18724(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12061 18724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(4314(a,1),18726(a,1,2))].">
      <j1 rule="para" parents="4314 18726"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,18727,a(flip),b,18728,a),flip(a)].">
      <j1 rule="hyper" parents="319 18727 18728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(7479(a,2),18722(a,2,2,2))].">
      <j1 rule="para" parents="7479 18722"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12879,a(flip),b,18725,a),flip(a)].">
      <j1 rule="hyper" parents="64 12879 18725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      K(x,((y \ z) \ (((z \ y) * u) * (u / ((z \ y) * u)))) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(3231(a,1),18731(a,2,2,1))].">
      <j1 rule="para" parents="3231 18731"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,14982,a(flip),b,18730,a),flip(a)].">
      <j1 rule="hyper" parents="319 14982 18730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17068,a(flip),b,18733,a)].">
      <j1 rule="hyper" parents="64 17068 18733"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,T(y,z))))
    ]]></literal>
    <justification jstring="[para(6492(a,1),18735(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6492 18735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(15858(a,1),18732(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="15858 18732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(22(a,2),18737(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 18737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(17253,a,18738,a)].">
      <j1 rule="hyper" parents="17253 18738"/>
    </justification>
  </clause>

  <clause id="18740">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(319,a,11121,a(flip),b,18739,a),flip(a)].">
      <j1 rule="hyper" parents="319 11121 18739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (z \ y)) / y) = w
    ]]></literal>
    <justification jstring="[para(18740(a,2),14825(a,1))].">
      <j1 rule="para" parents="18740 14825"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(18741,a,18340,a)].">
      <j1 rule="hyper" parents="18741 18340"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x,(y * T(z,z \ u)) / u) = K(x,u / ((z \ u) * (y \ u)))
    ]]></literal>
    <justification jstring="[para(110(a,2),18742(a,1,2,1,2))].">
      <j1 rule="para" parents="110 18742"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,(y * (z \ L(T(y,K(u,w)),v5,v6))) / L(T(y,K(u,w)),v5,v6)) = K(x,L(T(y,K(u,w)),v5,v6) / (z * (T(y,K(u,w)) \ L(y,v5,v6))))
    ]]></literal>
    <justification jstring="[para(16700(a,2),18742(a,2,2,2,2))].">
      <j1 rule="para" parents="16700 18742"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15509,a(flip),b,18743,a),flip(a)].">
      <j1 rule="hyper" parents="64 15509 18743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18746">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(L(y \ K(z,u),w,v5) \ (y \ K(z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(13164(a,1),18745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13164 18745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ y,K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18014,a(flip),b,18230,a)].">
      <j1 rule="hyper" parents="64 18014 18230"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,x \ y)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17987,a(flip),b,18747,a)].">
      <j1 rule="hyper" parents="64 17987 18747"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,y * x)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(14012(a,1),18749(a,1,2,1))].">
      <j1 rule="para" parents="14012 18749"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      (x \ y) \ T(K(y * x,K(z,u)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(7727(a,2),18750(a,1,2))].">
      <j1 rule="para" parents="7727 18750"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      (x \ y) \ T(K(z,K(u,y * x)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6748(a,2),18751(a,1,2,1,1))].">
      <j1 rule="para" parents="6748 18751"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ T(z,K(x,y))) = (u \ (K(x,y) * z)) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(16581,a,18752,a)].">
      <j1 rule="hyper" parents="16581 18752"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      T(x \ y,K(z,u)) \ T(y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14729,a(flip),b,18753,a)].">
      <j1 rule="hyper" parents="64 14729 18753"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(18754(a,2),11539(a,1,3,2))].">
      <j1 rule="para" parents="18754 11539"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[para(13437(a,1),18755(a,2,3,2))].">
      <j1 rule="para" parents="13437 18755"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (K(x,K(y,z)) * (u * (w * v5))) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16098(a,1),16145(a,1,2))].">
      <j1 rule="para" parents="16098 16145"/>
    </justification>
  </clause>

  <clause id="18758">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((w * K(x,K(y,z))) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16329(a,2),16379(a,1,1))].">
      <j1 rule="para" parents="16329 16379"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      K(x,(K(y,L(z \ 1,u,w)) * (L(z,u,w) \ v5)) * z) = K(x,z * ((K(y,L(z,u,w) \ 1) * v5) / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(10112(a,2),16427(a,1,2,1,1))].">
      <j1 rule="para" parents="10112 16427"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      K(x,L(((y \ L(y,z,u)) \ 1) \ w,y,L(y,z,u))) = K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),16634(a,1,2,3))].">
      <j1 rule="para" parents="10 16634"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w)) = K(x,((y \ L(y,z,u)) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(12627,a,18760,a),flip(a)].">
      <j1 rule="hyper" parents="12627 18760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18764">
    <literal><![CDATA[
      K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,11956,a(flip),b,18761,a),flip(a)].">
      <j1 rule="hyper" parents="319 11956 18761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      K(x,y \ (((L(y,z,u) \ y) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(10029(a,1),18764(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10029 18764"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3946(a,1),18765(a,1,2,2,1))].">
      <j1 rule="para" parents="3946 18765"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1165(a,1),18766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1165 18766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18768">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(16430,a,18767,a),flip(a)].">
      <j1 rule="hyper" parents="16430 18767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,13136,a(flip),b,18768,a)].">
      <j1 rule="hyper" parents="64 13136 18768"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(18161,a,18769,a),flip(a)].">
      <j1 rule="hyper" parents="18161 18769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(18769(a,1),18161(a,1))].">
      <j1 rule="para" parents="18769 18161"/>
    </justification>
  </clause>

  <clause id="18772">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * a((y / (z \ 1)) / z,u,u \ 1)) = K(x,z * L((y / (z \ 1)) / z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(8490(a,2),18770(a,1,2,1))].">
      <j1 rule="para" parents="8490 18770"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * (K(z,y) * z))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(12157(a,1),16828(a,1,2,2))].">
      <j1 rule="para" parents="12157 16828"/>
    </justification>
  </clause>

  <clause id="18774">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(16250(a,1),16910(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="16250 16910"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      L(K(x,((y / ((z \ 1) \ 1)) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(10847(a,2),17978(a,1,1,1))].">
      <j1 rule="para" parents="10847 17978"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16747,a(flip),b,18736,a),flip(a)].">
      <j1 rule="hyper" parents="319 16747 18736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,11119,a(flip),b,18776,a),flip(a)].">
      <j1 rule="hyper" parents="319 11119 18776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * T((w * y) \ y,K(y,z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[para(18643(a,1),18778(a,1,2,2,2))].">
      <j1 rule="para" parents="18643 18778"/>
    </justification>
  </clause>

  <clause id="18780">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(16438,a,18779,a)].">
      <j1 rule="hyper" parents="16438 18779"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(11313,a,18780,a)].">
      <j1 rule="hyper" parents="11313 18780"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,y \ (z * ((u * y) \ T(y,w)))) = K(x,T(y,w) \ (z / T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17520,a(flip),b,18781,a)].">
      <j1 rule="hyper" parents="64 17520 18781"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * u) / T(z,y))) = K(x,((z * ((z * y) / z)) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18324,a,b,18783,a),flip(a)].">
      <j1 rule="hyper" parents="64 18324 18783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      K(x,T(y \ ((y * z) / u),K(y,u))) = K(x,((u * ((u * y) / u)) / z) \ y)
    ]]></literal>
    <justification jstring="[para(6359(a,2),18784(a,1,2))].">
      <j1 rule="para" parents="6359 18784"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(14130,a,18785,a),flip(a)].">
      <j1 rule="hyper" parents="14130 18785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(13049(a,1),18786(a,1,2))].">
      <j1 rule="para" parents="13049 18786"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(15560,a,18788,a)].">
      <j1 rule="hyper" parents="15560 18788"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(17219,a,18789,a)].">
      <j1 rule="hyper" parents="17219 18789"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17372,a(flip),b,18790,a)].">
      <j1 rule="hyper" parents="64 17372 18790"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[para(3625(a,1),18790(a,1,2,2))].">
      <j1 rule="para" parents="3625 18790"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(y \ K(z,u)) \ L(y \ K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,5084,a(flip),b,18746,a),flip(a)].">
      <j1 rule="hyper" parents="319 5084 18746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      L(x,L(y,z,K(u,K(w,v5))),K(u,K(w,v5)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16139,a(flip),b,18757,a),flip(a)].">
      <j1 rule="hyper" parents="64 16139 18757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(16129(a,1),18794(a,1,2))].">
      <j1 rule="para" parents="16129 18794"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17370,a,b,18796,a)].">
      <j1 rule="hyper" parents="64 17370 18796"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(4292(a,1),18796(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4292 18796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(4646(a,1),18796(a,1,3))].">
      <j1 rule="para" parents="4646 18796"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6045(a,1),18796(a,1,3))].">
      <j1 rule="para" parents="6045 18796"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      L(x,y,z / T(u,K(w,v5))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(14246(a,1),18796(a,1,3))].">
      <j1 rule="para" parents="14246 18796"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      T(x,a(T(y,z),u,w)) = L(x,u,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(13303,a,18800,a)].">
      <j1 rule="hyper" parents="13303 18800"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      T(x,a(T(y,z),u,w)) = T(x,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a(flip),b,18802,a),flip(a)].">
      <j1 rule="hyper" parents="319 13261 18802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      T(x,a(y / z,u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(111(a,1),18803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 18803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(K(u,w) / z) \ v5)
    ]]></literal>
    <justification jstring="[para(11994(a,1),18798(a,1,3,1))].">
      <j1 rule="para" parents="11994 18798"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(7157(a,1),18799(a,1,3,2))].">
      <j1 rule="para" parents="7157 18799"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (K(w,v5) / u))
    ]]></literal>
    <justification jstring="[para(11994(a,1),18801(a,1,3,2))].">
      <j1 rule="para" parents="11994 18801"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      T(T(x,x * y),a(x \ (x * (x * y)),z,u)) = T(T(x,x * y),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12691,a(flip),b,18804,a),flip(a)].">
      <j1 rule="hyper" parents="64 12691 18804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,12471,a(flip),b,18805,a),flip(a)].">
      <j1 rule="hyper" parents="64 12471 18805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(x \ K(x,y)) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(18809(a,1),13083(a,1,2,2,2))].">
      <j1 rule="para" parents="18809 13083"/>
    </justification>
  </clause>

  <clause id="18811">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(u \ K(z,y)) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(18809(a,1),15618(a,1,2,2))].">
      <j1 rule="para" parents="18809 15618"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12472,a(flip),b,18807,a),flip(a)].">
      <j1 rule="hyper" parents="64 12472 18807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(18812(a,1),17628(a,1,2))].">
      <j1 rule="para" parents="18812 17628"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(16230,a,18813,a)].">
      <j1 rule="hyper" parents="16230 18813"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) * K(y,K(z,u)) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(18(a,2),18797(a,1,1))].">
      <j1 rule="para" parents="18 18797"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(130,a,18816,a(flip),b,6781,a),flip(a)].">
      <j1 rule="hyper" parents="130 18816 6781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14247(a,1),18816(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14247 18816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(18816(a,1),14975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18816 14975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6418(a,1),18819(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6418 18819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(18817(a,2),15018(a,1,2,2))].">
      <j1 rule="para" parents="18817 15018"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      K(x,y * L(K(z,K(u,w)) * v5,v6,v7)) = K(x,y * L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(18818(a,2),14988(a,1,2,2))].">
      <j1 rule="para" parents="18818 14988"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,v5,v6)) = K(x,L(T(y,z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6386(a,1),18820(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6386 18820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      K(x,y * L((z / K(u,w)) \ v5,v6,v7)) = K(x,y * L((K(u,w) \ z) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(4510(a,1),18822(a,1,2,2,1))].">
      <j1 rule="para" parents="4510 18822"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      T(T(x,x * y),a(x * y,z,u)) = T(T(x,x * y),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),18808(a,1,2,1))].">
      <j1 rule="para" parents="9 18808"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      T(T(x,x * y),a(y,z,u)) = T(x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12635,a(flip),b,18825,a),flip(a)].">
      <j1 rule="hyper" parents="64 12635 18825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12641,a(flip),b,18826,a)].">
      <j1 rule="hyper" parents="64 12641 18826"/>
    </justification>
  </clause>

  <clause id="18829">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,L(z,u,w)),z,(x \ y) * x) = K(y,L(((x \ y) * x) * z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(127,a,18828,a,b,12068,a)].">
      <j1 rule="hyper" parents="127 18828 12068"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L((w * K(u,z)) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(5174(a,1),18824(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5174 18824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(18814(a,1),18811(a,1,2))].">
      <j1 rule="para" parents="18814 18811"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(7280(a,1),18831(a,1,2))].">
      <j1 rule="para" parents="7280 18831"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(319,a,17406,a(flip),b,18832,a),flip(a)].">
      <j1 rule="hyper" parents="319 17406 18832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,K(x,y) \ x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(12984(a,1),18810(a,1,2,2))].">
      <j1 rule="para" parents="12984 18810"/>
    </justification>
  </clause>

  <clause id="18836">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x * K(y,x)))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(4232(a,1),18835(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4232 18835"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(10829(a,1),18836(a,1,2,2,2))].">
      <j1 rule="para" parents="10829 18836"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(12750(a,1),18837(a,1,2,2))].">
      <j1 rule="para" parents="12750 18837"/>
    </justification>
  </clause>

  <clause id="18840">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * K(z,u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(10114(a,1),18838(a,1,2))].">
      <j1 rule="para" parents="10114 18838"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5432,a,18840,a)].">
      <j1 rule="hyper" parents="5432 18840"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      (x * K(y,z)) / L(x * K(y,z),u,u \ 1) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(18841(a,2),13333(a,1,2))].">
      <j1 rule="para" parents="18841 13333"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      L((x \ T(y,z)) * K(z,y),u,u \ 1) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(18841(a,2),16819(a,1,1))].">
      <j1 rule="para" parents="18841 16819"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) \ (x * K(y,z)) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3947,a,18842,a)].">
      <j1 rule="hyper" parents="3947 18842"/>
    </justification>
  </clause>

  <clause id="18845">
    <literal><![CDATA[
      L(a(x \ 1,x,y),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(18844(a,1),1966(a,1))].">
      <j1 rule="para" parents="18844 1966"/>
    </justification>
  </clause>

  <clause id="18846">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(18845,a,17833,a)].">
      <j1 rule="hyper" parents="18845 17833"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[para(5925(a,1),18846(a,1,3))].">
      <j1 rule="para" parents="5925 18846"/>
    </justification>
  </clause>

  <clause id="18848">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(18847(a,1),3954(a,1,1))].">
      <j1 rule="para" parents="18847 3954"/>
    </justification>
  </clause>

  <clause id="18849">
    <literal><![CDATA[
      K(x,y) * (a(z \ 1,z,u) \ u) = L(K(x,y) * u,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,18295,a(flip),b,18848,a)].">
      <j1 rule="hyper" parents="64 18295 18848"/>
    </justification>
  </clause>

  <clause id="18850">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(3954(a,1),18849(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3954 18849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = (x \ y) / (x \ T(y,u))
    ]]></literal>
    <justification jstring="[para(12359(a,1),18843(a,1,1,1))].">
      <j1 rule="para" parents="12359 18843"/>
    </justification>
  </clause>

  <clause id="18852">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = K(u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,12405,a(flip),b,18851,a),flip(a)].">
      <j1 rule="hyper" parents="319 12405 18851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18854">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,L(z,u,w)),z,T(y,x)) = K(y,L(((x \ y) * x) * z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(10810(a,1),18829(a,1,2))].">
      <j1 rule="para" parents="10810 18829"/>
    </justification>
  </clause>

  <clause id="18855">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,L(z,u,w)),z,y) = K(y,L(((x \ y) * x) * z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(10895(a,1),18854(a,1,2))].">
      <j1 rule="para" parents="10895 18854"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      K(x,L(((y \ x) * y) * z,u,w)) * y = K(x,L(z,u,w)) * (a(x,z,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13958,a(flip),b,18855,a),flip(a)].">
      <j1 rule="hyper" parents="64 13958 18855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18858">
    <literal><![CDATA[
      K(x,L(T(x,y) * z,u,w)) * y = K(x,L(z,u,w)) * (a(x,z,x) \ y)
    ]]></literal>
    <justification jstring="[para(15656(a,1),18856(a,1,1))].">
      <j1 rule="para" parents="15656 18856"/>
    </justification>
  </clause>

  <clause id="18859">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (a(x,y,x) \ w) = K(x,L(x * y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(10193(a,1),18858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10193 18858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      K(x,L(x * y,z,u)) = K(x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11445,a,18859,a),flip(a)].">
      <j1 rule="hyper" parents="11445 18859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18862">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((K(x,K(y,z)) \ w) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(14243(a,2),18758(a,1,2,1))].">
      <j1 rule="para" parents="14243 18758"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w)) * ((L(z,u,w) \ v5) * z)) = K(x,z * ((K(y,L(z,u,w) \ 1) * v5) / L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(16907,a,18759,a)].">
      <j1 rule="hyper" parents="16907 18759"/>
    </justification>
  </clause>

  <clause id="18864">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * a(z \ (y / (z \ 1)),u,u \ 1)) = K(x,z * L((y / (z \ 1)) / z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(16811(a,1),18772(a,1,2,2))].">
      <j1 rule="para" parents="16811 18772"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * z)) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(6195(a,1),18773(a,1,2,2))].">
      <j1 rule="para" parents="6195 18773"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) / (T(y,z * y) \ 1))
    ]]></literal>
    <justification jstring="[para(9112(a,1),18865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9112 18865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12077,a(flip),b,18867,a),flip(a)].">
      <j1 rule="hyper" parents="319 12077 18867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,11193,a(flip),b,18868,a),flip(a)].">
      <j1 rule="hyper" parents="319 11193 18868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(319,a,16825,a(flip),b,18869,a),flip(a)].">
      <j1 rule="hyper" parents="319 16825 18869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(8492(a,1),18870(a,1,2,2,1))].">
      <j1 rule="para" parents="8492 18870"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      K(x,y * (L(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(13317(a,1),18774(a,1,2,2,1))].">
      <j1 rule="para" parents="13317 18774"/>
    </justification>
  </clause>

  <clause id="18873">
    <literal><![CDATA[
      L(K(x,((y / T(z,1)) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(18469(a,1),18775(a,1,1,1))].">
      <j1 rule="para" parents="18469 18775"/>
    </justification>
  </clause>

  <clause id="18874">
    <literal><![CDATA[
      L(K(x,((y / z) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(208(a,1),18873(a,1,1,1,2,1,1,2))].">
      <j1 rule="para" parents="208 18873"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,y / (u / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(12913(a,1),18874(a,1,1))].">
      <j1 rule="para" parents="12913 18874"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,(u / ((z \ 1) \ 1)) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10972,a(flip),b,18875,a),flip(a)].">
      <j1 rule="hyper" parents="319 10972 18875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18877">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,(u / z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11831,a(flip),b,18876,a),flip(a)].">
      <j1 rule="hyper" parents="319 11831 18876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18878">
    <literal><![CDATA[
      K(x,(y / (z * u)) \ x) \ T(x,(z * u) / y) = R(x,(y / u) \ z,x)
    ]]></literal>
    <justification jstring="[para(11641(a,1),18877(a,1,1))].">
      <j1 rule="para" parents="11641 18877"/>
    </justification>
  </clause>

  <clause id="18879">
    <literal><![CDATA[
      R(x,(y / z) \ u,x) = R(x,y \ (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10977,a(flip),b,18878,a),flip(a)].">
      <j1 rule="hyper" parents="64 10977 18878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18880">
    <literal><![CDATA[
      R(x,(y * z) \ (u * y),x) = R(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18309,a(flip),b,18879,a),flip(a)].">
      <j1 rule="hyper" parents="64 18309 18879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      R(x,y \ (z \ (u * z)),x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11431,a(flip),b,18880,a)].">
      <j1 rule="hyper" parents="64 11431 18880"/>
    </justification>
  </clause>

  <clause id="18882">
    <literal><![CDATA[
      R(x,T(y,z) \ u,x) = R(x,y \ T(u,z),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),18881(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 18881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      x \ R(x,y \ T(z,u),x) = a(x,T(y,u) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(127,a,18882,a(flip),b,8312,a)].">
      <j1 rule="hyper" parents="127 18882 8312"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      a(x,T(y,z) \ u,x) = a(x,y \ T(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(8325,a,18883,a),flip(a)].">
      <j1 rule="hyper" parents="8325 18883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      a(x,y \ (z \ (y * u)),x) = a(x,z \ T(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11439,a,b,18884,a)].">
      <j1 rule="hyper" parents="64 11439 18884"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / (K(x,K(y,z)) \ (w * v5)) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16099(a,2),18862(a,1,2))].">
      <j1 rule="para" parents="16099 18862"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w) \ 1) * v5) / L(y,u,w))) = K(x,K(z,y \ 1) * ((L(y,u,w) \ v5) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16892,a(flip),b,18863,a),flip(a)].">
      <j1 rule="hyper" parents="64 16892 18863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w) \ 1) * v5) / L(y,u,w))) = K(x,K(z,y) * ((L(y,u,w) \ v5) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,13639,a(flip),b,18888,a),flip(a)].">
      <j1 rule="hyper" parents="319 13639 18888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w) \ 1) * v5) / L(y,u,w))) = K(x,(L(y,u,w) \ v5) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14323,a(flip),b,18890,a),flip(a)].">
      <j1 rule="hyper" parents="319 14323 18890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y \ 1,u,w)) * v5) / L(y,u,w))) = K(x,(L(y,u,w) \ v5) * T(y,z))
    ]]></literal>
    <justification jstring="[para(10112(a,2),18891(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10112 18891"/>
    </justification>
  </clause>

  <clause id="18893">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * a(z \ ((z \ 1) \ y),u,u \ 1)) = K(x,z * L((y / (z \ 1)) / z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(16815(a,1),18864(a,1,2,2))].">
      <j1 rule="para" parents="16815 18864"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      K(x,y * (L(z,a(u,w,K(v5,v6)) * v7,a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(13331(a,1),18872(a,1,2,2,1))].">
      <j1 rule="para" parents="13331 18872"/>
    </justification>
  </clause>

  <clause id="18895">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(18067(a,1),18894(a,1,2,2,1))].">
      <j1 rule="para" parents="18067 18894"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (a(v7,v5,K(v6,w)) * u)))
    ]]></literal>
    <justification jstring="[para(16250(a,1),18895(a,2,2,2,2))].">
      <j1 rule="para" parents="16250 18895"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,16998,a(flip),b,18896,a),flip(a)].">
      <j1 rule="hyper" parents="64 16998 18896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(12701(a,1),18898(a,1,2,2,2))].">
      <j1 rule="para" parents="12701 18898"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      K(x,K(y,z)) \ (((u * w) * v5) / (K(x,K(y,z)) \ (w * v5))) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(16343,a,18887,a)].">
      <j1 rule="hyper" parents="16343 18887"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * a(y \ ((y \ 1) \ z),u,u \ 1)) = K(x,y * L((z / (y \ 1)) / y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,17349,a(flip),b,18893,a)].">
      <j1 rule="hyper" parents="64 17349 18893"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * a(y \ ((y \ 1) \ z),u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,18871,a(flip),b,18902,a),flip(a)].">
      <j1 rule="hyper" parents="319 18871 18902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = ((x * y) * v5) / (y * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16400,a(flip),b,18901,a),flip(a)].">
      <j1 rule="hyper" parents="64 16400 18901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,20,a,b,18904,a),flip(a)].">
      <j1 rule="hyper" parents="319 20 18904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(16371(a,1),18906(a,1,2))].">
      <j1 rule="para" parents="16371 18906"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(4644(a,1),18907(a,1,3))].">
      <j1 rule="para" parents="4644 18907"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      R(x,y,z \ K(u,T(w,v5))) = R(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(14244(a,1),18907(a,1,3))].">
      <j1 rule="para" parents="14244 18907"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      R(x,y,z \ (u \ K(w,K(v5,v6)))) = R(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(16337(a,1),18907(a,1,3))].">
      <j1 rule="para" parents="16337 18907"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      R(x,y,z \ ((u \ T(K(w,v5),v6)) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ T(K(w,v5),v6)) \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(12444(a,1),18908(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12444 18908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      R(x,y,(z * u) \ (K(w,v5) \ (u * z))) = R(x,y,K(z,u) \ K(v5,w))
    ]]></literal>
    <justification jstring="[para(18057(a,1),18910(a,1,3))].">
      <j1 rule="para" parents="18057 18910"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      R(x,y,K(x,y) \ K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(18913(a,1),521(a,1,1))].">
      <j1 rule="para" parents="18913 521"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      R(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(11695(a,1),18914(a,1,1))].">
      <j1 rule="para" parents="11695 18914"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(13256(a,1),18915(a,1,1))].">
      <j1 rule="para" parents="13256 18915"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      (x * y) \ (K(z,u) \ (y * x)) = y \ T(K(z,u) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(16456,a,18916,a),flip(a)].">
      <j1 rule="hyper" parents="16456 18916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      x * ((y * x) \ (K(z,u) \ (x * y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u) \ x,y) = w
    ]]></literal>
    <justification jstring="[para(18917(a,2),260(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18917 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ T(z,u) = (z \ T(K(x,y) \ z,u)) * z
    ]]></literal>
    <justification jstring="[para(18917(a,1),18149(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18917 18149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18920">
    <literal><![CDATA[
      K(x,y) \ (y * K(z,T(u,y \ x))) = T(K(u,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(18918,a,18061,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18918 18061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x \ y)) = T(K(u,z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4328,a,18920,a)].">
      <j1 rule="hyper" parents="4328 18920"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y \ x)) = T(K(u,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(7151(a,1),18921(a,1,2))].">
      <j1 rule="para" parents="7151 18921"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      K(x,T(K(y,z) \ u,w)) = K(x,K(y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(18921(a,1),15034(a,1,2))].">
      <j1 rule="para" parents="18921 15034"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      T(K(x,T(y,z \ u)) \ u,z) = T(u,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6851(a,1),18922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6851 18922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      T(x,T(K(y,z) \ u,w)) = T(x,K(y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,18923,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 18923 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      T(K(x,T(y,(((z / u) \ 1) * z) \ z)) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(10940(a,1),18924(a,1,1,1,2,2))].">
      <j1 rule="para" parents="10940 18924"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      T(T(x,K(y,z) \ T(x,u)),x \ T(K(y,z) \ x,u)) = (x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(18925(a,1),11387(a,1,1))].">
      <j1 rule="para" parents="18925 11387"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      R(x,y,z \ ((u \ T(K(w,v5),v6)) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(14706(a,1),18912(a,2,3,2))].">
      <j1 rule="para" parents="14706 18912"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,T(v5,v6))) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(6099(a,2),18928(a,1,3,2,1,2))].">
      <j1 rule="para" parents="6099 18928"/>
    </justification>
  </clause>

  <clause id="18930">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,T(v5,v6))) \ K(w,T(v5,u)))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(6099(a,2),18929(a,1,3,2,2))].">
      <j1 rule="para" parents="6099 18929"/>
    </justification>
  </clause>

  <clause id="18931">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(T(v5,v6),u)))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(15556(a,1),18930(a,1,3,2))].">
      <j1 rule="para" parents="15556 18930"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ ((u \ 1) \ K(w,K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(15586(a,1),18931(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="15586 18931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ ((u \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,18911,a(flip),b,18932,a),flip(a)].">
      <j1 rule="hyper" parents="319 18911 18932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ T(u,1))
    ]]></literal>
    <justification jstring="[hyper(319,a,11539,a(flip),b,18933,a),flip(a)].">
      <j1 rule="hyper" parents="319 11539 18933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(208(a,1),18935(a,2,3,2))].">
      <j1 rule="para" parents="208 18935"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      R(x,y,z \ T(T(u,K(w,v5)) \ v6,K(w,T(v5,u)))) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,12446,a,b,18936,a)].">
      <j1 rule="hyper" parents="64 12446 18936"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,18908,a(flip),b,18937,a)].">
      <j1 rule="hyper" parents="64 18908 18937"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18756,a(flip),b,18939,a),flip(a)].">
      <j1 rule="hyper" parents="64 18756 18939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,K(v5,v6)),w)) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13115,a,b,18941,a)].">
      <j1 rule="hyper" parents="64 13115 18941"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * (v5 \ T(v6,z))) = R(x,y,v5 \ T(v6,K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(16335(a,1),18943(a,1,3))].">
      <j1 rule="para" parents="16335 18943"/>
    </justification>
  </clause>

  <clause id="18945">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5) * v6)) = R(x,y,z \ T(u,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,18907,a(flip),b,18944,a),flip(a)].">
      <j1 rule="hyper" parents="64 18907 18944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,w)) \ T(u,w)) = K(x,z * (y \ T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(18945(a,1),16864(a,1,2,1))].">
      <j1 rule="para" parents="18945 16864"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(517(a,1),18947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="517 18947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <literal><![CDATA[
      T(T(x,K(y,z) \ x),x \ T(K(y,z) \ x,u)) = (x \ T(x * K(z,y),u)) \ T(K(y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(6595(a,1),18927(a,1,1))].">
      <j1 rule="para" parents="6595 18927"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(z,y)),x \ T(K(z,y) \ x,u))
    ]]></literal>
    <justification jstring="[para(11400(a,1),18950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11400 18950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(z,y)),K(z,y) \ K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,18041,a(flip),b,18952,a),flip(a)].">
      <j1 rule="hyper" parents="319 18041 18952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(z,y) \ 1),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,6600,a(flip),b,18953,a),flip(a)].">
      <j1 rule="hyper" parents="319 6600 18953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18956">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = T(T(x,K(y,z)),K(z,y))
    ]]></literal>
    <justification jstring="[para(4213(a,1),18954(a,2,1,2))].">
      <j1 rule="para" parents="4213 18954"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      (x \ T(x * K(y,z),u)) \ T(K(z,y) \ x,u) = x
    ]]></literal>
    <justification jstring="[hyper(319,a,6074,a(flip),b,18956,a),flip(a)].">
      <j1 rule="hyper" parents="319 6074 18956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      (x * T(K(y,z) \ x,u)) / x = (x \ T(K(y,z) \ x,u)) * x
    ]]></literal>
    <justification jstring="[para(18957(a,1),11388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18957 11388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      (x \ T(K(y,z) \ x,u)) * x = T(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11396,a(flip),b,18959,a),flip(a)].">
      <j1 rule="hyper" parents="64 11396 18959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ T(z,u) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18919,a,b,18960,a)].">
      <j1 rule="hyper" parents="64 18919 18960"/>
    </justification>
  </clause>

  <clause id="18962">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ T(u,z) = T(u * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7151(a,1),18961(a,1,1))].">
      <j1 rule="para" parents="7151 18961"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(u,z \ u) = T(u * K(y,x),z \ u)
    ]]></literal>
    <justification jstring="[para(14193(a,1),18961(a,1,1))].">
      <j1 rule="para" parents="14193 18961"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      K(x,T(y,L(T(z,z \ 1),z \ 1,u))) \ T(u,u * (z \ 1)) = T(u * K(y,x),u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(380(a,2),18962(a,1,1,2,2))].">
      <j1 rule="para" parents="380 18962"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      K(x,T(y,L(z,z \ 1,u))) \ T(u,u * (z \ 1)) = T(u * K(y,x),u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3970(a,1),18964(a,1,1,2))].">
      <j1 rule="para" parents="3970 18964"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(u,u * (z \ 1)) = T(u * K(y,x),u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(9574(a,1),18965(a,1,1,2))].">
      <j1 rule="para" parents="9574 18965"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      T(x * K(y,z),x * (u \ 1)) = K(z,T(y,u)) \ T(x,u \ x)
    ]]></literal>
    <justification jstring="[para(1453(a,1),18966(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1453 18966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      T(x * K(y,z),x * (u \ 1)) = T(x * K(y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(319,a,18963,a(flip),b,18967,a),flip(a)].">
      <j1 rule="hyper" parents="319 18963 18967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      x / K(y,L(z,(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(10096(a,1),18688(a,1,2))].">
      <j1 rule="para" parents="10096 18688"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(11794(a,1),18971(a,1,2,2))].">
      <j1 rule="para" parents="11794 18971"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,T(y,u)) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(16262(a,1),18972(a,1,2))].">
      <j1 rule="para" parents="16262 18972"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,y) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18806(a,1),18973(a,1,2,2))].">
      <j1 rule="para" parents="18806 18973"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (u \ T(z,y)))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(17536(a,1),18974(a,1,2))].">
      <j1 rule="para" parents="17536 18974"/>
    </justification>
  </clause>

  <clause id="18976">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(16678(a,1),18975(a,1,2))].">
      <j1 rule="para" parents="16678 18975"/>
    </justification>
  </clause>

  <clause id="18977">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(13172(a,1),18976(a,1,2))].">
      <j1 rule="para" parents="13172 18976"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      (x / (((y / z) \ 1) * K(u,y))) * ((y / z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(18977(a,1),12428(a,1))].">
      <j1 rule="para" parents="18977 12428"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      (x / ((y / z) \ 1)) * ((y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(17400(a,1),18979(a,1))].">
      <j1 rule="para" parents="17400 18979"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((u * (K(x,K(y,z)) * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16329(a,2),16146(a,1,1))].">
      <j1 rule="para" parents="16329 16146"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * (K(u,K(w,v5)) * ((v6 * z) / v6)))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(16307(a,1),16377(a,1,2,2,2))].">
      <j1 rule="para" parents="16307 16377"/>
    </justification>
  </clause>

  <clause id="18983">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((K(x,K(y,z)) \ (u * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16329(a,2),18981(a,1,2,1))].">
      <j1 rule="para" parents="16329 18981"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * ((v6 * z) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[hyper(16333,a,18982,a)].">
      <j1 rule="hyper" parents="16333 18982"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13586,a(flip),b,18984,a)].">
      <j1 rule="hyper" parents="64 13586 18984"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ (K(x,K(y,z)) \ ((u * w) * v5)) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16099(a,2),18983(a,1,2))].">
      <j1 rule="para" parents="16099 18983"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = (x * (w * v5)) \ ((x * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16304,a(flip),b,18986,a),flip(a)].">
      <j1 rule="hyper" parents="64 16304 18986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,14,a,b,18987,a),flip(a)].">
      <j1 rule="hyper" parents="319 14 18987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      a(x,K(K(y,z),u) \ w,L(v5,w,K(u,K(y,z)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(4356(a,2),18989(a,1,2))].">
      <j1 rule="para" parents="4356 18989"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) \ w,L(v5,w,K(u,K(y,z)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(6705(a,1),18990(a,1,2,1))].">
      <j1 rule="para" parents="6705 18990"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) \ w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(16129(a,1),18991(a,1,3))].">
      <j1 rule="para" parents="16129 18991"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      a(x,T(y,K(z,u)) \ w,v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(4285(a,1),18992(a,1,2))].">
      <j1 rule="para" parents="4285 18992"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(14243(a,1),18992(a,1,2))].">
      <j1 rule="para" parents="14243 18992"/>
    </justification>
  </clause>

  <clause id="18995">
    <literal><![CDATA[
      a(x,y \ T(z,K(u,w)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(14316(a,1),18992(a,1,2))].">
      <j1 rule="para" parents="14316 18992"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ w,v5) = a(x,K(y,z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(16394(a,1),18992(a,1,2))].">
      <j1 rule="para" parents="16394 18992"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      a(x,y \ (K(z,K(u,w)) \ v5),v6) = a(x,y \ v5,v6)
    ]]></literal>
    <justification jstring="[para(16404(a,1),18992(a,1,2))].">
      <j1 rule="para" parents="16404 18992"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w)) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(17449,a,18994,a)].">
      <j1 rule="hyper" parents="17449 18994"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      a(x,y \ (z * T(u,K(w,v5))),v6) = a(x,y \ (z * u),v6)
    ]]></literal>
    <justification jstring="[para(16300(a,1),18994(a,1,2))].">
      <j1 rule="para" parents="16300 18994"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      a(x,y,T(z,T(u,w))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6404(a,1),18998(a,1,3))].">
      <j1 rule="para" parents="6404 18998"/>
    </justification>
  </clause>

  <clause id="19001">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(319,a,13028,a(flip),b,19000,a),flip(a)].">
      <j1 rule="hyper" parents="319 13028 19000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9251(a,1),19001(a,1,3))].">
      <j1 rule="para" parents="9251 19001"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(19002(a,1),18538(a,1,1))].">
      <j1 rule="para" parents="19002 18538"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ ((w / u) \ v5)),x) = a(x,w \ (u * ((K(z,y) \ u) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17426,a(flip),b,18993,a)].">
      <j1 rule="hyper" parents="64 17426 18993"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ w),x) = a(x,u \ (K(y,z) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11440,a(flip),b,18993,a)].">
      <j1 rule="hyper" parents="64 11440 18993"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),v5) = a(x,y \ (w * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(5173(a,1),18995(a,1,2,2))].">
      <j1 rule="para" parents="5173 18995"/>
    </justification>
  </clause>

  <clause id="19007">
    <literal><![CDATA[
      a(x,y \ T(z,T(u,w)),v5) = a(x,y \ T(z,u),v5)
    ]]></literal>
    <justification jstring="[para(6386(a,1),18995(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6386 18995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19008">
    <literal><![CDATA[
      a(x,K(y,z) \ u,w) = a(x,u * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(6806(a,1),18995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6806 18995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ (u * (w / u)),x) = a(x,K(y,z) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,16724,a,b,19008,a)].">
      <j1 rule="hyper" parents="319 16724 19008"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      a(x,y \ (T(z,K(u,w)) \ v5),v6) = a(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(4285(a,1),18997(a,1,2,2))].">
      <j1 rule="para" parents="4285 18997"/>
    </justification>
  </clause>

  <clause id="19011">
    <literal><![CDATA[
      a(x,T(y \ z,u) \ T(w,z \ y),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11503,a(flip),b,19007,a),flip(a)].">
      <j1 rule="hyper" parents="64 11503 19007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,w) \ v5)),v6) = a(x,y \ (z * (v5 * K(w,u))),v6)
    ]]></literal>
    <justification jstring="[para(5173(a,1),18999(a,1,2,2,2))].">
      <j1 rule="para" parents="5173 18999"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      a(x,y \ (T(z,T(u,w)) \ v5),v6) = a(x,y \ (T(z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(6386(a,1),19010(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6386 19010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      a(x,K(y,z) \ (u * (w / u)),x) = a(x,K(y,z) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18996,a(flip),b,19009,a)].">
      <j1 rule="hyper" parents="64 18996 19009"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      a(x,K(y,z) \ T(u,w),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11506,a(flip),b,19014,a),flip(a)].">
      <j1 rule="hyper" parents="64 11506 19014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ T(y * T(w,v5),y)),x) = a(x,K(z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11508,a,b,19016,a)].">
      <j1 rule="hyper" parents="64 11508 19016"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      a(x,y \ (T(z,z \ u) \ w),v5) = a(x,y \ (((z \ u) \ u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(3124(a,1),19013(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3124 19013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),19003(a,1,2,2,2))].">
      <j1 rule="para" parents="109 19003"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),19019(a,1,2))].">
      <j1 rule="para" parents="109 19019"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,L(v5,w,u) * (w * u)))
    ]]></literal>
    <justification jstring="[para(19020(a,1),18460(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19020 18460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      a(x,y \ ((z * u) * K(w,v5)),x) = a(x,y \ (z * (K(v5,w) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,18087,a,b,19012,a)].">
      <j1 rule="hyper" parents="319 18087 19012"/>
    </justification>
  </clause>

  <clause id="19024">
    <literal><![CDATA[
      a(x,T(y,z) \ T(y * T(u,w),y),x) = a(x,K(y \ 1,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(17441,a,19017,a)].">
      <j1 rule="hyper" parents="17441 19017"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ (z \ u)),w) = a(x,y \ (((z \ 1) \ 1) \ u),w)
    ]]></literal>
    <justification jstring="[para(4423(a,2),19018(a,1,2,2))].">
      <j1 rule="para" parents="4423 19018"/>
    </justification>
  </clause>

  <clause id="19026">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ (w * v5)),x) = a(x,y \ (w * (K(z,u) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19006,a,b,19023,a)].">
      <j1 rule="hyper" parents="64 19006 19023"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ u,x) = a(x,K(y,z) \ T(u,w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11509,a(flip),b,19024,a),flip(a)].">
      <j1 rule="hyper" parents="64 11509 19024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ u,x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19016,a(flip),b,19027,a),flip(a)].">
      <j1 rule="hyper" parents="319 19016 19027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      a(x,T(T(y \ (y / z),u),z \ 1) * w,x) = a(x,K(z,u) \ ((y \ (y / z)) * w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17480,a(flip),b,19028,a)].">
      <j1 rule="hyper" parents="64 17480 19028"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) \ 1) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11501,a(flip),b,19025,a),flip(a)].">
      <j1 rule="hyper" parents="64 11501 19025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ ((w / u) \ v5)),x) = a(x,w \ (K(y,z) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,18088,a(flip),b,19004,a),flip(a)].">
      <j1 rule="hyper" parents="319 18088 19004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ ((w / y) \ v5)),x) = a(x,w \ (K(z,u) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19005,a(flip),b,19033,a)].">
      <j1 rule="hyper" parents="64 19005 19033"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ ((x \ u) \ w)),x) = a(x,u \ (K(y,z) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18535,a(flip),b,19035,a)].">
      <j1 rule="hyper" parents="64 18535 19035"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,(v5 * w) * u))
    ]]></literal>
    <justification jstring="[para(18191(a,1),19021(a,2,2,2))].">
      <j1 rule="para" parents="18191 19021"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,18464,a(flip),b,19037,a),flip(a)].">
      <j1 rule="hyper" parents="319 18464 19037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18395,a(flip),b,19038,a),flip(a)].">
      <j1 rule="hyper" parents="64 18395 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      a(x,T(T(y \ (y / z),u),z \ 1) * w,x) = a(x,(y \ (y / T(z,u))) * w,x)
    ]]></literal>
    <justification jstring="[para(10255(a,1),19029(a,2,2))].">
      <j1 rule="para" parents="10255 19029"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      a(x,T(y \ (y / z),u) * w,x) = a(x,(y \ (y / T(z,u))) * w,x)
    ]]></literal>
    <justification jstring="[para(5053(a,1),19041(a,1,2,1))].">
      <j1 rule="para" parents="5053 19041"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      a(x,(y \ (y / T(z \ u,w))) * T(y,u \ z),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18644,a(flip),b,19042,a),flip(a)].">
      <j1 rule="hyper" parents="64 18644 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      a(x,y \ ((y / T(z \ u,w)) * T(y,u \ z)),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11518,a,b,19043,a)].">
      <j1 rule="hyper" parents="64 11518 19043"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      a(x,K(y \ z,u) \ (u / T(z \ y,w)),x) = a(x,K(w,y \ (z * 1)) \ (u / (z \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(11307,a,19044,a)].">
      <j1 rule="hyper" parents="11307 19044"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(w,z \ u) / T(u \ z,y),x)
    ]]></literal>
    <justification jstring="[para(12115(a,1),19045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12115 19045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ T(w,z \ u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,10963,a(flip),b,19046,a),flip(a)].">
      <j1 rule="hyper" parents="319 10963 19046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19011,a(flip),b,19047,a),flip(a)].">
      <j1 rule="hyper" parents="319 19011 19047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19049">
    <literal><![CDATA[
      a(x,K(y,z \ u) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ w,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),19048(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 19048"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      a(x,(y \ z) \ (K(u,z \ y) \ w),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11436,a,b,19049,a)].">
      <j1 rule="hyper" parents="64 11436 19049"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,T(z \ y,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11425,a(flip),b,19050,a)].">
      <j1 rule="hyper" parents="64 11425 19050"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,(z \ y) \ T(w,u),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,18884,a(flip),b,19051,a),flip(a)].">
      <j1 rule="hyper" parents="319 18884 19051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19053">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,y \ (z * T(w,u)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11425,a(flip),b,19052,a),flip(a)].">
      <j1 rule="hyper" parents="319 11425 19052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      a(x,y \ (K(z,y \ u) \ (u * w)),x) = a(x,y \ (u * T(w,z)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19026,a,b,19053,a)].">
      <j1 rule="hyper" parents="64 19026 19053"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      L(K(x,K(y,x \ z) \ (z * u)),w,v5) \ L(K(x,x \ (K(y,x \ z) \ (z * u))),w,v5) = a(x,x \ (z * T(u,y)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11351,a,b,19054,a)].">
      <j1 rule="hyper" parents="64 11351 19054"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      K(x,L(T(1 / y,y * T(z,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(14166(a,1),16974(a,1,2,1,1))].">
      <j1 rule="para" parents="14166 16974"/>
    </justification>
  </clause>

  <clause id="19057">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(9411(a,2),19056(a,1,2,1,1))].">
      <j1 rule="para" parents="9411 19056"/>
    </justification>
  </clause>

  <clause id="19058">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(y \ K(z,u)) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(18809(a,1),19057(a,1,2))].">
      <j1 rule="para" parents="18809 19057"/>
    </justification>
  </clause>

  <clause id="19059">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,y * z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18814,a(flip),b,19058,a)].">
      <j1 rule="hyper" parents="64 18814 19058"/>
    </justification>
  </clause>

  <clause id="19061">
    <literal><![CDATA[
      K(x,L(T(1 / y,z * y) \ u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18823,a(flip),b,19059,a)].">
      <j1 rule="hyper" parents="64 18823 19059"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13683,a,19061,a)].">
      <j1 rule="hyper" parents="13683 19061"/>
    </justification>
  </clause>

  <clause id="19064">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(3327(a,1),19062(a,1,2,1,1))].">
      <j1 rule="para" parents="3327 19062"/>
    </justification>
  </clause>

  <clause id="19065">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(11337,a,19064,a)].">
      <j1 rule="hyper" parents="11337 19064"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,K(z,w) * (z \ (((K(z,w) / y) \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17649,a(flip),b,19065,a),flip(a)].">
      <j1 rule="hyper" parents="319 17649 19065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19067">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,T(z,w) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13458,a(flip),b,19066,a),flip(a)].">
      <j1 rule="hyper" parents="319 13458 19066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19068">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((K(z,w) / y) \ T(z,w)) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,18729,a(flip),b,19067,a),flip(a)].">
      <j1 rule="hyper" parents="319 18729 19067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(12064(a,1),19068(a,2,2,2,1))].">
      <j1 rule="para" parents="12064 19068"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13829,a(flip),b,19069,a),flip(a)].">
      <j1 rule="hyper" parents="319 13829 19069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17497,a(flip),b,19070,a)].">
      <j1 rule="hyper" parents="64 17497 19070"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ (T(y * z,z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11245,a(flip),b,19071,a)].">
      <j1 rule="hyper" parents="64 11245 19071"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17115,a(flip),b,19072,a)].">
      <j1 rule="hyper" parents="64 17115 19072"/>
    </justification>
  </clause>

  <clause id="19074">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,K(w,v5) * v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(17643(a,1),17395(a,1,2,2,2))].">
      <j1 rule="para" parents="17643 17395"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18948,a(flip),b,19074,a)].">
      <j1 rule="hyper" parents="64 18948 19074"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (z \ (v5 * (v6 * K(u,w)))))
    ]]></literal>
    <justification jstring="[hyper(64,a,15398,a(flip),b,19075,a),flip(a)].">
      <j1 rule="hyper" parents="64 15398 19075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * z) / (K(x,y) * z),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8220(a,1),17896(a,2,1))].">
      <j1 rule="para" parents="8220 17896"/>
    </justification>
  </clause>

  <clause id="19080">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * z) / (K(x,y) * z),K(z,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,6791,a,b,19079,a),flip(a)].">
      <j1 rule="hyper" parents="319 6791 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = (u * z) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(319,a,14161,a(flip),b,19080,a),flip(a)].">
      <j1 rule="hyper" parents="319 14161 19080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (T(x,K(y,z)) * K(z,y))) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6757(a,1),19081(a,1,1))].">
      <j1 rule="para" parents="6757 19081"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (K(z,y) * x)) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6052(a,1),19083(a,1,2,1,2))].">
      <j1 rule="para" parents="6052 19083"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(14380,a,19084,a)].">
      <j1 rule="hyper" parents="14380 19084"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(12057(a,1),19085(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12057 19085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      (K(x,L(y,z * (K(u,w) * v5),v5)) * (z * (K(u,w) * v5))) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(19085(a,1),12903(a,2,2))].">
      <j1 rule="para" parents="19085 12903"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (K(w,v5) * z))) / z = K(x,y) * ((u * z) / (K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(17793(a,1),19087(a,1,1,1))].">
      <j1 rule="para" parents="17793 19087"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (K(w,v5) * u))) / u = K(x,y) * ((z * u) / (K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(12733(a,1),19088(a,1,1,1))].">
      <j1 rule="para" parents="12733 19088"/>
    </justification>
  </clause>

  <clause id="19091">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(17534(a,1),19089(a,1,1))].">
      <j1 rule="para" parents="17534 19089"/>
    </justification>
  </clause>

  <clause id="19092">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(w,v5) * u) = K(x,y) * ((z * u) / (K(w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19085,a(flip),b,19091,a)].">
      <j1 rule="hyper" parents="64 19085 19091"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      K(x,y) * (((z * K(u,w)) * v5) / (K(u,w) * v5)) = L(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16763,a(flip),b,19092,a),flip(a)].">
      <j1 rule="hyper" parents="64 16763 19092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19094">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * R(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),19093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 19093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19095">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(15706(a,1),19094(a,2,2))].">
      <j1 rule="para" parents="15706 19094"/>
    </justification>
  </clause>

  <clause id="19096">
    <literal><![CDATA[
      L(K(x,y) * (K(y,x) * z),K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,15720,a(flip),b,19095,a),flip(a)].">
      <j1 rule="hyper" parents="319 15720 19095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(4363(a,1),19096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 19096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19098">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(12116(a,1),19097(a,1,1,2))].">
      <j1 rule="para" parents="12116 19097"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,18002,a(flip),b,19098,a),flip(a)].">
      <j1 rule="hyper" parents="319 18002 19098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19100">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(319,a,17390,a(flip),b,19099,a),flip(a)].">
      <j1 rule="hyper" parents="319 17390 19099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((z / y) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(17816(a,1),16657(a,1,1,3))].">
      <j1 rule="para" parents="17816 16657"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((y \ z) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(17545(a,1),19101(a,1,1))].">
      <j1 rule="para" parents="17545 19101"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,((K(u,w) * y) * x) / (u \ w)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(17783(a,1),19102(a,1,1))].">
      <j1 rule="para" parents="17783 19102"/>
    </justification>
  </clause>

  <clause id="19104">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) * ((u \ w) \ K(u,w))) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(17154(a,1),19103(a,1,2))].">
      <j1 rule="para" parents="17154 19103"/>
    </justification>
  </clause>

  <clause id="19106">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (T(u,w) \ w)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(12182(a,1),19104(a,1,2))].">
      <j1 rule="para" parents="12182 19104"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(17850(a,1),19106(a,1,2))].">
      <j1 rule="para" parents="17850 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y * (((u \ w) / x) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16352,a(flip),b,19107,a),flip(a)].">
      <j1 rule="hyper" parents="319 16352 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19109">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((T(u,w) \ w) / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,18598,a(flip),b,19108,a),flip(a)].">
      <j1 rule="hyper" parents="319 18598 19108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((w / u) / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,18225,a(flip),b,19109,a),flip(a)].">
      <j1 rule="hyper" parents="319 18225 19109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      T(K(x,L(T(y,y * z),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(3327(a,1),18625(a,1,1,2,1))].">
      <j1 rule="para" parents="3327 18625"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      T(K(x,L(T(y,z),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(7859(a,1),19111(a,1,1))].">
      <j1 rule="para" parents="7859 19111"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14127,a,19112,a),flip(a)].">
      <j1 rule="hyper" parents="14127 19112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      K(x,(y \ T(z,u)) \ (y \ (z * u))) = K(x,L(T(u,z),z,y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),19113(a,1,2,1,2))].">
      <j1 rule="para" parents="22 19113"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      T(K(x,T(y,T(1 \ (z / u),z))) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7556(a,1),18926(a,1,1,1,2))].">
      <j1 rule="para" parents="7556 18926"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      T(K(x,T(y,T(z / u,z))) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(66(a,1),19116(a,1,1,1,2,2,1))].">
      <j1 rule="para" parents="66 19116"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      T(K(x,T(y,z \ u)) \ (z * (u / z)),((z \ u) \ 1) * u) = T(z * (u / z),((z \ u) \ 1) * u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5705(a,1),19117(a,1,1,1,2))].">
      <j1 rule="para" parents="5705 19117"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      T(x * ((y * K(z,u)) / x),((x \ y) \ 1) * y) = T(x * (y / x),((x \ y) \ 1) * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(18183(a,1),19118(a,1,1))].">
      <j1 rule="para" parents="18183 19118"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      T(x * ((y * K(z,u)) / x),y * ((y / x) \ 1)) = T(x * (y / x),((x \ y) \ 1) * y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9254,a(flip),b,19119,a)].">
      <j1 rule="hyper" parents="64 9254 19119"/>
    </justification>
  </clause>

  <clause id="19121">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),y * ((y / x) \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3795,a(flip),b,19120,a),flip(a)].">
      <j1 rule="hyper" parents="64 3795 19120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),(y / x) \ y) / x)
    ]]></literal>
    <justification jstring="[para(18970(a,1),19121(a,2,2,1))].">
      <j1 rule="para" parents="18970 19121"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),19122(a,2,2,1,2))].">
      <j1 rule="para" parents="81 19122"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      T(x * (y / x),y * ((y / x) \ 1)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(9254(a,1),19123(a,1,1))].">
      <j1 rule="para" parents="9254 19123"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      (x * (T(y,y * ((y / x) \ 1)) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(3795(a,1),19124(a,1,1))].">
      <j1 rule="para" parents="3795 19124"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      (x * (T(y,(y / x) \ y) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(1453(a,1),19125(a,1,1,2,1))].">
      <j1 rule="para" parents="1453 19125"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      (x * (T(y,x) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(81(a,1),19126(a,1,1,2,1,2))].">
      <j1 rule="para" parents="81 19126"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      (x * (T((y * z) * K(z,u),x) / x)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(19127(a,1),13393(a,1,1))].">
      <j1 rule="para" parents="19127 13393"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      (x * (T(y * T(z,u),x) / x)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(4922(a,1),19128(a,1,1,2,1,1))].">
      <j1 rule="para" parents="4922 19128"/>
    </justification>
  </clause>

  <clause id="19130">
    <literal><![CDATA[
      (x * T(y,z)) \ (u * (T(x * T(y,z),u) / u)) = a(u,u \ (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14697,a(flip),b,19129,a)].">
      <j1 rule="hyper" parents="64 14697 19129"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(8712,a,19130,a)].">
      <j1 rule="hyper" parents="8712 19130"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,18530,a,b,19131,a),flip(a)].">
      <j1 rule="hyper" parents="319 18530 19131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      a(x,x \ (1 \ (y * z)),x) = a(x,x \ (z * T(y,u)),x)
    ]]></literal>
    <justification jstring="[para(66(a,2),19132(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="66 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) \ z),x) = a(x,x \ (z * T(y,u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11357,a,b,19133,a)].">
      <j1 rule="hyper" parents="64 11357 19133"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) \ z),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19131,a(flip),b,19134,a),flip(a)].">
      <j1 rule="hyper" parents="319 19131 19134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      a(x,x \ (y * (z \ 1)),x) = a(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19030,a(flip),b,19135,a),flip(a)].">
      <j1 rule="hyper" parents="64 19030 19135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) * z),x) = a(x,x \ (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18530,a,b,19136,a)].">
      <j1 rule="hyper" parents="64 18530 19136"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      a(x,x \ (((T(y,z) \ 1) \ 1) * ((y \ 1) * u)),x) = a(x,x \ (K(z,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(9856(a,1),19137(a,2,2,2))].">
      <j1 rule="para" parents="9856 19137"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      a(x,x \ (T(y,z) * ((1 / y) * u)),x) = a(x,x \ (K(z,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(9698(a,1),19138(a,1,2,2))].">
      <j1 rule="para" parents="9698 19138"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      T(x,((y * K(z,L(u,w,v5))) * v6) / a(K(z,L(u,w,v5)),T(y,K(z,u)),v6)) = T(x,K(z,u) * (T(y,K(z,L(u,w,v5))) * v6))
    ]]></literal>
    <justification jstring="[para(16088(a,1),16484(a,1,2,2,2))].">
      <j1 rule="para" parents="16088 16484"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      T(x,((y * K(z,L(u,w,v5))) * v6) / a(z,T(y,K(z,u)),K(v6,L(u,w,v5)))) = T(x,K(z,u) * (T(y,K(z,L(u,w,v5))) * v6))
    ]]></literal>
    <justification jstring="[para(12521(a,1),19140(a,1,2,2))].">
      <j1 rule="para" parents="12521 19140"/>
    </justification>
  </clause>

  <clause id="19143">
    <literal><![CDATA[
      T(x,((y * K(z,L(u,w,v5))) * v6) / a(z,y,K(v6,L(u,w,v5)))) = T(x,K(z,u) * (T(y,K(z,L(u,w,v5))) * v6))
    ]]></literal>
    <justification jstring="[para(17785(a,1),19141(a,1,2,2))].">
      <j1 rule="para" parents="17785 19141"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      T(x,a(L(y,z,u),w,K(v5,v6)) * ((w * K(v6,L(y,z,u))) * v5)) = T(x,K(v6,y) * (T(w,K(v6,L(y,z,u))) * v5))
    ]]></literal>
    <justification jstring="[para(16250(a,1),19143(a,1,2))].">
      <j1 rule="para" parents="16250 19143"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u,K(y,L(z,w,v5))) * v6)) = T(x,(u * K(y,L(z,w,v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,16464,a(flip),b,19144,a),flip(a)].">
      <j1 rule="hyper" parents="64 16464 19144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19148">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u,K(y,L(z,w,v5))) * v6)) = T(x,u * (K(y,L(z,w,v5)) * v6))
    ]]></literal>
    <justification jstring="[hyper(319,a,16600,a(flip),b,19146,a),flip(a)].">
      <j1 rule="hyper" parents="319 16600 19146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19149">
    <literal><![CDATA[
      T(x,y * (K(z,L(u,w,v5)) * v6)) = T(x,K(z,u) * (y * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,14637,a(flip),b,19148,a),flip(a)].">
      <j1 rule="hyper" parents="64 14637 19148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19151">
    <literal><![CDATA[
      T(x,((K(y,z) * u) * w) * v5) = T(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16604,a(flip),b,19149,a)].">
      <j1 rule="hyper" parents="64 16604 19149"/>
    </justification>
  </clause>

  <clause id="19153">
    <literal><![CDATA[
      T(x,K(y * z,y) * ((u * T(y,z)) * w)) = T(x,(u * R(y,z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16609,a(flip),b,19151,a),flip(a)].">
      <j1 rule="hyper" parents="64 16609 19151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * T(z,y)) * w)) = T(x,(u * R(z,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(14903,a,19153,a)].">
      <j1 rule="hyper" parents="14903 19153"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,(T(v5,y * T(T(z,u),w)) * (y * T(z,u))) * K(z,w))
    ]]></literal>
    <justification jstring="[para(4022(a,2),16610(a,1,2,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4022 16610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,T(v5,y * T(T(z,u),w)) * ((y * T(z,u)) * K(z,w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16468,a(flip),b,19155,a),flip(a)].">
      <j1 rule="hyper" parents="319 16468 19155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19157">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,T(v5,y * T(T(z,u),w)) * (y * (K(z,u) * T(z,w))))
    ]]></literal>
    <justification jstring="[para(9659(a,1),19156(a,2,2,2))].">
      <j1 rule="para" parents="9659 19156"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,T(v5,y * T(T(z,u),w)) * (y * T(T(z,u),w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,17261,a(flip),b,19157,a),flip(a)].">
      <j1 rule="hyper" parents="319 17261 19157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(319,a,9307,a(flip),b,19158,a),flip(a)].">
      <j1 rule="hyper" parents="319 9307 19158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19160">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * T(z,w))) * R(v5,y * T(z,u),K(z,w))) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[para(9659(a,1),19159(a,1,2,1))].">
      <j1 rule="para" parents="9659 19159"/>
    </justification>
  </clause>

  <clause id="19161">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * T(z,w))) * L(v5,y * T(z,u),K(z,w))) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[para(13256(a,1),19160(a,1,2,2))].">
      <j1 rule="para" parents="13256 19160"/>
    </justification>
  </clause>

  <clause id="19162">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * T(z,w))) * v5) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16474,a(flip),b,19161,a)].">
      <j1 rule="hyper" parents="64 16474 19161"/>
    </justification>
  </clause>

  <clause id="19164">
    <literal><![CDATA[
      K(x,(L(T(y,K(z,u)),w,v5) \ v6) * T((v6 \ L(y,w,v5)) * v6,K(z,u))) = K(x,((v6 * (L(T(y,K(z,u)),w,v5) / v6)) \ v6) * L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(3830(a,2),15105(a,1,2,2))].">
      <j1 rule="para" parents="3830 15105"/>
    </justification>
  </clause>

  <clause id="19165">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (T(y,K(z,u)) \ L(y,w,v5)))) = K(x,(y * (v6 \ L(T(y,K(z,u)),w,v5))) / L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(15057,a,18744,a),flip(a)].">
      <j1 rule="hyper" parents="15057 18744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (T(y,K(z,u)) \ L(y,w,v5)))) = K(x,y * ((v6 \ L(T(y,K(z,u)),w,v5)) / L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(319,a,16578,a(flip),b,19165,a),flip(a)].">
      <j1 rule="hyper" parents="319 16578 19165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (y \ L(T(y,K(z,u)),w,v5)))) = K(x,y * ((v6 \ L(T(y,K(z,u)),w,v5)) / L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(16700(a,1),19166(a,1,2,2,2))].">
      <j1 rule="para" parents="16700 19166"/>
    </justification>
  </clause>

  <clause id="19168">
    <literal><![CDATA[
      K(x,y * ((z \ L(T(y,K(u,w)),v5,v6)) / L(y,v5,v6))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(18669,a,19167,a),flip(a)].">
      <j1 rule="hyper" parents="18669 19167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19169">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1327(a,1),19168(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1327 19168"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15427,a(flip),b,19169,a)].">
      <j1 rule="hyper" parents="64 15427 19169"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(T(z,K(u,w)),v5,v6) \ y) * ((y \ L(z,v5,v6)) * y))
    ]]></literal>
    <justification jstring="[hyper(15011,a,19164,a),flip(a)].">
      <j1 rule="hyper" parents="15011 19164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19173">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(T(z,K(u,w)),v5,v6) \ y) * T(L(z,v5,v6),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,14535,a(flip),b,19171,a),flip(a)].">
      <j1 rule="hyper" parents="319 14535 19171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(T(z,K(u,w)),v5,v6) \ y) * L(T(z,y),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),19173(a,2,2,2))].">
      <j1 rule="para" parents="25 19173"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(z,v5,v6) \ y) * L(T(z,y),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(319,a,16381,a(flip),b,19174,a),flip(a)].">
      <j1 rule="hyper" parents="319 16381 19174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(z \ y) * T(z,y))
    ]]></literal>
    <justification jstring="[para(11361(a,1),19175(a,2,2))].">
      <j1 rule="para" parents="11361 19175"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,T(y * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(319,a,9285,a,b,19177,a),flip(a)].">
      <j1 rule="hyper" parents="319 9285 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4130(a,1),19178(a,2,2))].">
      <j1 rule="para" parents="4130 19178"/>
    </justification>
  </clause>

  <clause id="19181">
    <literal><![CDATA[
      K(x,(L(y * (T(z,K(u,w)) / y),v5,v6) \ y) * L(z,v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3937(a,2),19180(a,1,2,1,1))].">
      <j1 rule="para" parents="3937 19180"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      K(x,(L(y * (z / y),u,w) \ y) * L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1327(a,1),19181(a,1,2,1,1,1,2,1))].">
      <j1 rule="para" parents="1327 19181"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * L((w \ y) * w,z,u)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(77(a,1),19182(a,1,2,1,1,1))].">
      <j1 rule="para" parents="77 19182"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((u \ z) * (y / (u \ z)))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(15879(a,1),13223(a,1,2,2,2,2))].">
      <j1 rule="para" parents="15879 13223"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(95(a,1),19184(a,1,2,2))].">
      <j1 rule="para" parents="95 19184"/>
    </justification>
  </clause>

  <clause id="19186">
    <literal><![CDATA[
      K(x,T((y \ z) * u,u) \ L(u / (z \ y),z \ y,z)) = a(x,z,K((((y \ z) * u) \ u) * ((y \ z) * u),y))
    ]]></literal>
    <justification jstring="[hyper(13506,a,19185,a)].">
      <j1 rule="hyper" parents="13506 19185"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[hyper(13547,a,19186,a)].">
      <j1 rule="hyper" parents="13547 19186"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((u \ z) * (y / (u \ z)),z))
    ]]></literal>
    <justification jstring="[para(15879(a,1),19187(a,2,3,1))].">
      <j1 rule="para" parents="15879 19187"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,T(z,u \ z)))
    ]]></literal>
    <justification jstring="[para(9298(a,1),19188(a,2,3))].">
      <j1 rule="para" parents="9298 19188"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,16204,a(flip),b,19189,a),flip(a)].">
      <j1 rule="hyper" parents="319 16204 19189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y / (u \ z))) * K(x,L(y / (u \ z),u \ z,u) / (y * (z \ u))) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16090,a,b,19190,a)].">
      <j1 rule="hyper" parents="64 16090 19190"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      K(x,1) * K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(16875(a,1),19192(a,1,1,2))].">
      <j1 rule="para" parents="16875 19192"/>
    </justification>
  </clause>

  <clause id="19194">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(218,a,19193,a)].">
      <j1 rule="hyper" parents="218 19193"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,L(K(v7,T(z,K(u,w))),v5,v6))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(10096(a,2),16677(a,1,2,3))].">
      <j1 rule="para" parents="10096 16677"/>
    </justification>
  </clause>

  <clause id="19197">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,L(K(v7,z),v5,v6))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(14108(a,1),19196(a,1,2,3,1))].">
      <j1 rule="para" parents="14108 19196"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      L(K(x,y \ (L(T(z,K(u,w)),v5,v6) * v7)),y,L(K(v7,z),v5,v6)) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(10097,a,19197,a)].">
      <j1 rule="hyper" parents="10097 19197"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      L(K(x,y \ (L(z,u,w) * v5)),y,L(K(v5,z),u,w)) = K(x,(K(L(T(z,K(v6,v7)),u,w),v5) \ y) \ (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(16416(a,1),19198(a,1,1))].">
      <j1 rule="para" parents="16416 19198"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      K(x,(K(L(T(y,K(z,u)),w,v5),v6) \ v7) \ (v6 * L(y,w,v5))) = K(x,v7 \ (L(y,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,16155,a(flip),b,19200,a),flip(a)].">
      <j1 rule="hyper" parents="64 16155 19200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19204">
    <literal><![CDATA[
      K(x,(L(K(T(y,K(z,u)),w),v5,v6) \ v7) \ (w * L(y,v5,v6))) = K(x,v7 \ (L(y,v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(10129(a,2),19201(a,1,2,1,1))].">
      <j1 rule="para" parents="10129 19201"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ (z * L(y,u,w))) = K(x,v5 \ (L(y,u,w) * z))
    ]]></literal>
    <justification jstring="[para(1327(a,1),19204(a,1,2,1,1,1,1))].">
      <j1 rule="para" parents="1327 19204"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (z * L(y,w,v5)))) = K(x,u \ (L(y,w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17888,a(flip),b,19205,a)].">
      <j1 rule="hyper" parents="64 17888 19205"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) = K(x,y \ (w * L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(6470,a,19206,a),flip(a)].">
      <j1 rule="hyper" parents="6470 19206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (w * L(x,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(19206(a,1),6470(a,1))].">
      <j1 rule="para" parents="19206 6470"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      L(K(x,(y \ z) \ L(x,u,w)),y \ z,y) = K(x,z \ (L(x,u,w) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,10118,a,b,19207,a)].">
      <j1 rule="hyper" parents="319 10118 19207"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      L(K(x,(y \ z) \ x),y \ z,y) = K(x,z \ (L(x,u,w) * y))
    ]]></literal>
    <justification jstring="[para(12246(a,1),19210(a,1,1))].">
      <j1 rule="para" parents="12246 19210"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) = K(x,y \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10118,a(flip),b,19211,a),flip(a)].">
      <j1 rule="hyper" parents="64 10118 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      K(x,y \ (z * L(x,u,w))) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(19209,a,19212,a)].">
      <j1 rule="hyper" parents="19209 19212"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      K(x,y \ ((z * u) * x)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[para(94(a,1),19214(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="94 19214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19217">
    <literal><![CDATA[
      K(x,y \ (z * ((z \ u) * x))) = K(x,y \ (u * x))
    ]]></literal>
    <justification jstring="[para(437(a,1),19214(a,1,2,2))].">
      <j1 rule="para" parents="437 19214"/>
    </justification>
  </clause>

  <clause id="19219">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * (z * x))) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,17522,a(flip),b,19216,a),flip(a)].">
      <j1 rule="hyper" parents="64 17522 19216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19220">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12508,a(flip),b,19216,a)].">
      <j1 rule="hyper" parents="64 12508 19216"/>
    </justification>
  </clause>

  <clause id="19221">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,(z \ u) * x))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(4790(a,2),19217(a,1,2))].">
      <j1 rule="para" parents="4790 19217"/>
    </justification>
  </clause>

  <clause id="19222">
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(9210,a,19220,a)].">
      <j1 rule="hyper" parents="9210 19220"/>
    </justification>
  </clause>

  <clause id="19223">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,z \ (u * x)))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(11618(a,2),19221(a,1,2,3))].">
      <j1 rule="para" parents="11618 19221"/>
    </justification>
  </clause>

  <clause id="19224">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,u * x))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(10780(a,1),19223(a,1,2))].">
      <j1 rule="para" parents="10780 19223"/>
    </justification>
  </clause>

  <clause id="19225">
    <literal><![CDATA[
      L(K(x,y \ (((z \ u) * x) * z)),y,K(z,u * x)) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(10097,a,19224,a)].">
      <j1 rule="hyper" parents="10097 19224"/>
    </justification>
  </clause>

  <clause id="19226">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * (z * x))),y,K(z,u * x)) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(19222(a,1),19225(a,1,1))].">
      <j1 rule="para" parents="19222 19225"/>
    </justification>
  </clause>

  <clause id="19227">
    <literal><![CDATA[
      L(K(x,y \ (T(z,u) * x)),y,K(u,z * x)) = K(x,(K((u \ z) * x,u) \ y) \ (z * x))
    ]]></literal>
    <justification jstring="[para(19219(a,1),19226(a,1,1))].">
      <j1 rule="para" parents="19219 19226"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      K(x,(K((y \ z) * x,y) \ u) \ (z * x)) = K(x,u \ (T(z,y) * x))
    ]]></literal>
    <justification jstring="[hyper(16227,a,19227,a),flip(a)].">
      <j1 rule="hyper" parents="16227 19227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      K(x,(K(y \ (z * x),y) \ u) \ (z * x)) = K(x,u \ (T(z,y) * x))
    ]]></literal>
    <justification jstring="[para(12433(a,2),19228(a,1,2,1,1))].">
      <j1 rule="para" parents="12433 19228"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ (u * x)) \ (u * x))) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16308,a(flip),b,19230,a)].">
      <j1 rule="hyper" parents="64 16308 19230"/>
    </justification>
  </clause>

  <clause id="19232">
    <literal><![CDATA[
      K(x,y \ ((z \ (u * x)) * z)) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[para(4000(a,1),19231(a,1,2,2))].">
      <j1 rule="para" parents="4000 19231"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      K(x,y \ T(z * x,u)) = K(x,y \ (T(z,u) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11216,a(flip),b,19232,a)].">
      <j1 rule="hyper" parents="64 11216 19232"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      K(x,((y * x) / z) \ (T(y,u) * x)) = K(x,K(u,y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(14420,a,19233,a),flip(a)].">
      <j1 rule="hyper" parents="14420 19233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      K(x,K(y,z * x) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17031,a(flip),b,19234,a),flip(a)].">
      <j1 rule="hyper" parents="64 17031 19234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      K(x,y * K(x * z,u)) = K(x,K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15042,a(flip),b,19235,a)].">
      <j1 rule="hyper" parents="64 15042 19235"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      K(x,K(y,x * z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(14220,a,19237,a)].">
      <j1 rule="hyper" parents="14220 19237"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      K(x,K(y,x * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(19238(a,2),14421(a,1))].">
      <j1 rule="para" parents="19238 14421"/>
    </justification>
  </clause>

  <clause id="19240">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / (x \ 1)) \ u)) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(19239,a,18480,a)].">
      <j1 rule="hyper" parents="19239 18480"/>
    </justification>
  </clause>

  <clause id="19241">
    <literal><![CDATA[
      K(x,(T(y,z) / (x \ 1)) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18144,a(flip),b,19240,a)].">
      <j1 rule="hyper" parents="64 18144 19240"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      K(x,T(x * y,z) \ u) = K(x,T(y,z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7509,a(flip),b,19241,a),flip(a)].">
      <j1 rule="hyper" parents="64 7509 19241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),19242(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 19242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      K(x,T(y,z) \ (y * u)) = K(x,K(z,x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17879,a(flip),b,19243,a),flip(a)].">
      <j1 rule="hyper" parents="64 17879 19243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      K(x,K(y,x \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4284(a,1),19244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4284 19244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19246">
    <literal><![CDATA[
      K(x,y \ (K(z,x \ u) \ w)) = K(x,K(u,z) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17870,a(flip),b,19245,a)].">
      <j1 rule="hyper" parents="64 17870 19245"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      L(K(x,K(y,z) \ (y * u)),w,v5) \ L(K(x,x \ (K(z,x \ y) \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(19245(a,1),19055(a,1,1,1))].">
      <j1 rule="para" parents="19245 19055"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,x \ (K(z,x \ y) \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(13461(a,1),19247(a,1,1,1))].">
      <j1 rule="para" parents="13461 19247"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,K(y,z) \ (x \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(19246(a,1),19248(a,1,2,1))].">
      <j1 rule="para" parents="19246 19248"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,x \ (T(y,z) * u)),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(17013(a,1),19249(a,1,2,1))].">
      <j1 rule="para" parents="17013 19249"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      a(x,x \ (T(y,z) * u),x) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11351,a(flip),b,19250,a)].">
      <j1 rule="hyper" parents="64 11351 19250"/>
    </justification>
  </clause>

  <clause id="19252">
    <literal><![CDATA[
      a(x,x \ (y * T((1 / y) * z,u)),x) = a(x,x \ (K(u,y) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19139,a(flip),b,19251,a),flip(a)].">
      <j1 rule="hyper" parents="64 19139 19251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ u),x) = a(x,x \ (z * ((1 / z) * u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19131,a(flip),b,19252,a),flip(a)].">
      <j1 rule="hyper" parents="64 19131 19252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      a(x,x \ L(y,z \ 1,z),x) = a(x,x \ (K(u,z) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11514,a(flip),b,19253,a)].">
      <j1 rule="hyper" parents="319 11514 19253"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ u),x) = a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11354,a(flip),b,19255,a),flip(a)].">
      <j1 rule="hyper" parents="64 11354 19255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19258">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,x \ ((x \ y) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19036,a(flip),b,19256,a)].">
      <j1 rule="hyper" parents="64 19036 19256"/>
    </justification>
  </clause>

  <clause id="19260">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,x \ (y \ (x * w)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,11357,a(flip),b,19258,a),flip(a)].">
      <j1 rule="hyper" parents="319 11357 19258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19261">
    <literal><![CDATA[
      a(x,y \ T(z,x),x) = a(x,y \ (K(u,w) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,18886,a(flip),b,19260,a)].">
      <j1 rule="hyper" parents="319 18886 19260"/>
    </justification>
  </clause>

  <clause id="19262">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,y \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8350,a(flip),b,19261,a),flip(a)].">
      <j1 rule="hyper" parents="64 8350 19261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      a(x,y \ (z / u),x) = a(x,y \ (u \ z),x)
    ]]></literal>
    <justification jstring="[para(4126(a,1),19262(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4126 19262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      a(x,y \ (T(z,u) \ w),x) = a(x,y \ (z \ w),x)
    ]]></literal>
    <justification jstring="[para(4285(a,1),19262(a,1,2,2))].">
      <j1 rule="para" parents="4285 19262"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      a(x,y \ (((z * u) * w) / (z * w)),x) = a(x,y \ R(u,z,w),x)
    ]]></literal>
    <justification jstring="[para(13970(a,1),19262(a,1,2,2))].">
      <j1 rule="para" parents="13970 19262"/>
    </justification>
  </clause>

  <clause id="19270">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11436,a,b,19266,a)].">
      <j1 rule="hyper" parents="64 11436 19266"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ w),x) = a(x,u \ (z \ (y \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(11434,a,19270,a),flip(a)].">
      <j1 rule="hyper" parents="11434 19270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ w),x) = a(x,z \ (u \ (y \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19270,a,b,19271,a),flip(a)].">
      <j1 rule="hyper" parents="319 19270 19271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      a(x,y \ (z \ (u \ (z * (y * w)))),x) = a(x,u \ L(w,y,z),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),19271(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 19271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      a(x,y \ ((z * T(u,w)) \ v5),x) = a(x,z \ (u \ (y \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19268,a(flip),b,19273,a),flip(a)].">
      <j1 rule="hyper" parents="319 19268 19273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19276">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((z * w) * u)),x) = a(x,y \ R(w,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,19266,a(flip),b,19269,a)].">
      <j1 rule="hyper" parents="64 19266 19269"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,y \ ((u * T(w,u * z)) \ (w * (u * z))),x)
    ]]></literal>
    <justification jstring="[para(16868(a,1),19276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16868 19276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,u \ (w \ (y \ (w * (u * z)))),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19275,a(flip),b,19277,a),flip(a)].">
      <j1 rule="hyper" parents="319 19275 19277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,y \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(319,a,19274,a(flip),b,19278,a),flip(a)].">
      <j1 rule="hyper" parents="319 19274 19278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19281">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(13014,a,19280,a),flip(a)].">
      <j1 rule="hyper" parents="13014 19280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(19281(a,1),12659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19281 12659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(y \ K(z,u),w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(125,a,19282,a(flip),b,18793,a),flip(a)].">
      <j1 rule="hyper" parents="125 19282 18793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,17546,a(flip),b,19283,a),flip(a)].">
      <j1 rule="hyper" parents="319 17546 19283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) * K(u,z)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(5174(a,1),19285(a,1,2))].">
      <j1 rule="para" parents="5174 19285"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (T(y,K(z,u)) * K(u,z))) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(16573,a,19287,a)].">
      <j1 rule="hyper" parents="16573 19287"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(u,z) * y)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(6052(a,1),19288(a,1,2,2))].">
      <j1 rule="para" parents="6052 19288"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      T(K(x,K(y,y \ z) * (u * w)),w \ T(w * (u * K(y \ z,y)),x)) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(16931(a,1),12214(a,1,1))].">
      <j1 rule="para" parents="16931 12214"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      T(K(x,K(y \ z,y) * (u * w)),w \ T(w * (u * K(y,y \ z)),x)) = (w \ T(w * (u * K(y,y \ z)),x)) \ ((u / y) * ((y \ z) \ z))
    ]]></literal>
    <justification jstring="[para(16931(a,1),12215(a,1,1))].">
      <j1 rule="para" parents="16931 12215"/>
    </justification>
  </clause>

  <clause id="19292">
    <literal><![CDATA[
      T((K(x,L(x \ K(y,z),u,w)) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(10096(a,1),14357(a,1,1,1,1))].">
      <j1 rule="para" parents="10096 14357"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z * K(u,K(w,v5)),v7)))
    ]]></literal>
    <justification jstring="[para(16339(a,1),15109(a,2,2,2,1))].">
      <j1 rule="para" parents="16339 15109"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = (x * K(z,u)) * L(K(x,y) * ((T(x,y) * K(z,u)) \ w),v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(18850(a,2),18172(a,2,2))].">
      <j1 rule="para" parents="18850 18172"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(y \ z,y)),x)) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(13470(a,1),19290(a,1,1))].">
      <j1 rule="para" parents="13470 19290"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(y \ z,y)),x))) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6173,a,19295,a)].">
      <j1 rule="hyper" parents="6173 19295"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(y \ z,y))))) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(15170,a,19296,a)].">
      <j1 rule="hyper" parents="15170 19296"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,T(K(z,u) * (y * x),y * K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(9(a,1),19297(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,T(K(z,u) * (y * x),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,15131,a(flip),b,19299,a),flip(a)].">
      <j1 rule="hyper" parents="319 15131 19299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(z,z \ y)),x)) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[para(11166(a,1),19291(a,1,1))].">
      <j1 rule="para" parents="11166 19291"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(z,z \ y)),x))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(6173,a,19303,a)].">
      <j1 rule="hyper" parents="6173 19303"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(z,z \ y))))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(15170,a,19304,a)].">
      <j1 rule="hyper" parents="15170 19304"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),19305(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y))
    ]]></literal>
    <justification jstring="[hyper(319,a,15131,a(flip),b,19307,a),flip(a)].">
      <j1 rule="hyper" parents="319 15131 19307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15573,a(flip),b,19308,a),flip(a)].">
      <j1 rule="hyper" parents="64 15573 19308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19300,a,b,19311,a)].">
      <j1 rule="hyper" parents="64 19300 19311"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ (y * K(z \ u,z)) = K(w,x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(5233(a,1),19312(a,1,2))].">
      <j1 rule="para" parents="5233 19312"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(12195,a,19313,a)].">
      <j1 rule="hyper" parents="12195 19313"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(12489(a,1),19314(a,1,2,2))].">
      <j1 rule="para" parents="12489 19314"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15008,a(flip),b,19315,a),flip(a)].">
      <j1 rule="hyper" parents="319 15008 19315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,(z \ u) * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15092,a(flip),b,19316,a)].">
      <j1 rule="hyper" parents="64 15092 19316"/>
    </justification>
  </clause>

  <clause id="19318">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,u * (z \ y))))
    ]]></literal>
    <justification jstring="[para(12877(a,1),19317(a,2,2,2,2))].">
      <j1 rule="para" parents="12877 19317"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,11247,a(flip),b,19318,a),flip(a)].">
      <j1 rule="hyper" parents="319 11247 19318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19320">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(16263,a,19319,a)].">
      <j1 rule="hyper" parents="16263 19319"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ T(z,u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[para(11108(a,1),19320(a,1,2))].">
      <j1 rule="para" parents="11108 19320"/>
    </justification>
  </clause>

  <clause id="19322">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ z)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(15170,a,19321,a)].">
      <j1 rule="hyper" parents="15170 19321"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = w
    ]]></literal>
    <justification jstring="[para(19322(a,1),14424(a,1))].">
      <j1 rule="para" parents="19322 14424"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(19324,a,18572,a)].">
      <j1 rule="hyper" parents="19324 18572"/>
    </justification>
  </clause>

  <clause id="19326">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18198,a(flip),b,19325,a),flip(a)].">
      <j1 rule="hyper" parents="64 18198 19325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      T((K(L(x \ K(y,z),u,w),x) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4356(a,1),19292(a,1,1,1))].">
      <j1 rule="para" parents="4356 19292"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15112,a(flip),b,19293,a),flip(a)].">
      <j1 rule="hyper" parents="319 15112 19293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z,v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[para(14577(a,1),19328(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="14577 19328"/>
    </justification>
  </clause>

  <clause id="19332">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * (v6 * K(z,v7)))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[para(16339(a,1),19330(a,1,2,2,1))].">
      <j1 rule="para" parents="16339 19330"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,K(w,v5)) * (v6 * K(z,v7))) * z))) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11136,a(flip),b,19332,a)].">
      <j1 rule="hyper" parents="64 11136 19332"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      K(x,y * (z * ((u * K(z,w)) * (z * K(v5,K(v6,v7)))))) = K(x,y * ((z * (K(v5,K(v6,v7)) * u)) * T(z,w)))
    ]]></literal>
    <justification jstring="[para(16302(a,1),19333(a,1,2,2,2))].">
      <j1 rule="para" parents="16302 19333"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7))) = K(x,y * (z * (v6 * T(z * K(u,K(w,v5)),v7))))
    ]]></literal>
    <justification jstring="[para(14583(a,1),19334(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14583 19334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      K(x,y * (z * (u * T(z * K(w,K(v5,v6)),u)))) = K(x,y * ((u * (z * K(w,K(v5,v6)))) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18985,a(flip),b,19335,a),flip(a)].">
      <j1 rule="hyper" parents="64 18985 19335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * ((u * K(w,K(v5,v6))) * z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),19336(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 19336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * (u * (K(w,K(v5,v6)) * z))))
    ]]></literal>
    <justification jstring="[para(16339(a,1),19337(a,2,2,2,2))].">
      <j1 rule="para" parents="16339 19337"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,15416,a(flip),b,19338,a),flip(a)].">
      <j1 rule="hyper" parents="319 15416 19338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(16637,a,19339,a)].">
      <j1 rule="hyper" parents="16637 19339"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      K(x,y * (((z * T(u,w)) * K(v5,u)) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(5797(a,2),19340(a,2,2,2,2))].">
      <j1 rule="para" parents="5797 19340"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w \ (1 / u))))) = K(x,y * ((w \ (1 / T(u,z))) * K(z,u)))
    ]]></literal>
    <justification jstring="[para(12881(a,1),19340(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12881 19340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w \ (1 / u))))) = K(x,y * (w \ (K(z,u) / T(u,z))))
    ]]></literal>
    <justification jstring="[para(13129(a,1),19343(a,2,2,2))].">
      <j1 rule="para" parents="13129 19343"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w \ (1 / u))))) = K(x,y * (w \ (T(u,z) \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(319,a,15077,a(flip),b,19344,a),flip(a)].">
      <j1 rule="hyper" parents="319 15077 19344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19346">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) \ K(w,u)))) = K(x,y * (z \ (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13719,a(flip),b,19345,a),flip(a)].">
      <j1 rule="hyper" parents="64 13719 19345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) \ K(w,u)))) = K(x,y * (z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,4695,a(flip),b,19346,a),flip(a)].">
      <j1 rule="hyper" parents="319 4695 19346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      K(x,y * ((z * (T(u,w) * K(v5,u))) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(6231(a,1),19342(a,1,2,2,1))].">
      <j1 rule="para" parents="6231 19342"/>
    </justification>
  </clause>

  <clause id="19350">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * ((T(u,v5) * K(z,u)) * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16909,a(flip),b,19349,a),flip(a)].">
      <j1 rule="hyper" parents="64 16909 19349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * (T(u,v5) * (K(z,u) * K(z,u)))))
    ]]></literal>
    <justification jstring="[para(4542(a,1),19350(a,2,2,2,2))].">
      <j1 rule="para" parents="4542 19350"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T(u * (K(z,u) * K(z,u)),v5)))
    ]]></literal>
    <justification jstring="[para(13818(a,2),19351(a,2,2,2,2))].">
      <j1 rule="para" parents="13818 19351"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(6451(a,1),19352(a,2,2,2,2,1))].">
      <j1 rule="para" parents="6451 19352"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w * T(u,v5))))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(5797(a,1),19353(a,1,2,2,2))].">
      <j1 rule="para" parents="5797 19353"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      K(x,y * (z * T((T(u,w) * w) / u,v5))) = K(x,y * (z * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13719,a(flip),b,19354,a),flip(a)].">
      <j1 rule="hyper" parents="64 13719 19354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19357">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5),w))) = K(x,y * (z * T((T(v6,u) * u) / v6,v5)))
    ]]></literal>
    <justification jstring="[para(4135(a,2),19355(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4135 19355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19358">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T((T(v7,u) * u) / v7,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(319,a,18568,a(flip),b,19357,a),flip(a)].">
      <j1 rule="hyper" parents="319 18568 19357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19359">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T(u,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(319,a,19355,a(flip),b,19358,a),flip(a)].">
      <j1 rule="hyper" parents="319 19355 19358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19360">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(4130(a,1),19359(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4130 19359"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(15329,a,19360,a)].">
      <j1 rule="hyper" parents="15329 19360"/>
    </justification>
  </clause>

  <clause id="19362">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,19360,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19360 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(129,a,19361,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19361 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(v5,z) * T(z,w * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15395,a,b,19361,a)].">
      <j1 rule="hyper" parents="64 15395 19361"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,y * z))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18715,a(flip),b,19362,a),flip(a)].">
      <j1 rule="hyper" parents="64 18715 19362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      K(T(x,y / z),(u * w) \ T(v5,w * (u * T(x,y * z)))) = K(T(x,y / z),v5 / (u * w))
    ]]></literal>
    <justification jstring="[para(19363(a,1),15330(a,1,2,2))].">
      <j1 rule="para" parents="19363 15330"/>
    </justification>
  </clause>

  <clause id="19367">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,15393,a(flip),b,19364,a),flip(a)].">
      <j1 rule="hyper" parents="319 15393 19364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(15104,a,19367,a)].">
      <j1 rule="hyper" parents="15104 19367"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * (T(w \ u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15394,a(flip),b,19368,a),flip(a)].">
      <j1 rule="hyper" parents="64 15394 19368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13716,a(flip),b,19369,a),flip(a)].">
      <j1 rule="hyper" parents="319 13716 19369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19371">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,(x * (z \ 1)) * T(y,z))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[para(19365(a,1),19366(a,1,2,2))].">
      <j1 rule="para" parents="19365 19366"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,y * (x * (z \ 1)))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16865,a(flip),b,19371,a)].">
      <j1 rule="hyper" parents="64 16865 19371"/>
    </justification>
  </clause>

  <clause id="19374">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = (x * K(z,u)) * L((x * K(z,u)) \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(18173(a,1),19294(a,2,2,1))].">
      <j1 rule="para" parents="18173 19294"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * (K(z,u) * L(K(z,u) \ (x \ w),v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(319,a,981,a(flip),b,19374,a),flip(a)].">
      <j1 rule="hyper" parents="319 981 19374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * (K(z,u) * L(K(u,z) * (x \ w),v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(4356(a,1),19375(a,2,2,2,1))].">
      <j1 rule="para" parents="4356 19375"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * L(K(z,u) * (K(u,z) * (x \ w)),v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(18850(a,2),19377(a,2,2))].">
      <j1 rule="para" parents="18850 19377"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(4363(a,1),19378(a,2,2,1))].">
      <j1 rule="para" parents="4363 19378"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      T(T(x,y) * (K(z,u) * L(K(z,u) \ (T(x,y) \ w),v5,v5 \ 1)),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(981(a,1),19379(a,1,1))].">
      <j1 rule="para" parents="981 19379"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      T(T(x,y) * (K(z,u) * L(K(u,z) * (T(x,y) \ w),v5,v5 \ 1)),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(4356(a,1),19380(a,1,1,2,2,1))].">
      <j1 rule="para" parents="4356 19380"/>
    </justification>
  </clause>

  <clause id="19383">
    <literal><![CDATA[
      T(T(x,y) * L(K(z,u) * (K(u,z) * (T(x,y) \ w)),v5,v5 \ 1),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(18850(a,2),19382(a,1,1,2))].">
      <j1 rule="para" parents="18850 19382"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      T(T(x,y) * L(T(x,y) \ z,u,u \ 1),z) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2526(a,1),19383(a,1,1,2,1))].">
      <j1 rule="para" parents="2526 19383"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(16722,a,19384,a)].">
      <j1 rule="hyper" parents="16722 19384"/>
    </justification>
  </clause>

  <clause id="19386">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2000,a,19385,a)].">
      <j1 rule="hyper" parents="2000 19385"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      (x \ (x * L(x \ y,z,z \ 1))) / L(x \ T(y,u),z,z \ 1) = K(u,T(x * L(x \ y,z,z \ 1),x))
    ]]></literal>
    <justification jstring="[para(19386(a,1),12405(a,1,2))].">
      <j1 rule="para" parents="19386 12405"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      K(x,y * L(((z \ T(u,w)) / (y \ 1)) / y,v5,v5 \ 1)) = K(x,y * (z \ T(z * L(z \ u,v5,v5 \ 1),w)))
    ]]></literal>
    <justification jstring="[para(19386(a,2),18871(a,2,2,2))].">
      <j1 rule="para" parents="19386 18871"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = L(y \ z,u,u \ 1) / L(y \ T(z,x),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),19387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 19387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19390">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,18852,a(flip),b,19389,a),flip(a)].">
      <j1 rule="hyper" parents="319 18852 19389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(9327,a,19390,a)].">
      <j1 rule="hyper" parents="9327 19390"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) / (w \ 1),w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19392,a(flip),b,19388,a)].">
      <j1 rule="hyper" parents="64 19392 19388"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) * w,w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12348,a(flip),b,19394,a)].">
      <j1 rule="hyper" parents="64 12348 19394"/>
    </justification>
  </clause>

  <clause id="19397">
    <literal><![CDATA[
      K(x,y * (z \ T(z * L(z \ u,w,w \ 1),v5))) = K(x,y * (z \ T(u,v5)))
    ]]></literal>
    <justification jstring="[hyper(9326,a,19396,a),flip(a)].">
      <j1 rule="hyper" parents="9326 19396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(19386(a,1),19397(a,1,2,2))].">
      <j1 rule="para" parents="19386 19397"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      T((K(x \ K(y,z),L(x,u,w)) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(10133(a,1),19327(a,1,1,1,1))].">
      <j1 rule="para" parents="10133 19327"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      T(a(x \ K(y,z),u,K(w,x)) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12532(a,1),19399(a,1,1,1))].">
      <j1 rule="para" parents="12532 19399"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      T(a(K(x,y),z,K(u,w)) * L(K(w,w \ K(x,y)),z,u),K(K(y,x) * w,w \ 1)) = K(K(y,x) * w,w \ 1)
    ]]></literal>
    <justification jstring="[para(12620(a,1),19400(a,1,1,1))].">
      <j1 rule="para" parents="12620 19400"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      T(1 * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(16102(a,1),19401(a,1,1,1))].">
      <j1 rule="para" parents="16102 19401"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      T(1 * K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(5379(a,1),19402(a,1,1,2))].">
      <j1 rule="para" parents="5379 19402"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      T(K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),19403(a,1,1))].">
      <j1 rule="para" parents="7 19403"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(14127,a,19405,a)].">
      <j1 rule="hyper" parents="14127 19405"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(x,x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,14114,a(flip),b,19406,a),flip(a)].">
      <j1 rule="hyper" parents="319 14114 19406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,y \ K(z,u)) * v6)) = K(x,T(L(y \ K(z,u),w,v5),y) * v6)
    ]]></literal>
    <justification jstring="[para(19407(a,1),13471(a,1,2,2,1))].">
      <j1 rule="para" parents="19407 13471"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,K(z,u)) * v6)) = K(x,T(L(y \ K(z,u),w,v5),y) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,11323,a(flip),b,19409,a)].">
      <j1 rule="hyper" parents="64 11323 19409"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      K(x,T(L(y \ K(z,u),w,v5),y) * v6) = K(x,L(y \ K(z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(15094,a,19410,a),flip(a)].">
      <j1 rule="hyper" parents="15094 19410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * v6) = K(x,L(u \ K(y,z),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,15295,a(flip),b,19411,a)].">
      <j1 rule="hyper" parents="64 15295 19411"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(u \ K(y,z),w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18626,a,b,19413,a)].">
      <j1 rule="hyper" parents="64 18626 19413"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = a(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(319,a,19289,a(flip),b,19414,a),flip(a)].">
      <j1 rule="hyper" parents="319 19289 19414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      T(K(x,K(y,z) * ((u * w) * v5)),v5 \ T(v5 * ((u * K(z,y)) * w),x)) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[para(17187(a,1),14464(a,1,1))].">
      <j1 rule="para" parents="17187 14464"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      T(K(x,T(y,z / u) * w),w \ T(w * T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[para(14990(a,1),16755(a,1,1))].">
      <j1 rule="para" parents="14990 16755"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),w \ T(w * T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[para(18575(a,1),19418(a,1,1))].">
      <j1 rule="para" parents="18575 19418"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),w * T(w \ T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18443,a(flip),b,19420,a)].">
      <j1 rule="hyper" parents="64 18443 19420"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),T(w * T(w \ y,x),T(z / u,v5))) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18158,a,b,19421,a)].">
      <j1 rule="hyper" parents="64 18158 19421"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,T(T(y,z * u) * w,w * T(w \ y,x))) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(14190,a,19422,a)].">
      <j1 rule="hyper" parents="14190 19422"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T((u * z) \ (z * z),w)) = K(v5,T(T(y,z * u) * x,y))
    ]]></literal>
    <justification jstring="[hyper(15168,a,19423,a),flip(a)].">
      <j1 rule="hyper" parents="15168 19423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19426">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T((u * z) \ (z * z),w)) = K(v5,x * T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,14191,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="319 14191 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T(z / u,w)) = K(v5,x * T(y,z * u))
    ]]></literal>
    <justification jstring="[para(16754(a,1),19426(a,1,2))].">
      <j1 rule="para" parents="16754 19426"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(12195,a,19427,a)].">
      <j1 rule="hyper" parents="12195 19427"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(111(a,1),19428(a,1,2,2,2))].">
      <j1 rule="para" parents="111 19428"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(18246,a,19429,a)].">
      <j1 rule="hyper" parents="18246 19429"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      K(x,y * T(z,u * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(213(a,1),19429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="213 19429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(19429(a,1),14437(a,1))].">
      <j1 rule="para" parents="19429 14437"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      T(x,y * T(z,u * u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,19431,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19431 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      T(x,(y / z) * T(z,u * u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),19433(a,2,2))].">
      <j1 rule="para" parents="12 19433"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      T(x,y * K(z,u * u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4921(a,1),19434(a,1,2))].">
      <j1 rule="para" parents="4921 19434"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      T(x,y * K(z * z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(14418,a,19435,a)].">
      <j1 rule="hyper" parents="14418 19435"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      T(x,T(y * y,z) * u) = T(x,(y * y) * u)
    ]]></literal>
    <justification jstring="[para(6434(a,1),19436(a,1,2))].">
      <j1 rule="para" parents="6434 19436"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      T(x,T(y * y,z) * u) = T(x,y * (y * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,12967,a(flip),b,19437,a),flip(a)].">
      <j1 rule="hyper" parents="319 12967 19437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      T(x,(y / (z * (u * u))) \ w) = T(x,u * (u * ((y / z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17251,a(flip),b,19438,a)].">
      <j1 rule="hyper" parents="64 17251 19438"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ T(w,y * L(y,z,u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (y \ L(y,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(18767(a,1),19432(a,1))].">
      <j1 rule="para" parents="18767 19432"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19429,a(flip),b,19430,a)].">
      <j1 rule="hyper" parents="64 19429 19430"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      T(x,y * (y * ((z / (z / u)) \ w))) = T(x,T((y * y) \ u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13500,a(flip),b,19439,a),flip(a)].">
      <j1 rule="hyper" parents="64 13500 19439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      K(T(x,y),(z \ u) * T(w,u * (x * z))) = K(T(x,y),w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15442,a(flip),b,19441,a),flip(a)].">
      <j1 rule="hyper" parents="64 15442 19441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      T(x,T((y * y) \ z,u) \ w) = T(x,y * (y * (T(z,u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13689,a(flip),b,19443,a),flip(a)].">
      <j1 rule="hyper" parents="64 13689 19443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6244,a,19444,a)].">
      <j1 rule="hyper" parents="6244 19444"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(14030,a,19446,a)].">
      <j1 rule="hyper" parents="14030 19446"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a(flip),b,19447,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 19447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ z) * y) = w
    ]]></literal>
    <justification jstring="[para(19448(a,2),14029(a,1))].">
      <j1 rule="para" parents="19448 14029"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      K(x,(y / z) * T(L(z,u,w),z)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(19440,a,19326,a),flip(a)].">
      <j1 rule="hyper" parents="19440 19326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(187(a,1),19450(a,1,2,2))].">
      <j1 rule="para" parents="187 19450"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,(y / (z \ T(u,w))) * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19398,a(flip),b,19451,a),flip(a)].">
      <j1 rule="hyper" parents="64 19398 19451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),19452(a,2,2))].">
      <j1 rule="para" parents="12 19452"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13919,a,19453,a)].">
      <j1 rule="hyper" parents="13919 19453"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(81(a,1),19454(a,1,2,2,1))].">
      <j1 rule="para" parents="81 19454"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(18771,a,19457,a)].">
      <j1 rule="hyper" parents="18771 19457"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,18903,a(flip),b,19457,a)].">
      <j1 rule="hyper" parents="64 18903 19457"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(14710,a,19458,a)].">
      <j1 rule="hyper" parents="14710 19458"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(x,(L(y,z,z \ 1) \ u) * ((u \ y) * u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19183,a(flip),b,19458,a),flip(a)].">
      <j1 rule="hyper" parents="64 19183 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x,y * L(z,u,u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1584(a,1),19458(a,1,2,2))].">
      <j1 rule="para" parents="1584 19458"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,19464,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19464 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      T(x,y * ((z * z) \ u)) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(302(a,1),19466(a,1,2,2))].">
      <j1 rule="para" parents="302 19466"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4684,a(flip),b,19460,a),flip(a)].">
      <j1 rule="hyper" parents="64 4684 19460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(19459(a,2),12190(a,1))].">
      <j1 rule="para" parents="19459 12190"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ u))),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(19469(a,1),18581(a,1,1))].">
      <j1 rule="para" parents="19469 18581"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(14709(a,1),19474(a,1))].">
      <j1 rule="para" parents="14709 19474"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      K(x,(L(y,z,z \ 1) \ u) * T(y,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(14536,a,19463,a)].">
      <j1 rule="hyper" parents="14536 19463"/>
    </justification>
  </clause>

  <clause id="19478">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u \ z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(15593(a,2),19476(a,1))].">
      <j1 rule="para" parents="15593 19476"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ T(v5 * ((u * K(z,y)) * w),x))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6173,a,19417,a)].">
      <j1 rule="hyper" parents="6173 19417"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ (v5 * ((u * K(z,y)) * w)))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(15170,a,19479,a)].">
      <j1 rule="hyper" parents="15170 19479"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),(y * K(z,u)) * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),19480(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),y * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,15148,a(flip),b,19482,a),flip(a)].">
      <j1 rule="hyper" parents="319 15148 19482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[hyper(319,a,19311,a(flip),b,19483,a),flip(a)].">
      <j1 rule="hyper" parents="319 19311 19483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ ((y * K(z,u)) * w) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[para(14275(a,1),19486(a,1,2))].">
      <j1 rule="para" parents="14275 19486"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(12195,a,19487,a)].">
      <j1 rule="hyper" parents="12195 19487"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * ((v5 \ w) / w)))) = K(x,y * (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17375,a(flip),b,19488,a),flip(a)].">
      <j1 rule="hyper" parents="64 17375 19488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(4922(a,1),19488(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4922 19488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(16548,a,19490,a),flip(a)].">
      <j1 rule="hyper" parents="16548 19490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * (u \ (w \ u))) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,17254,a(flip),b,19491,a),flip(a)].">
      <j1 rule="hyper" parents="64 17254 19491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w \ v5,v5))) = K(x,y * (v5 / (K(u,z) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15369,a(flip),b,19489,a)].">
      <j1 rule="hyper" parents="64 15369 19489"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * v5))) = K(x,y * (K(w,u) * (z / v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13583,a(flip),b,19493,a),flip(a)].">
      <j1 rule="hyper" parents="64 13583 19493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17176,a,b,19494,a)].">
      <j1 rule="hyper" parents="64 17176 19494"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      K(x,y * (K(z,L(y \ 1,u,w)) * (v5 / L(y,u,w)))) = K(x,(L(y,u,w) \ v5) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18892,a(flip),b,19495,a),flip(a)].">
      <j1 rule="hyper" parents="64 18892 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      K(x,y * (K(z,L(y,u,w)) * (v5 / L(y,u,w)))) = K(x,(L(T(y,z),u,w) \ v5) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16869,a(flip),b,19495,a),flip(a)].">
      <j1 rule="hyper" parents="64 16869 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(v5,w)))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16768,a(flip),b,19495,a),flip(a)].">
      <j1 rule="hyper" parents="64 16768 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11328,a(flip),b,19498,a),flip(a)].">
      <j1 rule="hyper" parents="64 11328 19498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(15334,a,19499,a),flip(a)].">
      <j1 rule="hyper" parents="15334 19499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19501">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(15332,a,19499,a)].">
      <j1 rule="hyper" parents="15332 19499"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w * K(v5,v6))))) = K(x,y * (K(v5,v6) * (z \ (u * w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18900,a(flip),b,19501,a)].">
      <j1 rule="hyper" parents="64 18900 19501"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) \ (w * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16898,a(flip),b,19501,a),flip(a)].">
      <j1 rule="hyper" parents="64 16898 19501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      K(x,y * (z \ (u \ K(w,w * v5)))) = K(x,y * (K(w,v5) * (z \ (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(64,a,11294,a(flip),b,19500,a),flip(a)].">
      <j1 rule="hyper" parents="64 11294 19500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(11797(a,1),19500(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11797 19500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) * v5) = K(x,K(w,u) * ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),19492(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 19492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * ((v5 \ y) * v6)) = K(x,(v5 \ ((K(z,u) * (w * y)) / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,16999,a,b,19507,a),flip(a)].">
      <j1 rule="hyper" parents="64 16999 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (K(u,w) * (z \ (v5 * v6))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19078,a,b,19503,a)].">
      <j1 rule="hyper" parents="64 19078 19503"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x,y * (z \ (u \ K(w,w * v5)))) = K(x,y * (z \ (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(319,a,19500,a(flip),b,19505,a),flip(a)].">
      <j1 rule="hyper" parents="319 19500 19505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) / (u / (w \ 1))))) = K(x,y * (z \ (T(w,u) \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,15822,a(flip),b,19511,a)].">
      <j1 rule="hyper" parents="64 15822 19511"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ (w \ K(u,z)))) = v5
    ]]></literal>
    <justification jstring="[para(19506(a,1),18303(a,1))].">
      <j1 rule="para" parents="19506 18303"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) / (u / (w \ 1))))) = K(x,y * (z \ (w \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,19348,a(flip),b,19512,a),flip(a)].">
      <j1 rule="hyper" parents="319 19348 19512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      K(x,(L(T(y,z),u,w) \ v5) * y) = K(x,y * (v5 / T(L(y,u,w),z)))
    ]]></literal>
    <justification jstring="[hyper(15053,a,19497,a),flip(a)].">
      <j1 rule="hyper" parents="15053 19497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      K(x,(L(T(y,z),u,w) \ v5) * y) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(25(a,2),19516(a,2,2,2,2))].">
      <j1 rule="para" parents="25 19516"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17447,a,b,19517,a)].">
      <j1 rule="hyper" parents="64 17447 19517"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ ((K(u,z) * w) * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(17383(a,1),19504(a,1,2,2,2))].">
      <j1 rule="para" parents="17383 19504"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),K(u,w),v5)) = K(x,y * (z * K(v5 * z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(18620(a,1),19519(a,1,2,2))].">
      <j1 rule="para" parents="18620 19519"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      K(x,y * (z * K(u * z,K(w,v5)))) = K(x,y * L(z,K(w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(18821,a,19520,a),flip(a)].">
      <j1 rule="hyper" parents="18821 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(15018,a,19521,a),flip(a)].">
      <j1 rule="hyper" parents="15018 19521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19523">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(19521(a,1),15018(a,1))].">
      <j1 rule="para" parents="19521 15018"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(u,w) \ (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(567(a,1),19522(a,1,2,2))].">
      <j1 rule="para" parents="567 19522"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(5183(a,1),19523(a,1,2))].">
      <j1 rule="para" parents="5183 19523"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(w,u) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(4356(a,1),19525(a,2,2,2,1))].">
      <j1 rule="para" parents="4356 19525"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L(K(z,u) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,18830,a,b,19527,a)].">
      <j1 rule="hyper" parents="64 18830 19527"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(K(u,z) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(4356(a,1),19528(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4356 19528"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      K(x,y * L(z \ (K(u,w) * v5),v6,v7)) = K(x,y * L(K(u,w) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,17188,a(flip),b,19529,a)].">
      <j1 rule="hyper" parents="64 17188 19529"/>
    </justification>
  </clause>

  <clause id="19531">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * (w \ v5),w,v6)) = K(x,y * ((v6 * w) \ (v6 * (K(z,u) * v5))))
    ]]></literal>
    <justification jstring="[hyper(14224,a,19530,a),flip(a)].">
      <j1 rule="hyper" parents="14224 19530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * (K(w,v5) * (u * v6))))) = K(x,y * L(K(w,v5) * v6,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),19531(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 19531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * (y * (u / L(y,w,v5)))) = K(x,(L(y,w,v5) \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16912,a(flip),b,19496,a)].">
      <j1 rule="hyper" parents="64 16912 19496"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      K(x,y * (K(y \ 1,z) * (u / L(y,w,v5)))) = K(x,(L(y,w,v5) \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(4764(a,1),19533(a,1,2))].">
      <j1 rule="para" parents="4764 19533"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      K(x,T(y,z) * (u / L(y,w,v5))) = K(x,(L(y,w,v5) \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16563,a,19535,a)].">
      <j1 rule="hyper" parents="16563 19535"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * (K(v5,w) * v6)))) = K(x,y * (K(v5,w) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[para(17393(a,1),19510(a,1,2,2,2))].">
      <j1 rule="para" parents="17393 19510"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(16436,a,19537,a)].">
      <j1 rule="hyper" parents="16436 19537"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * v5) \ (w * (v5 * v6))))) = K(x,y * L(K(z,u) * v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19532,a(flip),b,19538,a),flip(a)].">
      <j1 rule="hyper" parents="64 19532 19538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * w,v5,v6)) = K(x,y * (K(z,u) * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18(a,2),19539(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * L(K(u,z) * w,v5,v6)) = K(x,y * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19526,a,19540,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19526 19540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19542">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * w,v5,v6))) = K(x,u * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(17036,a,19541,a)].">
      <j1 rule="hyper" parents="17036 19541"/>
    </justification>
  </clause>

  <clause id="19543">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19415,a(flip),b,19542,a),flip(a)].">
      <j1 rule="hyper" parents="64 19415 19542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      K(x,y * L(((z * u) / z) \ z,w,v5)) = K(x,y * L(z / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18640,a(flip),b,19542,a)].">
      <j1 rule="hyper" parents="64 18640 19542"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(T(1 / (y / z),y),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15985,a(flip),b,19543,a)].">
      <j1 rule="hyper" parents="64 15985 19543"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(13993,a,19544,a),flip(a)].">
      <j1 rule="hyper" parents="13993 19544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(1 / (y / z),T(w,y)))
    ]]></literal>
    <justification jstring="[para(6102(a,1),19545(a,2,3))].">
      <j1 rule="para" parents="6102 19545"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(z / y,T(w,y)))
    ]]></literal>
    <justification jstring="[para(4648(a,1),19548(a,2,3))].">
      <j1 rule="para" parents="4648 19548"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(6156(a,1),19549(a,2,3))].">
      <j1 rule="para" parents="6156 19549"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      K(x,y * (K(z,z \ L(y,u,w)) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19495,a(flip),b,19518,a)].">
      <j1 rule="hyper" parents="64 19495 19518"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      K(x,y * (K(z,L(y,u,w) * z) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18565,a(flip),b,19551,a)].">
      <j1 rule="hyper" parents="64 18565 19551"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      K(x,y * (K(z,z * L(y,u,w)) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(4394(a,1),19552(a,1,2,2,1))].">
      <j1 rule="para" parents="4394 19552"/>
    </justification>
  </clause>

  <clause id="19554">
    <literal><![CDATA[
      K(x,y * (K(z,L(z * y,u,w)) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(18860(a,2),19553(a,1,2,2,1))].">
      <j1 rule="para" parents="18860 19553"/>
    </justification>
  </clause>

  <clause id="19555">
    <literal><![CDATA[
      K(x,K(y * z,y) * (z * (u / L(z,w,v5)))) = K(x,z * (u / L(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16912,a(flip),b,19554,a)].">
      <j1 rule="hyper" parents="64 16912 19554"/>
    </justification>
  </clause>

  <clause id="19557">
    <literal><![CDATA[
      K(x,y * (K(z * y,z) * (u / L(y,w,v5)))) = K(x,y * (u / L(T(y,z),w,v5)))
    ]]></literal>
    <justification jstring="[para(11805(a,1),19555(a,1,2))].">
      <j1 rule="para" parents="11805 19555"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      K(x,y * (K(z,y) * (u / L(y,w,v5)))) = K(x,y * (u / L(T(y,z),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15300,a(flip),b,19557,a)].">
      <j1 rule="hyper" parents="64 15300 19557"/>
    </justification>
  </clause>

  <clause id="19559">
    <literal><![CDATA[
      K(x,T(y,z) * (u / L(y,w,v5))) = K(x,y * (u / L(T(y,z),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(15304,a,19558,a)].">
      <j1 rule="hyper" parents="15304 19558"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * T(y,v5)) = K(x,y * (w / L(T(y,v5),z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19536,a(flip),b,19559,a)].">
      <j1 rule="hyper" parents="64 19536 19559"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      K(x,y * (z / L(T(y,z),u,u \ 1))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19477,a(flip),b,19560,a),flip(a)].">
      <j1 rule="hyper" parents="64 19477 19560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19562">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11235,a(flip),b,19561,a)].">
      <j1 rule="hyper" parents="64 11235 19561"/>
    </justification>
  </clause>

  <clause id="19563">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19170,a(flip),b,19562,a),flip(a)].">
      <j1 rule="hyper" parents="64 19170 19562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17944,a(flip),b,19562,a)].">
      <j1 rule="hyper" parents="64 17944 19562"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),19562(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,w * (L(w,v5,v5 \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,19562,a,b,19564,a),flip(a)].">
      <j1 rule="hyper" parents="319 19562 19564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      K(x,L(y,z,z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(1584(a,1),19565(a,1,2,1))].">
      <j1 rule="para" parents="1584 19565"/>
    </justification>
  </clause>

  <clause id="19568">
    <literal><![CDATA[
      T(x,L(y,z,z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,19567,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19567 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * u) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(469(a,1),19568(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="469 19568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      T(x,((y / z) * y) * (z \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14839,a(flip),b,19569,a),flip(a)].">
      <j1 rule="hyper" parents="64 14839 19569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1168(a,2),19566(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1168 19566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(u / T(a(v5 \ 1,v5,w),L(w,v5,v5 \ 1))) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,18326,a,b,19571,a),flip(a)].">
      <j1 rule="hyper" parents="64 18326 19571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19574">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15474,a(flip),b,19546,a)].">
      <j1 rule="hyper" parents="64 15474 19546"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      K(x,((y * z) / z) * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13795,a,19574,a)].">
      <j1 rule="hyper" parents="13795 19574"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),19575(a,1,2,1))].">
      <j1 rule="para" parents="11 19575"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13114,a,b,19576,a)].">
      <j1 rule="hyper" parents="64 13114 19576"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ T(v5,K(z,u) * w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17008,a(flip),b,19508,a),flip(a)].">
      <j1 rule="hyper" parents="64 17008 19508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / (K(w,v5) * (K(v5,w) * z)))) * v6) = K(x,(y \ T(u,K(v5,w) * z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17492,a(flip),b,19578,a)].">
      <j1 rule="hyper" parents="64 17492 19578"/>
    </justification>
  </clause>

  <clause id="19580">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(4363(a,1),19579(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4363 19579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(319,a,15474,a(flip),b,19580,a),flip(a)].">
      <j1 rule="hyper" parents="319 15474 19580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(x,(y \ T(z,u * K(w,v5))) * v6) = K(x,(y \ T(z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,14930,a(flip),b,19581,a)].">
      <j1 rule="hyper" parents="64 14930 19581"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(u / a(v5 \ 1,v5,w)) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(10567(a,1),19572(a,2,2,1,2))].">
      <j1 rule="para" parents="10567 19572"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(a(v5 \ 1,v5,w) \ u) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(11972(a,1),19585(a,2,2,1))].">
      <j1 rule="para" parents="11972 19585"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ (a(v5 \ 1,v5,w) * L(w,v5,v5 \ 1)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13088,a(flip),b,19586,a),flip(a)].">
      <j1 rule="hyper" parents="319 13088 19586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(3949(a,1),19587(a,2,2,2))].">
      <j1 rule="para" parents="3949 19587"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19564,a(flip),b,19588,a)].">
      <j1 rule="hyper" parents="64 19564 19588"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13921,a(flip),b,19589,a),flip(a)].">
      <j1 rule="hyper" parents="64 13921 19589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13916,a(flip),b,19589,a)].">
      <j1 rule="hyper" parents="64 13916 19589"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13210,a(flip),b,19589,a),flip(a)].">
      <j1 rule="hyper" parents="64 13210 19589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      K(x,y \ L(z,u,u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1584(a,1),19589(a,1,2,2))].">
      <j1 rule="para" parents="1584 19589"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,19593,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19593 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(469(a,1),19594(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="469 19594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19073,a(flip),b,19592,a),flip(a)].">
      <j1 rule="hyper" parents="64 19073 19592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(9164(a,1),19600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9164 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,17524,a(flip),b,19601,a),flip(a)].">
      <j1 rule="hyper" parents="319 17524 19601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17527,a,b,19602,a)].">
      <j1 rule="hyper" parents="64 17527 19602"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(12077(a,1),17343(a,1,1,1))].">
      <j1 rule="para" parents="12077 17343"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(u / w) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(11956(a,1),19604(a,1,1,2,3))].">
      <j1 rule="para" parents="11956 19604"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(w \ u) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(17958(a,1),19605(a,1,1,2))].">
      <j1 rule="para" parents="17958 19605"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (T((u \ w) \ 1,w) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,18277,a(flip),b,19606,a)].">
      <j1 rule="hyper" parents="64 18277 19606"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (((w / u) \ 1) / x))
    ]]></literal>
    <justification jstring="[hyper(319,a,17342,a(flip),b,19607,a),flip(a)].">
      <j1 rule="hyper" parents="319 17342 19607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[para(17043(a,1),12216(a,1,1))].">
      <j1 rule="para" parents="17043 12216"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 * T(v5 \ K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18443,a(flip),b,19610,a)].">
      <j1 rule="hyper" parents="64 18443 19610"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(v5,x) * K(y,w \ (u * (z \ 1)))) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(15691,a,19611,a)].">
      <j1 rule="hyper" parents="15691 19611"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(y,z * (u \ w)) * K(v5,x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17130,a(flip),b,19612,a)].">
      <j1 rule="hyper" parents="64 17130 19612"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,T(K(w,u * (z \ y)) * x,K(w,u * (z \ y))))
    ]]></literal>
    <justification jstring="[hyper(15175,a,19613,a),flip(a)].">
      <j1 rule="hyper" parents="15175 19613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,9269,a(flip),b,19614,a),flip(a)].">
      <j1 rule="hyper" parents="319 9269 19614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (u \ 1)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(3907(a,1),19616(a,1,2))].">
      <j1 rule="para" parents="3907 19616"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(12195,a,19617,a)].">
      <j1 rule="hyper" parents="12195 19617"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(14528,a,19618,a)].">
      <j1 rule="hyper" parents="14528 19618"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(12363(a,1),19619(a,2,2))].">
      <j1 rule="para" parents="12363 19619"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4763(a,1),19620(a,1,2,2))].">
      <j1 rule="para" parents="4763 19620"/>
    </justification>
  </clause>

  <clause id="19622">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18460,a(flip),b,19621,a)].">
      <j1 rule="hyper" parents="64 18460 19621"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(319,a,19039,a(flip),b,19622,a),flip(a)].">
      <j1 rule="hyper" parents="319 19039 19622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,z * (x * y))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19372,a(flip),b,19623,a),flip(a)].">
      <j1 rule="hyper" parents="64 19372 19623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z / y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(6244,a,19624,a)].">
      <j1 rule="hyper" parents="6244 19624"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z * y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(14426,a,19625,a)].">
      <j1 rule="hyper" parents="14426 19625"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(T(x,u / z),y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14031,a,19626,a)].">
      <j1 rule="hyper" parents="14031 19626"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(y / ((z \ 1) * u),u / z))
    ]]></literal>
    <justification jstring="[hyper(319,a,6102,a(flip),b,19627,a),flip(a)].">
      <j1 rule="hyper" parents="319 6102 19627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(((z \ 1) * u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(15547(a,1),19628(a,2,2))].">
      <j1 rule="para" parents="15547 19628"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(19629(a,2),14130(a,1))].">
      <j1 rule="para" parents="19629 14130"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      (L(x * K(y,z),K(z,T(y,x)),K(z,T(y,x))) \ L(K(z,T(y,x)) \ (x * u),K(z,T(y,x)),K(z,T(y,x)))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(6874(a,1),13345(a,1,1,1,1))].">
      <j1 rule="para" parents="6874 13345"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      ((x * K(y,z)) \ L(K(z,T(y,x)) \ (x * u),K(z,T(y,x)),K(z,T(y,x)))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8021(a,1),19631(a,1,1,1))].">
      <j1 rule="para" parents="8021 19631"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      ((x * K(y,z)) \ L(K(y,T(z,x)) * (x * u),K(z,T(y,x)),K(z,T(y,x)))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(6151(a,1),19632(a,1,1,2,1))].">
      <j1 rule="para" parents="6151 19632"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      ((x * K(y,z)) \ (K(y,T(z,x)) * (x * u))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8021(a,1),19633(a,1,1,2))].">
      <j1 rule="para" parents="8021 19633"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) * (K(u,z) * y) = (x * y) * K(u,T(z,y))
    ]]></literal>
    <justification jstring="[para(6918(a,1),19637(a,1,1))].">
      <j1 rule="para" parents="6918 19637"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(u,z) * y) = (x * y) * K(u,T(z,y))
    ]]></literal>
    <justification jstring="[para(18800(a,1),19638(a,1,1))].">
      <j1 rule="para" parents="18800 19638"/>
    </justification>
  </clause>

  <clause id="19644">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(y \ L(z,u,u \ 1),x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14639,a(flip),b,17090,a)].">
      <j1 rule="hyper" parents="64 14639 17090"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),(z * u) * ((1 / u) * K(y \ L(z,u,u \ 1),x))) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16468,a(flip),b,19644,a)].">
      <j1 rule="hyper" parents="64 16468 19644"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),(z * u) * (u \ K(y \ L(z,u,u \ 1),x))) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12016,a(flip),b,19645,a)].">
      <j1 rule="hyper" parents="64 12016 19645"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),K(y \ L(z,u,u \ 1),x) * z) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(17857,a,19646,a)].">
      <j1 rule="hyper" parents="17857 19646"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(((x * y) * (1 / y)) / z,u)) \ T((y * x) * (1 / y),y) = K(u,T(z \ R(x,y,y \ 1),x))
    ]]></literal>
    <justification jstring="[hyper(15172,a,19647,a),flip(a)].">
      <j1 rule="hyper" parents="15172 19647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(((x * y) * (1 / y)) / z,u)) \ T((y * x) * (1 / y),y) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(319,a,16193,a(flip),b,19648,a),flip(a)].">
      <j1 rule="hyper" parents="319 16193 19648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(L(x,y,y \ 1) / z,u)) \ T((y * x) * (1 / y),y) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(17089(a,1),19649(a,1,1,2))].">
      <j1 rule="para" parents="17089 19649"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(L(x,y,y \ 1) / z,u)) \ ((x * y) * (1 / y)) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(2176(a,1),19650(a,1,2))].">
      <j1 rule="para" parents="2176 19650"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(5187,a,19651,a),flip(a)].">
      <j1 rule="hyper" parents="5187 19651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,L(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13138,a,b,19652,a)].">
      <j1 rule="hyper" parents="64 13138 19652"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16835,a(flip),b,19654,a),flip(a)].">
      <j1 rule="hyper" parents="64 16835 19654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19563,a(flip),b,19655,a)].">
      <j1 rule="hyper" parents="64 19563 19655"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (T(u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17271,a(flip),b,19655,a)].">
      <j1 rule="hyper" parents="64 17271 19655"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,17215,a(flip),b,19657,a),flip(a)].">
      <j1 rule="hyper" parents="319 17215 19657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19563,a(flip),b,19659,a)].">
      <j1 rule="hyper" parents="64 19563 19659"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      T(x,y / ((z \ 1) * u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,19660,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19660 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17270,a(flip),b,19660,a),flip(a)].">
      <j1 rule="hyper" parents="64 17270 19660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((u \ z) \ (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(19660(a,1),17448(a,1,2))].">
      <j1 rule="para" parents="19660 17448"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      K(x,y / ((T(z,u) / (z / (u \ 1))) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(19660(a,1),17490(a,1))].">
      <j1 rule="para" parents="19660 17490"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(19660(a,1),19630(a,1))].">
      <j1 rule="para" parents="19660 19630"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      T(x,y * T(z \ (u * u),u)) = T(x,y / (u \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18589,a(flip),b,19662,a)].">
      <j1 rule="hyper" parents="64 18589 19662"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((z \ u) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(18338(a,1),19665(a,1,2))].">
      <j1 rule="para" parents="18338 19665"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,u)) / u) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(18745(a,1),19669(a,1,2))].">
      <j1 rule="para" parents="18745 19669"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16647,a(flip),b,19670,a)].">
      <j1 rule="hyper" parents="64 16647 19670"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17213,a(flip),b,19671,a)].">
      <j1 rule="hyper" parents="64 17213 19671"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(19667,a,19672,a),flip(a)].">
      <j1 rule="hyper" parents="19667 19672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,w) / (u / (w \ 1))))) = K(x,y / (w * z))
    ]]></literal>
    <justification jstring="[hyper(19666,a,19672,a),flip(a)].">
      <j1 rule="hyper" parents="19666 19672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19675">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,19672,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19672 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19676">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19663,a(flip),b,19672,a)].">
      <j1 rule="hyper" parents="64 19663 19672"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (y \ z)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19550,a(flip),b,19672,a),flip(a)].">
      <j1 rule="hyper" parents="64 19550 19672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18792,a(flip),b,19672,a),flip(a)].">
      <j1 rule="hyper" parents="64 18792 19672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,y * ((z * y) \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18791,a(flip),b,19672,a)].">
      <j1 rule="hyper" parents="64 18791 19672"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      x * K(y,x * ((z * x) \ (u * z))) = (x * z) / (z * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,19672,a(flip),b,18613,a(flip))].">
      <j1 rule="hyper" parents="131 19672 18613"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      T(x,y / ((z \ 1) * u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19662,a,b,19675,a)].">
      <j1 rule="hyper" parents="64 19662 19675"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      T(x,(y \ z) * (z / y)) = T(x,z * (y \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18588,a(flip),b,19682,a)].">
      <j1 rule="hyper" parents="64 18588 19682"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13787,a(flip),b,19676,a),flip(a)].">
      <j1 rule="hyper" parents="319 13787 19676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19656,a(flip),b,19684,a)].">
      <j1 rule="hyper" parents="64 19656 19684"/>
    </justification>
  </clause>

  <clause id="19686">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18494,a,b,19685,a)].">
      <j1 rule="hyper" parents="64 18494 19685"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15470,a(flip),b,19678,a),flip(a)].">
      <j1 rule="hyper" parents="64 15470 19678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19449,a,19673,a),flip(a)].">
      <j1 rule="hyper" parents="19449 19673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19590,a(flip),b,19689,a)].">
      <j1 rule="hyper" parents="64 19590 19689"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,19690,a,b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="129 19690 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19692">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (u \ (y * z))) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,19115,a(flip),b,19690,a),flip(a)].">
      <j1 rule="hyper" parents="64 19115 19690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) / (u / w)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(19690(a,1),19110(a,1,1,3))].">
      <j1 rule="para" parents="19690 19110"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(319,a,11334,a,b,19691,a)].">
      <j1 rule="hyper" parents="319 11334 19691"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      T(x,(y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(19694(a,1),14837(a,1))].">
      <j1 rule="para" parents="19694 14837"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19514,a(flip),b,19674,a)].">
      <j1 rule="hyper" parents="64 19514 19674"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(19513,a,19696,a)].">
      <j1 rule="hyper" parents="19513 19696"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      K(x,((y * z) / (u * y)) * u) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19688,a(flip),b,19679,a)].">
      <j1 rule="hyper" parents="64 19688 19679"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(319,a,19472,a(flip),b,19686,a),flip(a)].">
      <j1 rule="hyper" parents="319 19472 19686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,16571,a(flip),b,19692,a)].">
      <j1 rule="hyper" parents="64 16571 19692"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,18639,a,b,19700,a)].">
      <j1 rule="hyper" parents="64 18639 19700"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      K(x,(y \ z) * L((y * (y \ z)) \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19577,a(flip),b,19677,a)].">
      <j1 rule="hyper" parents="64 19577 19677"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),19702(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10 19702"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17191,a,b,19703,a)].">
      <j1 rule="hyper" parents="64 17191 19703"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(19685(a,1),19693(a,1,2))].">
      <j1 rule="para" parents="19685 19693"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19608,a(flip),b,19706,a)].">
      <j1 rule="hyper" parents="64 19608 19706"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19685,a(flip),b,19707,a)].">
      <j1 rule="hyper" parents="64 19685 19707"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19472,a(flip),b,19708,a),flip(a)].">
      <j1 rule="hyper" parents="64 19472 19708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19685,a(flip),b,19709,a)].">
      <j1 rule="hyper" parents="64 19685 19709"/>
    </justification>
  </clause>

  <clause id="19711">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18605,a(flip),b,19709,a),flip(a)].">
      <j1 rule="hyper" parents="64 18605 19709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18559,a,19710,a),flip(a)].">
      <j1 rule="hyper" parents="18559 19710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17066,a(flip),b,19711,a),flip(a)].">
      <j1 rule="hyper" parents="64 17066 19711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      K(x,y \ ((T(z,y * K(u,w)) * y) * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17519,a,b,19713,a)].">
      <j1 rule="hyper" parents="64 17519 19713"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19591,a(flip),b,19713,a),flip(a)].">
      <j1 rule="hyper" parents="64 19591 19713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(319,a,19688,a(flip),b,19715,a),flip(a)].">
      <j1 rule="hyper" parents="319 19688 19715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19370,a(flip),b,19712,a),flip(a)].">
      <j1 rule="hyper" parents="64 19370 19712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19697,a(flip),b,19717,a),flip(a)].">
      <j1 rule="hyper" parents="64 19697 19717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19719">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(19478,a,19718,a),flip(a)].">
      <j1 rule="hyper" parents="19478 19718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) * ((z \ u) / y)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19194,a(flip),b,19719,a),flip(a)].">
      <j1 rule="hyper" parents="64 19194 19719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19704,a(flip),b,19720,a)].">
      <j1 rule="hyper" parents="64 19704 19720"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12708,a,19721,a)].">
      <j1 rule="hyper" parents="12708 19721"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(10208,a,19722,a)].">
      <j1 rule="hyper" parents="10208 19722"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19721,a(flip),b,19723,a),flip(a)].">
      <j1 rule="hyper" parents="64 19721 19723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(19723(a,1),18162(a,2,2))].">
      <j1 rule="para" parents="19723 18162"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(19723(a,1),18520(a,2,2))].">
      <j1 rule="para" parents="19723 18520"/>
    </justification>
  </clause>

  <clause id="19727">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(319,a,13272,a(flip),b,19726,a),flip(a)].">
      <j1 rule="hyper" parents="319 13272 19726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18518,a(flip),b,19727,a)].">
      <j1 rule="hyper" parents="64 18518 19727"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(19724(a,1),19728(a,1,2))].">
      <j1 rule="para" parents="19724 19728"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,13272,a,b,19729,a)].">
      <j1 rule="hyper" parents="35 13272 19729"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * u) * x)) = T(L(u,y,K(x,z)),x)
    ]]></literal>
    <justification jstring="[para(19729(a,1),18063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19729 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * u) * x)) = T(L(u,z,K(y,x)),x)
    ]]></literal>
    <justification jstring="[para(19729(a,1),18065(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19729 18065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,12524,a(flip),b,19730,a)].">
      <j1 rule="hyper" parents="319 12524 19730"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(19730(a,1),12606(a,1,2))].">
      <j1 rule="para" parents="19730 12606"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(w,v5,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,17784,a,b,19733,a)].">
      <j1 rule="hyper" parents="319 17784 19733"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(12560,a,19734,a)].">
      <j1 rule="hyper" parents="12560 19734"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,17587,a(flip),b,19736,a),flip(a)].">
      <j1 rule="hyper" parents="319 17587 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19741">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,19736,a,b,4518,a)].">
      <j1 rule="hyper" parents="129 19736 4518"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,13294,a,b,19741,a)].">
      <j1 rule="hyper" parents="319 13294 19741"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      T(x,L((y * z) \ u,y,z)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13071,a(flip),b,19741,a),flip(a)].">
      <j1 rule="hyper" parents="319 13071 19741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(17596,a,19739,a)].">
      <j1 rule="hyper" parents="17596 19739"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19701,a,b,19739,a)].">
      <j1 rule="hyper" parents="64 19701 19739"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19699,a(flip),b,19739,a),flip(a)].">
      <j1 rule="hyper" parents="64 19699 19739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19748">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19739,a(flip),b,19744,a),flip(a)].">
      <j1 rule="hyper" parents="64 19739 19744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19603,a(flip),b,19748,a),flip(a)].">
      <j1 rule="hyper" parents="64 19603 19748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19750">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(19748(a,1),18834(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19748 18834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19751">
    <literal><![CDATA[
      T(x,y \ (z \ (y * u))) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13072,a(flip),b,19743,a),flip(a)].">
      <j1 rule="hyper" parents="64 13072 19743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      T(x,T(y,z) \ ((1 / z) \ u)) = T(x,z \ (y \ ((z * z) * u)))
    ]]></literal>
    <justification jstring="[para(451(a,1),19751(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="451 19751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y \ (((y * y) \ z) \ (y * u)))
    ]]></literal>
    <justification jstring="[para(1949(a,2),19751(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1949 19751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19747,a(flip),b,19749,a),flip(a)].">
      <j1 rule="hyper" parents="64 19747 19749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      K(x,(y \ T(z,y * K(u,w))) * (y * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,19714,a(flip),b,19754,a),flip(a)].">
      <j1 rule="hyper" parents="64 19714 19754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(19725(a,2),13300(a,1))].">
      <j1 rule="para" parents="19725 13300"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,19731,a(flip),b,19732,a(flip))].">
      <j1 rule="hyper" parents="41 19731 19732"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      L(T(x,y),y,K(z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,19742,a(flip),b,19757,a),flip(a)].">
      <j1 rule="hyper" parents="319 19742 19757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      T(x,T(y,z) \ ((1 / z) \ u)) = T(x,z * (z * (z \ (y \ u))))
    ]]></literal>
    <justification jstring="[hyper(319,a,17331,a(flip),b,19752,a),flip(a)].">
      <j1 rule="hyper" parents="319 17331 19752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      T(x,T(y,z) \ ((1 / z) \ u)) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),19760(a,2,2,2))].">
      <j1 rule="para" parents="10 19760"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      T(x,y \ ((z \ K(z,y)) \ u)) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17099,a(flip),b,19761,a)].">
      <j1 rule="hyper" parents="64 17099 19761"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      T(x,T(y,z \ 1) \ (z \ u)) = T(x,(z \ 1) * (y \ u))
    ]]></literal>
    <justification jstring="[para(78(a,1),19761(a,1,2,2,1))].">
      <j1 rule="para" parents="78 19761"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,T(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(4161(a,1),19762(a,1,2,2,1))].">
      <j1 rule="para" parents="4161 19762"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = T(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19596,a(flip),b,19765,a),flip(a)].">
      <j1 rule="hyper" parents="64 19596 19765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19767">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) = T(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17317,a(flip),b,19766,a)].">
      <j1 rule="hyper" parents="64 17317 19766"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      T(x,T(y,z * 1) \ (z \ u)) = T(x,(z \ 1) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14906,a(flip),b,19764,a)].">
      <j1 rule="hyper" parents="64 14906 19764"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,(z \ 1) * (y \ u))
    ]]></literal>
    <justification jstring="[para(8(a,1),19768(a,1,2,1,2))].">
      <j1 rule="para" parents="8 19768"/>
    </justification>
  </clause>

  <clause id="19770">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(19769(a,2),12244(a,1))].">
      <j1 rule="para" parents="19769 12244"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(17017(a,1),19770(a,1))].">
      <j1 rule="para" parents="17017 19770"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,y * z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y \ z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(17316(a,1),19771(a,1))].">
      <j1 rule="para" parents="17316 19771"/>
    </justification>
  </clause>

  <clause id="19773">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,19582,a(flip),b,19755,a)].">
      <j1 rule="hyper" parents="64 19582 19755"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(13795,a,19773,a),flip(a)].">
      <j1 rule="hyper" parents="13795 19773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19716,a(flip),b,19774,a),flip(a)].">
      <j1 rule="hyper" parents="64 19716 19774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19776">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(19476,a,19775,a),flip(a)].">
      <j1 rule="hyper" parents="19476 19775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19777">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19698,a(flip),b,19776,a),flip(a)].">
      <j1 rule="hyper" parents="64 19698 19776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (u * z))) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19746,a(flip),b,19777,a),flip(a)].">
      <j1 rule="hyper" parents="64 19746 19777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19779">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(19778(a,1),19680(a,1,2))].">
      <j1 rule="para" parents="19778 19680"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19750,a,b,19779,a)].">
      <j1 rule="hyper" parents="64 19750 19779"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18310,a(flip),b,19780,a),flip(a)].">
      <j1 rule="hyper" parents="64 18310 19780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19782">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(5925(a,1),19781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5925 19781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(18980,a,19782,a),flip(a)].">
      <j1 rule="hyper" parents="18980 19782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19086,a(flip),b,19783,a)].">
      <j1 rule="hyper" parents="64 19086 19783"/>
    </justification>
  </clause>

  <clause id="19785">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(19784(a,1),19100(a,1,1))].">
      <j1 rule="para" parents="19784 19100"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19756,a,19785,a),flip(a)].">
      <j1 rule="hyper" parents="19756 19785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19787">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18004,a(flip),b,19786,a),flip(a)].">
      <j1 rule="hyper" parents="64 18004 19786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(10856,a,19787,a),flip(a)].">
      <j1 rule="hyper" parents="10856 19787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19791">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(319,a,19757,a,b,19788,a),flip(a)].">
      <j1 rule="hyper" parents="319 19757 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      L(x,K(y,z),u) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,13261,a(flip),b,19788,a),flip(a)].">
      <j1 rule="hyper" parents="319 13261 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x * w) = L(x,K(y,u),z) * w
    ]]></literal>
    <justification jstring="[para(19788(a,2),13291(a,2,1))].">
      <j1 rule="para" parents="19788 13291"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,19791,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="131 19791 18"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(u,z) * y) = (x * K(u,z)) * y
    ]]></literal>
    <justification jstring="[para(19791(a,1),15713(a,1,1))].">
      <j1 rule="para" parents="19791 15713"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      T(x,y * (z * L(u,K(w,v5),v6))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(19792(a,2),16466(a,1,2,2,2))].">
      <j1 rule="para" parents="19792 16466"/>
    </justification>
  </clause>

  <clause id="19799">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x * (K(y,u) * z)) = (x * K(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(319,a,15713,a(flip),b,19793,a),flip(a)].">
      <j1 rule="hyper" parents="319 15713 19793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19800">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9587,a(flip),b,19794,a)].">
      <j1 rule="hyper" parents="64 9587 19794"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(6845(a,1),19800(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6845 19800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7653,a(flip),b,19801,a)].">
      <j1 rule="hyper" parents="64 7653 19801"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,z) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(6074(a,1),19803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6074 19803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * (u * z)) = T(T(u,K(x,y)),K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(417,a,xx,b,19804,a),flip(a)].">
      <j1 rule="hyper" parents="417 19804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19806">
    <literal><![CDATA[
      K(x,y) * (z * (K(x,y) \ u)) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(331,a,19804,a),flip(a)].">
      <j1 rule="hyper" parents="331 19804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      a(x,K(x,y) \ z,K(y,T(u,K(x,y) \ z))) = T(u,K(y,x) * z) \ (z \ (T(u,K(x,y)) * z))
    ]]></literal>
    <justification jstring="[para(19806(a,1),13410(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19806 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,19642,a(flip),b,19795,a)].">
      <j1 rule="hyper" parents="64 19642 19795"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      T(x,T(y,(z * K(u,w)) * v5) * ((z * v5) / (1 / K(u,T(w,v5))))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(19809(a,1),12159(a,1,2,1,2))].">
      <j1 rule="para" parents="19809 12159"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      T(x,y * ((z * K(u,w)) * v5)) = T(x,y * (z * (K(u,w) * v5)))
    ]]></literal>
    <justification jstring="[para(94(a,1),19797(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="94 19797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19815">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,12701,a,b,19799,a)].">
      <j1 rule="hyper" parents="36 12701 19799"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      (x * ((x * x) \ y)) * a(z,u,K(w,u \ 1)) = (1 / (1 / (1 / x))) * y
    ]]></literal>
    <justification jstring="[para(19815(a,1),8066(a,1,2))].">
      <j1 rule="para" parents="19815 8066"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z) * u) = L(T(x,u),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(743,a,19805,a),flip(a)].">
      <j1 rule="hyper" parents="743 19805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z) * u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(319,a,19758,a(flip),b,19817,a),flip(a)].">
      <j1 rule="hyper" parents="319 19758 19817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(6791(a,1),19818(a,1,1))].">
      <j1 rule="para" parents="6791 19818"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      T(T(x,K(y,z)),L(u,y,z)) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6797(a,1),19818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6797 19818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19822">
    <literal><![CDATA[
      T(T(T(x,L(y,z,u)),K(u,z)),K(z,u) * y) \ w = K(L(y,z,u),x) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(19820(a,2),4447(a,2,1)),flip(a)].">
      <j1 rule="para" parents="19820 4447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((z \ y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19691(a,1),19772(a,1))].">
      <j1 rule="para" parents="19691 19772"/>
    </justification>
  </clause>

  <clause id="19824">
    <literal><![CDATA[
      (1 / (1 / (1 / x))) * y = x * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11558,a(flip),b,19816,a),flip(a)].">
      <j1 rule="hyper" parents="64 11558 19816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      T(x,K(1 / (1 / (1 / y)),z) * (u * (y * ((y * y) \ w)))) = T(x,u * (T(1 / (1 / (1 / y)),z) * w))
    ]]></literal>
    <justification jstring="[para(19824(a,1),16556(a,1,2,2,2))].">
      <j1 rule="para" parents="19824 16556"/>
    </justification>
  </clause>

  <clause id="19826">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ w)) = T(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(19823,a,19767,a)].">
      <j1 rule="hyper" parents="19823 19767"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      T(x,(y \ z) \ ((u \ w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((w \ u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(19826(a,2),19695(a,1))].">
      <j1 rule="para" parents="19826 19695"/>
    </justification>
  </clause>

  <clause id="19828">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y \ (z \ ((y * y) * (y * u))))
    ]]></literal>
    <justification jstring="[para(638(a,1),19753(a,2,2,2))].">
      <j1 rule="para" parents="638 19753"/>
    </justification>
  </clause>

  <clause id="19829">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y * (y * (y \ (z \ (y * u)))))
    ]]></literal>
    <justification jstring="[hyper(319,a,17331,a(flip),b,19828,a),flip(a)].">
      <j1 rule="hyper" parents="319 17331 19828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19830">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),19829(a,2,2,2))].">
      <j1 rule="para" parents="10 19829"/>
    </justification>
  </clause>

  <clause id="19832">
    <literal><![CDATA[
      T(x,T((y * y) \ z,y) \ u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[para(1949(a,1),19830(a,1,2,1))].">
      <j1 rule="para" parents="1949 19830"/>
    </justification>
  </clause>

  <clause id="19833">
    <literal><![CDATA[
      T(x,y * (y * (T(z,y) \ u))) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19445,a(flip),b,19832,a)].">
      <j1 rule="hyper" parents="64 19445 19832"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      a(x,K(x,y) \ z,K(y,T(u,K(x,y) \ z))) = T(u,K(y,x) * z) \ T(T(u,K(x,y)),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),19807(a,2,2))].">
      <j1 rule="para" parents="22 19807"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      a(x,K(y,x) * z,K(y,T(u,K(x,y) \ z))) = T(u,K(y,x) * z) \ T(T(u,K(x,y)),z)
    ]]></literal>
    <justification jstring="[para(4356(a,1),19834(a,1,2))].">
      <j1 rule="para" parents="4356 19834"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      T(x,K(y,z) * u) \ T(T(x,K(z,y)),u) = a(z,K(y,z) * u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(16233,a,19835,a),flip(a)].">
      <j1 rule="hyper" parents="16233 19835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      T(x,K(y,z) * u) \ T(T(x,K(z,y)),u) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(319,a,19735,a(flip),b,19836,a),flip(a)].">
      <j1 rule="hyper" parents="319 19735 19836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19840">
    <literal><![CDATA[
      T(x,K(y,z) * u) \ T(T(x,K(y,z)),u) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[para(6791(a,1),19838(a,1,2,1))].">
      <j1 rule="para" parents="6791 19838"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      T(T(T(x,L(y,z,u)),K(u,z)),K(z,u) * y) \ w = K(y,L(x,z,u)) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(10133(a,1),19822(a,2,1))].">
      <j1 rule="para" parents="10133 19822"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      T(T(T(x,L(y,z,u)),K(u,z)),K(z,u) * y) \ w = T(T(x,y),y) \ w
    ]]></literal>
    <justification jstring="[hyper(319,a,13371,a(flip),b,19841,a),flip(a)].">
      <j1 rule="hyper" parents="319 13371 19841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      T(T(T(x,K(y,z)),L(u,y,z)),K(y,z) * u) \ w = T(T(x,u),u) \ w
    ]]></literal>
    <justification jstring="[para(6802(a,2),19842(a,1,1,1))].">
      <j1 rule="para" parents="6802 19842"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      T(T(x,K(y,z) * u),K(y,z) * u) \ w = T(T(x,u),u) \ w
    ]]></literal>
    <justification jstring="[para(19821(a,1),19844(a,1,1,1))].">
      <j1 rule="para" parents="19821 19844"/>
    </justification>
  </clause>

  <clause id="19846">
    <literal><![CDATA[
      K(K(x,y) * z,u) * K(K(x,y) * z,u) = T(T(u,z),z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,4666,a(flip),b,19845,a)].">
      <j1 rule="hyper" parents="64 4666 19845"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      K(K(x,y) * z,u) * K(K(x,y) * z,u) = K(z,u) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(319,a,4666,a(flip),b,19846,a),flip(a)].">
      <j1 rule="hyper" parents="319 4666 19846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      K(x,y) * (z * (K(z,u) * K(z,u))) = T(T(K(x,y) * z,u),u)
    ]]></literal>
    <justification jstring="[para(19847(a,1),13408(a,1,2,2))].">
      <j1 rule="para" parents="19847 13408"/>
    </justification>
  </clause>

  <clause id="19849">
    <literal><![CDATA[
      K(x,y) * (T(z,u) * K(z,u)) = T(T(K(x,y) * z,u),u)
    ]]></literal>
    <justification jstring="[para(4036(a,1),19848(a,1,2))].">
      <j1 rule="para" parents="4036 19848"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),u) = K(x,y) * T(T(z,u),u)
    ]]></literal>
    <justification jstring="[para(4164(a,1),19849(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4164 19849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      T(x,(y \ z) * T(T(K(y,T(y \ z,u)) * (y \ z),u),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(19851(a,2),15745(a,1,2,2))].">
      <j1 rule="para" parents="19851 15745"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      T(x,(y \ z) * T(T((y \ z) * K(y,T(y \ z,u)),u),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(2841(a,1),19852(a,1,2,2,1,1))].">
      <j1 rule="para" parents="2841 19852"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      T(x,(y \ z) * T(T(T(z / y,K(z,u)),u),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(18113(a,1),19853(a,1,2,2,1,1))].">
      <j1 rule="para" parents="18113 19853"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      T(x,(y \ z) * T(T(T(z / y,u),K(z,u)),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),19854(a,1,2,2,1))].">
      <j1 rule="para" parents="23 19854"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      T(x,T(y \ z,u) * T(z / y,u)) = T(x,(y \ z) * T(T(z / y,u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14623,a(flip),b,19855,a),flip(a)].">
      <j1 rule="hyper" parents="64 14623 19855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      T(x,T(y \ z,u) * T(z / y,u)) = T(x,(y \ z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(319,a,13556,a(flip),b,19856,a),flip(a)].">
      <j1 rule="hyper" parents="319 13556 19856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      T(x,T(y \ z,u) * T(z / y,u)) = T(x,z * (y \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(319,a,19683,a(flip),b,19858,a),flip(a)].">
      <j1 rule="hyper" parents="319 19683 19858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * (y \ (y \ z))),(y \ z) \ ((y \ z) \ w))
    ]]></literal>
    <justification jstring="[para(19860(a,1),17054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19860 17054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19862">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * (y \ (y \ z))),(z \ y) * ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(19827,a,19861,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19827 19861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      T(x,K(1 / y,z) * (u * (y * ((y * y) \ w)))) = T(x,u * (T(1 / (1 / (1 / y)),z) * w))
    ]]></literal>
    <justification jstring="[para(2919(a,1),19825(a,1,2,1))].">
      <j1 rule="para" parents="2919 19825"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (y * ((y * y) \ w)))) = T(x,u * (T(1 / (1 / (1 / y)),z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13632,a(flip),b,19864,a)].">
      <j1 rule="hyper" parents="64 13632 19864"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      T(x,y * (T(1 / (1 / (1 / z)),u) * w)) = T(x,y * (T(z,u) * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16556,a(flip),b,19865,a),flip(a)].">
      <j1 rule="hyper" parents="64 16556 19865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      T(x,y * (T((1 / (1 / z)) \ 1,u) * w)) = T(x,y * (T(z,u) * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16758,a(flip),b,19866,a)].">
      <j1 rule="hyper" parents="64 16758 19866"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z * z) \ w))) = T(x,y * (T(1 / z,u) * w))
    ]]></literal>
    <justification jstring="[para(81(a,1),19867(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="81 19867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z * z) \ w))) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(319,a,16758,a(flip),b,19868,a),flip(a)].">
      <j1 rule="hyper" parents="319 16758 19868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      T(x,y * (T(z \ 1,u) * w)) = T(x,y * ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16760,a(flip),b,19869,a),flip(a)].">
      <j1 rule="hyper" parents="64 16760 19869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * (T(z \ 1,u \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,17424,a,b,19871,a)].">
      <j1 rule="hyper" parents="319 17424 19871"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * (T(z \ 1,u * 1) * y))
    ]]></literal>
    <justification jstring="[hyper(319,a,16694,a(flip),b,19872,a),flip(a)].">
      <j1 rule="hyper" parents="319 16694 19872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * (T(z \ 1,u) * y))
    ]]></literal>
    <justification jstring="[para(8(a,1),19873(a,2,2,2,1,2))].">
      <j1 rule="para" parents="8 19873"/>
    </justification>
  </clause>

  <clause id="19875">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,u * (u * (T(z \ 1,u) * y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,12967,a(flip),b,19874,a),flip(a)].">
      <j1 rule="hyper" parents="319 12967 19874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,u * (u * (T(z,u) \ y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,13827,a(flip),b,19875,a),flip(a)].">
      <j1 rule="hyper" parents="319 13827 19875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19877">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,u * (z \ (u * y)))
    ]]></literal>
    <justification jstring="[hyper(319,a,19833,a(flip),b,19876,a),flip(a)].">
      <j1 rule="hyper" parents="319 19833 19876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (z / u))) = T(x,u * (z \ (u * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19668,a(flip),b,19877,a)].">
      <j1 rule="hyper" parents="64 19668 19877"/>
    </justification>
  </clause>

  <clause id="19879">
    <literal><![CDATA[
      T(x,(y \ (z / y)) \ u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17218,a(flip),b,19878,a)].">
      <j1 rule="hyper" parents="64 17218 19878"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      T(x,((y / z) \ z) * u) = T(x,z * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(19695,a,19879,a)].">
      <j1 rule="hyper" parents="19695 19879"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) / (1 / K(u,T(w,v5))))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(16600(a,1),19812(a,1,2,1))].">
      <j1 rule="para" parents="16600 19812"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) / (1 * K(w,T(u,v5))))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(6146(a,1),19881(a,1,2,2,2))].">
      <j1 rule="para" parents="6146 19881"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) / K(w,T(u,v5)))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),19882(a,1,2,2,2))].">
      <j1 rule="para" parents="7 19882"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) * K(u,T(w,v5)))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(6146(a,1),19883(a,1,2,2))].">
      <j1 rule="para" parents="6146 19883"/>
    </justification>
  </clause>

  <clause id="19885">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * K(u,w)) * v5)) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(19809(a,1),19884(a,1,2,2))].">
      <j1 rule="para" parents="19809 19884"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * (z * (K(u,w) * v5))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,19814,a(flip),b,19885,a)].">
      <j1 rule="hyper" parents="64 19814 19885"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      T(x,((y * z) / (1 / K(u,T(w,z)))) * v5) = T(x,(y * (K(u,w) * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(9318,a,19886,a),flip(a)].">
      <j1 rule="hyper" parents="9318 19886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      T(x,((y * z) / (1 * K(u,T(w,z)))) * v5) = T(x,(y * (K(w,u) * z)) * v5)
    ]]></literal>
    <justification jstring="[para(6146(a,1),19887(a,1,2,1,2))].">
      <j1 rule="para" parents="6146 19887"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      T(x,((y * z) / K(u,T(w,z))) * v5) = T(x,(y * (K(w,u) * z)) * v5)
    ]]></literal>
    <justification jstring="[para(7(a,1),19888(a,1,2,1,2))].">
      <j1 rule="para" parents="7 19888"/>
    </justification>
  </clause>

  <clause id="19890">
    <literal><![CDATA[
      T(x,((y * z) * K(u,T(w,z))) * v5) = T(x,(y * (K(u,w) * z)) * v5)
    ]]></literal>
    <justification jstring="[para(6146(a,1),19889(a,1,2,1))].">
      <j1 rule="para" parents="6146 19889"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * w)) * v5) = T(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16606,a(flip),b,19890,a),flip(a)].">
      <j1 rule="hyper" parents="64 16606 19890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * T(z,w)) * v5)) = T(x,(u * T(T(z,y),w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19162,a(flip),b,19891,a),flip(a)].">
      <j1 rule="hyper" parents="64 19162 19891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      T(x,(y * T(T(z,u),u)) * w) = T(x,(y * R(z,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19154,a(flip),b,19893,a),flip(a)].">
      <j1 rule="hyper" parents="64 19154 19893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      T(x,(y * R(z,u,z)) * w) = T(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13698,a(flip),b,19894,a),flip(a)].">
      <j1 rule="hyper" parents="64 13698 19894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      T(x,(y * (T(z,u \ z) / u)) * w) = T(x,(y * (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13710,a(flip),b,19895,a)].">
      <j1 rule="hyper" parents="64 13710 19895"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      T(x,((y / z) * y) * u) = T(x,(y * (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13705,a(flip),b,19897,a)].">
      <j1 rule="hyper" parents="64 13705 19897"/>
    </justification>
  </clause>

  <clause id="19900">
    <literal><![CDATA[
      T(x,((y / z) \ z) * u) = T(x,(z * (y \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15483,a,b,19899,a)].">
      <j1 rule="hyper" parents="64 15483 19899"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      T(x,(y * (z \ y)) * (z \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19570,a(flip),b,19899,a),flip(a)].">
      <j1 rule="hyper" parents="64 19570 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19902">
    <literal><![CDATA[
      T(x,(y * (z \ y)) * u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19880,a(flip),b,19900,a),flip(a)].">
      <j1 rule="hyper" parents="64 19880 19900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * u)) = T(x,z * (y \ (z * (y \ u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19902,a(flip),b,19901,a),flip(a)].">
      <j1 rule="hyper" parents="64 19902 19901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19904">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * (y \ (y \ z))),y * (z \ (y * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19862,a,b,19903,a)].">
      <j1 rule="hyper" parents="64 19862 19903"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),y \ (y \ (y * (z \ (y * (z \ w))))))
    ]]></literal>
    <justification jstring="[hyper(319,a,19475,a(flip),b,19904,a),flip(a)].">
      <j1 rule="hyper" parents="319 19475 19904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),y \ (z \ (y * (z \ w))))
    ]]></literal>
    <justification jstring="[para(9(a,1),19905(a,2,2,2))].">
      <j1 rule="para" parents="9 19905"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),T(z,y) \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,19751,a(flip),b,19906,a),flip(a)].">
      <j1 rule="hyper" parents="319 19751 19906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),z \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(319,a,17015,a(flip),b,19907,a),flip(a)].">
      <j1 rule="hyper" parents="319 17015 19907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19910">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(x,z * (z * (z \ (T(z,y) \ w))))
    ]]></literal>
    <justification jstring="[hyper(319,a,12969,a(flip),b,19909,a),flip(a)].">
      <j1 rule="hyper" parents="319 12969 19909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19911">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(x,z * (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),19910(a,2,2,2))].">
      <j1 rule="para" parents="10 19910"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(319,a,11399,a(flip),b,19911,a),flip(a)].">
      <j1 rule="hyper" parents="319 11399 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      T(T(x,K(y,y \ z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(108(a,1),19912(a,1,1,2,2))].">
      <j1 rule="para" parents="108 19912"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6827(a,1),19914(a,1,1))].">
      <j1 rule="para" parents="6827 19914"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      T(x,K(y,z) * u) \ T(x,K(y,z) * u) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[para(19916(a,1),19840(a,1,2))].">
      <j1 rule="para" parents="19916 19840"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(216,a,19926,a),flip(a)].">
      <j1 rule="hyper" parents="216 19926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19936">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,12602,a,b,19927,a)].">
      <j1 rule="hyper" parents="64 12602 19927"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aK1")
    ]]></attribute>
    <justification jstring="[resolve(19936,a,65,a)].">
      <j1 rule="resolve" parents="19936 65"/>
    </justification>
  </clause>

</proof>

</proofs>
